IAIFI Foundational AI Papers

Foundational AI

A Lorentz-Equivariant Transformer for All of the LHC
Johann Brehmer, Víctor Bresó, Pim de Haan, Tilman Plehn, Huilin Qu, Jonas Spinner, Jesse Thaler
[ arXiv:2411.00446 | code ]

Abstract We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over space-time and is equivariant under Lorentz transformations. The underlying architecture is a versatile and scalable transformer, which is able to break symmetries if needed. We demonstrate the power of L-GATr for amplitude regression and jet classification, and then benchmark it as the first Lorentz-equivariant generative network. For all three LHC tasks, we find significant improvements over previous architectures.

Linearized Wasserstein Barycenters: Synthesis, Analysis, Representational Capacity, and Applications
Matthew Werenski, Brendan Mallery, Shuchin Aeron, James M. Murphy
[ arXiv:2410.23602 | code ]

Abstract We propose the extit{linear barycentric coding model (LBCM)} that utilizes the linear optimal transport (LOT) metric for analysis and synthesis of probability measures. We provide a closed-form solution to the variational problem characterizing the probability measures in the LBCM and establish equivalence of the LBCM to the set of Wasserstein-2 barycenters in the special case of compatible measures. Computational methods for synthesizing and analyzing measures in the LBCM are developed with finite sample guarantees. One of our main theoretical contributions is to identify an LBCM, expressed in terms of a simple family, which is sufficient to express all probability measures on the interval [0,1]. We show that a natural analogous construction of an LBCM in ℝ2 fails, and we leave it as an open problem to identify the proper extension in more than one dimension. We conclude by demonstrating the utility of LBCM for covariance estimation and data imputation.

Reinforcement Learning for Control of Non-Markovian Cellular Population Dynamics
Josiah C. Kratz, Jacob Adamczyk
[ arXiv:2410.08439 | code ]

Abstract Many organisms and cell types, from bacteria to cancer cells, exhibit a remarkable ability to adapt to fluctuating environments. Additionally, cells can leverage memory of past environments to better survive previously-encountered stressors. From a control perspective, this adaptability poses significant challenges in driving cell populations toward extinction, and is thus an open question with great clinical significance. In this work, we focus on drug dosing in cell populations exhibiting phenotypic plasticity. For specific dynamical models switching between resistant and susceptible states, exact solutions are known. However, when the underlying system parameters are unknown, and for complex memory-based systems, obtaining the optimal solution is currently intractable. To address this challenge, we apply reinforcement learning (RL) to identify informed dosing strategies to control cell populations evolving under novel non-Markovian dynamics. We find that model-free deep RL is able to recover exact solutions and control cell populations even in the presence of long-range temporal dynamics.

Seeing Faces in Things: A Model and Dataset for Pareidolia
Mark Hamilton, Simon Stent, Vasha DuTell, Anne Harrington, Jennifer Corbett, Ruth Rosenholtz, William T. Freeman
[ arXiv:2409.16143 | code ]

Abstract The human visual system is well-tuned to detect faces of all shapes and sizes. While this brings obvious survival advantages, such as a better chance of spotting unknown predators in the bush, it also leads to spurious face detections. ``Face pareidolia'' describes the perception of face-like structure among otherwise random stimuli: seeing faces in coffee stains or clouds in the sky. In this paper, we study face pareidolia from a computer vision perspective. We present an image dataset of ``Faces in Things'', consisting of five thousand web images with human-annotated pareidolic faces. Using this dataset, we examine the extent to which a state-of-the-art human face detector exhibits pareidolia, and find a significant behavioral gap between humans and machines. We find that the evolutionary need for humans to detect animal faces, as well as human faces, may explain some of this gap. Finally, we propose a simple statistical model of pareidolia in images. Through studies on human subjects and our pareidolic face detectors we confirm a key prediction of our model regarding what image conditions are most likely to induce pareidolia. Dataset and Website: this https URL

Remove Symmetries to Control Model Expressivity
Liu Ziyin, Yizhou Xu, Isaac Chuang
[ arXiv:2408.15495 ]

Abstract When symmetry is present in the loss function, the model is likely to be trapped in a low-capacity state that is sometimes known as a "collapse." Being trapped in these low-capacity states can be a major obstacle to training across many scenarios where deep learning technology is applied. We first prove two concrete mechanisms through which symmetries lead to reduced capacities and ignored features during training. We then propose a simple and theoretically justified algorithm, syre, to remove almost all symmetry-induced low-capacity states in neural networks. The proposed method is shown to improve the training of neural networks in scenarios when this type of entrapment is especially a concern. A remarkable merit of the proposed method is that it is model-agnostic and does not require any knowledge of the symmetry.

Low-Budget Simulation-Based Inference with Bayesian Neural Networks
Arnaud Delaunoy, Maxence de la Brassinne Bonardeaux, Siddharth Mishra-Sharma, Gilles Louppe
[ arXiv:2408.16829 | code ]

Abstract Simulation-based inference methods have been shown to be inaccurate in the data-poor regime, when training simulations are limited or expensive. Under these circumstances, the inference network is particularly prone to overfitting, and using it without accounting for the computational uncertainty arising from the lack of identifiability of the network weights can lead to unreliable results. To address this issue, we propose using Bayesian neural networks in low-budget simulation-based inference, thereby explicitly accounting for the computational uncertainty of the posterior approximation. We design a family of Bayesian neural network priors that are tailored for inference and show that they lead to well-calibrated posteriors on tested benchmarks, even when as few as O(10) simulations are available. This opens up the possibility of performing reliable simulation-based inference using very expensive simulators, as we demonstrate on a problem from the field of cosmology where single simulations are computationally expensive. We show that Bayesian neural networks produce informative and well-calibrated posterior estimates with only a few hundred simulations.

Quantum inception score
Akira Sone, Akira Tanji, and Naoki Yamamoto
Physical Review Research, 2024, Volume 6, Issue 3 [ arXiv:2311.12163 ]

Abstract Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the (classical) inception score (cIS). In this paper, as a natural extension of cIS, we propose the quantum inception score (qIS) for quantum generators. Importantly, qIS relates the quality to the Holevo information of the quantum channel that classifies a given dataset. In this context, we show several properties of qIS. First, qIS is greater than or equal to the corresponding cIS, which is defined through projection measurements on the system output. Second, the difference between qIS and cIS arises from the presence of quantum coherence, as characterized by the resource theory of asymmetry. Third, when a set of entangled generators is prepared, there exists a classifying process leading to the further enhancement of qIS. Fourth, we harness the quantum fluctuation theorem to characterize the physical limitation of qIS. Finally, we apply qIS to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics.

KAN 2.0: Kolmogorov-Arnold Networks Meet Science
Ziming Liu, Pingchuan Ma, Yixuan Wang, Wojciech Matusik, Max Tegmark
[ arXiv:2408.10205 | code ]

Abstract A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

Hyperspectral Multilevel GCN and CNN Feature Fusion for Change Detection
Chhaya Katiyar, Vidya Manian
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2024 [ ]

Abstract Hyperspectral Image Change Detection (HSI-CD) focuses on identifying differences in multi-temporal HSIs. Graph Convolutional Networks (GCN) have demonstrated greater promise than convolutional neural networks (CNNs) in remote sensing, particularly for processing HSIs. This is due to GCN's ability to handle non-Euclidean graph-structured information, as opposed to the fixed kernel operations of CNN based on Euclidean structures. Specifically, GCN operates predominantly on superpixel-based nodes. This paper proposes a method, named Hyperspectral Multilevel GCN and CNN Feature Fusion for Change Detection (HMGCF-CD), that integrates superpixel-level GCN with pixel-level CNN for feature extraction and efficient change detection in HSIs. The proposed method utilizes the strengths of both CNN and GCN; the CNN branch focuses on feature learning in small-scale, regular regions, while the GCN branch handles large-scale, irregular regions. This approach generates complementary spectral-spatial features at both pixel and superpixel levels. To bridge the structural incompatibility between the Euclidean-data-oriented CNN and the non-Euclideandata-oriented GCN, HMGCF introduces a graph encoder and decoder. These elements help in propagating features between image pixels and graph nodes, allowing CNN and GCN to function within an integrated end-to-end framework. HMGCF integrates graph encoding into the network, edge weights, and node representations from training data. This innovation improves node feature learning and adapts the graph more effectively to HSI content. Fusion of features from different branches within the HMGCF enables precise changes in HSI. Experiments carried out on four datasets demonstrate that the proposed HMGCF method outperforms existing methods, marking a significant advancement in HSI-CD techniques.

Automatic Environment Shaping is the Next Frontier in RL
Younghyo Park, Gabriel B. Margolis, Pulkit Agrawal
[ arXiv:2407.16186 ]

Abstract Many roboticists dream of presenting a robot with a task in the evening and returning the next morning to find the robot capable of solving the task. What is preventing us from achieving this? Sim-to-real reinforcement learning (RL) has achieved impressive performance on challenging robotics tasks, but requires substantial human effort to set up the task in a way that is amenable to RL. It's our position that algorithmic improvements in policy optimization and other ideas should be guided towards resolving the primary bottleneck of shaping the training environment, i.e., designing observations, actions, rewards and simulation dynamics. Most practitioners don't tune the RL algorithm, but other environment parameters to obtain a desirable controller. We posit that scaling RL to diverse robotic tasks will only be achieved if the community focuses on automating environment shaping procedures.

A multicategory jet image classification framework using deep neural network
Jairo Orozco Sandoval, Vidya Manian, Sudhir Malik
[ arXiv:2407.03524 ]

Abstract Jet point cloud images are high dimensional data structures that needs to be transformed to a separable feature space for machine learning algorithms to distinguish them with simple decision boundaries. In this article, the authors focus on jet category separability by particle and jet feature extraction, resulting in more efficient training of a simple deep neural network, resulting in a computational efficient interpretable model for jet classification. The methodology is tested with three to five categories of jets from the JetNet benchmark jet tagging dataset, resulting in comparable performance to particle flow network. This work demonstrates that high dimensional datasets represented in separable latent spaces lead to simpler architectures for jet classification.

Boosting Soft Q-Learning by Bounding
Jacob Adamczyk, Volodymyr Makarenko, Stas Tiomkin, Rahul V. Kulkarni
Reinforcement Learning Journal, Volume 5, 2024, pp. 2373–2399 [ arXiv:2406.18033 | code ]

Abstract An agent's ability to leverage past experience is critical for efficiently solving new tasks. Prior work has focused on using value function estimates to obtain zero-shot approximations for solutions to a new task. In soft Q-learning, we show how any value function estimate can also be used to derive double-sided bounds on the optimal value function. The derived bounds lead to new approaches for boosting training performance which we validate experimentally. Notably, we find that the proposed framework suggests an alternative method for updating the Q-function, leading to boosted performance.

An Elliptic Kernel Unsupervised Autoencoder-Graph Convolutional Network Ensemble Model for Hyperspectral Unmixing
Estefania Alfaro-Mejia, Carlos J Delgado, Vidya Manian
[ arXiv:2406.06742 ]

Abstract Spectral Unmixing is an important technique in remote sensing used to analyze hyperspectral images to identify endmembers and estimate abundance maps. Over the past few decades, performance of techniques for endmember extraction and fractional abundance map estimation have significantly improved. This article presents an ensemble model workflow called Autoencoder Graph Ensemble Model (AEGEM) designed to extract endmembers and fractional abundance maps. An elliptical kernel is applied to measure spectral distances, generating the adjacency matrix within the elliptical neighborhood. This information is used to construct an elliptical graph, with centroids as senders and remaining pixels within the geometry as receivers. The next step involves stacking abundance maps, senders, and receivers as inputs to a Graph Convolutional Network, which processes this input to refine abundance maps. Finally, an ensemble decision-making process determines the best abundance maps based on root mean square error metric. The proposed AEGEM is assessed with benchmark datasets such as Samson, Jasper, and Urban, outperforming results obtained by baseline algorithms. For the Samson dataset, AEGEM excels in three abundance maps: water, tree and soil yielding values of 0.081, 0.158, and 0.182, respectively. For the Jasper dataset, results are improved for the tree and water endmembers with values of 0.035 and 0.060 in that order, as well as for the mean average of the spectral angle distance metric 0.109. For the Urban dataset, AEGEM outperforms previous results for the abundance maps of roof and asphalt, achieving values of 0.135 and 0.240, respectively. Additionally, for the endmembers of grass and roof, AEGEM achieves values of 0.063 and 0.094.

Separating the ‘Chirp’ from the ‘Chat’: Self-supervised Visual Grounding of Sound and Language
Mark Hamilton, Andrew Zisserman, John R. Hershey, William T. Freeman
[ arXiv:2406.05629 | code ]

Abstract We present DenseAV, a novel dual encoder grounding architecture that learns high-resolution, semantically meaningful, and audio-visually aligned features solely through watching videos. We show that DenseAV can discover the ``meaning'' of words and the ``location'' of sounds without explicit localization supervision. Furthermore, it automatically discovers and distinguishes between these two types of associations without supervision. We show that DenseAV's localization abilities arise from a new multi-head feature aggregation operator that directly compares dense image and audio representations for contrastive learning. In contrast, many other systems that learn ``global'' audio and video representations cannot localize words and sound. Finally, we contribute two new datasets to improve the evaluation of AV representations through speech and sound prompted semantic segmentation. On these and other datasets we show DenseAV dramatically outperforms the prior art on speech and sound prompted semantic segmentation. DenseAV outperforms the previous state-of-the-art, ImageBind, on cross-modal retrieval using fewer than half of the parameters.

OccamLLM: Fast and Exact Language Model Arithmetic in a Single Step
Owen Dugan, Donato Manuel Jimenez Beneto, Charlotte Loh, Zhuo Chen, Rumen Dangovski, Marin Soljačić
[ arXiv:2406.06576 ]

Abstract Despite significant advancements in text generation and reasoning, Large Language Models (LLMs) still face challenges in accurately performing complex arithmetic operations. Language model systems often enable LLMs to generate code for arithmetic operations to achieve accurate calculations. However, this approach compromises speed and security, and fine-tuning risks the language model losing prior capabilities. We propose a framework that enables exact arithmetic in a single autoregressive step, providing faster, more secure, and more interpretable LLM systems with arithmetic capabilities. We use the hidden states of a LLM to control a symbolic architecture that performs arithmetic. Our implementation using Llama 3 with OccamNet as a symbolic model (OccamLlama) achieves 100% accuracy on single arithmetic operations (+,−,×,÷,sin,cos,log,exp,√), outperforming GPT 4o with and without a code interpreter. Furthermore, OccamLlama outperforms GPT 4o with and without a code interpreter on average across a range of mathematical problem solving benchmarks, demonstrating that OccamLLMs can excel in arithmetic tasks, even surpassing much larger models. We will make our code public shortly.

Exploratory Preference Optimization: Harnessing Implicit Q-Approximation for Sample-Efficient RLHF*
Tengyang Xie, Dylan J. Foster, Akshay Krishnamurthy, Corby Rosset, Ahmed Awadallah, Alexander Rakhlin
[ arXiv:2405.21046 ]

Abstract Reinforcement learning from human feedback (RLHF) has emerged as a central tool for language model alignment. We consider online exploration in RLHF, which exploits interactive access to human or AI feedback by deliberately encouraging the model to produce diverse, maximally informative responses. By allowing RLHF to confidently stray from the pre-trained model, online exploration offers the possibility of novel, potentially super-human capabilities, but its full potential as a paradigm for language model training has yet to be realized, owing to computational and statistical bottlenecks in directly adapting existing reinforcement learning techniques. We propose a new algorithm for online exploration in RLHF, Exploratory Preference Optimization (XPO), which is simple and practical -- a one-line change to (online) Direct Preference Optimization (DPO; Rafailov et al., 2023) -- yet enjoys the strongest known provable guarantees and promising empirical performance. XPO augments the DPO objective with a novel and principled exploration bonus, empowering the algorithm to explore outside the support of the initial model and human feedback data. In theory, we show that XPO is provably sample-efficient and converges to a near-optimal language model policy under natural exploration conditions, irrespective of whether the initial model has good coverage. Our analysis, which builds on the observation that DPO implicitly performs a form of Q⋆-approximation (or, Bellman error minimization), combines previously disparate techniques from language modeling and theoretical reinforcement learning in a serendipitous fashion through the perspective of KL-regularized Markov decision processes. Empirically, we find that XPO is more sample-efficient than non-exploratory DPO variants in a preliminary evaluation.

Survival of the Fittest Representation: A Case Study with Modular Addition
Xiaoman Delores Ding, Zifan Carl Guo, Eric J. Michaud, Ziming Liu, Max Tegmark
[ arXiv:2405.17420 | code ]

Abstract When a neural network can learn multiple distinct algorithms to solve a task, how does it 'choose' between them during training? To approach this question, we take inspiration from ecology: when multiple species coexist, they eventually reach an equilibrium where some survive while others die out. Analogously, we suggest that a neural network at initialization contains many solutions (representations and algorithms), which compete with each other under pressure from resource constraints, with the 'fittest' ultimately prevailing. To investigate this Survival of the Fittest hypothesis, we conduct a case study on neural networks performing modular addition, and find that these networks' multiple circular representations at different Fourier frequencies undergo such competitive dynamics, with only a few circles surviving at the end. We find that the frequencies with high initial signals and gradients, the 'fittest,' are more likely to survive. By increasing the embedding dimension, we also observe more surviving frequencies. Inspired by the Lotka-Volterra equations describing the dynamics between species, we find that the dynamics of the circles can be nicely characterized by a set of linear differential equations. Our results with modular addition show that it is possible to decompose complicated representations into simpler components, along with their basic interactions, to offer insight on the training dynamics of representations.

How Do Transformers ‘Do’ Physics? Investigating the Simple Harmonic Oscillator
Subhash Kantamneni, Ziming Liu, Max Tegmark
[ arXiv:2405.17209 ]

Abstract How do transformers model physics? Do transformers model systems with interpretable analytical solutions, or do they create 'alien physics' that are difficult for humans to decipher? We take a step in demystifying this larger puzzle by investigating the simple harmonic oscillator (SHO), ẍ+2γẋ+ω20x=0, one of the most fundamental systems in physics. Our goal is to identify the methods transformers use to model the SHO, and to do so we hypothesize and evaluate possible methods by analyzing the encoding of these methods' intermediates. We develop four criteria for the use of a method within the simple testbed of linear regression, where our method is y=wx and our intermediate is w - (1) Can the intermediate be predicted from hidden states? (2) Is the intermediate's encoding quality correlated with model performance? (3) Can the majority of variance in hidden states be explained by the intermediate? (4) Can we intervene on hidden states to produce predictable outcomes? Armed with these two correlational (1,2), weak causal (3) and strong causal (4) criteria, we determine that transformers use known numerical methods to model trajectories of the simple harmonic oscillator, specifically the matrix exponential method. Our analysis framework can conveniently extend to high-dimensional linear systems and nonlinear systems, which we hope will help reveal the 'world model' hidden in transformers.

Improved Distribution Matching Distillation for Fast Image Synthesis
Tianwei Yin, Michaël Gharbi, Taesung Park, Richard Zhang, Eli Shechtman, Fredo Durand, William T. Freeman
[ arXiv:2405.14867 | code ]

Abstract Recent approaches have shown promises distilling diffusion models into efficient one-step generators. Among them, Distribution Matching Distillation (DMD) produces one-step generators that match their teacher in distribution, without enforcing a one-to-one correspondence with the sampling trajectories of their teachers. However, to ensure stable training, DMD requires an additional regression loss computed using a large set of noise-image pairs generated by the teacher with many steps of a deterministic sampler. This is costly for large-scale text-to-image synthesis and limits the student's quality, tying it too closely to the teacher's original sampling paths. We introduce DMD2, a set of techniques that lift this limitation and improve DMD training. First, we eliminate the regression loss and the need for expensive dataset construction. We show that the resulting instability is due to the fake critic not estimating the distribution of generated samples accurately and propose a two time-scale update rule as a remedy. Second, we integrate a GAN loss into the distillation procedure, discriminating between generated samples and real images. This lets us train the student model on real data, mitigating the imperfect real score estimation from the teacher model, and enhancing quality. Lastly, we modify the training procedure to enable multi-step sampling. We identify and address the training-inference input mismatch problem in this setting, by simulating inference-time generator samples during training time. Taken together, our improvements set new benchmarks in one-step image generation, with FID scores of 1.28 on ImageNet-64x64 and 8.35 on zero-shot COCO 2014, surpassing the original teacher despite a 500X reduction in inference cost. Further, we show our approach can generate megapixel images by distilling SDXL, demonstrating exceptional visual quality among few-step methods.

Not All Language Model Features Are Linear
Joshua Engels, Isaac Liao, Eric J. Michaud, Wes Gurnee, Max Tegmark
[ arXiv:2405.14860 | code ]

Abstract Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ('features') in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.

Multistable Shape from Shading Emerges from Patch Diffusion
Xinran Nicole Han, Todd Zickler, Ko Nishino
[ arXiv:2405.14530 ]

Abstract Models for monocular shape reconstruction of surfaces with diffuse reflection -- shape from shading -- ought to produce distributions of outputs, because there are fundamental mathematical ambiguities of both continuous (e.g., bas-relief) and discrete (e.g., convex/concave) varieties which are also experienced by humans. Yet, the outputs of current models are limited to point estimates or tight distributions around single modes, which prevent them from capturing these effects. We introduce a model that reconstructs a multimodal distribution of shapes from a single shading image, which aligns with the human experience of multistable perception. We train a small denoising diffusion process to generate surface normal fields from 16×16 patches of synthetic images of everyday 3D objects. We deploy this model patch-wise at multiple scales, with guidance from inter-patch shape consistency constraints. Despite its relatively small parameter count and predominantly bottom-up structure, we show that multistable shape explanations emerge from this model for 'ambiguous' test images that humans experience as being multistable. At the same time, the model produces veridical shape estimates for object-like images that include distinctive occluding contours and appear less ambiguous. This may inspire new architectures for stochastic 3D shape perception that are more efficient and better aligned with human experience.

OptPDE: Discovering Novel Integrable Systems via AI-Human Collaboration
Subhash Kantamneni, Ziming Liu, Max Tegmark
[ arXiv:2405.04484 ]

Abstract Integrable partial differential equation (PDE) systems are of great interest in natural science, but are exceedingly rare and difficult to discover. To solve this, we introduce OptPDE, a first-of-its-kind machine learning approach that Optimizes PDEs' coefficients to maximize their number of conserved quantities, nCQ, and thus discover new integrable systems. We discover four families of integrable PDEs, one of which was previously known, and three of which have at least one conserved quantity but are new to the literature to the best of our knowledge. We investigate more deeply the properties of one of these novel PDE families, ut=(ux+a2uxxx)3. Our paper offers a promising schema of AI-human collaboration for integrable system discovery; machine learning generates interpretable hypotheses for possible integrable systems, which human scientists can verify and analyze, to truly close the discovery loop.

Learning Force Control for Legged Manipulation
Tifanny Portela, Gabriel B. Margolis, Yandong Ji, Pulkit Agrawal
[ arXiv:2405.01402 | code ]

Abstract Controlling contact forces during interactions is critical for locomotion and manipulation tasks. While sim-to-real reinforcement learning (RL) has succeeded in many contact-rich problems, current RL methods achieve forceful interactions implicitly without explicitly regulating forces. We propose a method for training RL policies for direct force control without requiring access to force sensing. We showcase our method on a whole-body control platform of a quadruped robot with an arm. Such force control enables us to perform gravity compensation and impedance control, unlocking compliant whole-body manipulation. The learned whole-body controller with variable compliance makes it intuitive for humans to teleoperate the robot by only commanding the manipulator, and the robot's body adjusts automatically to achieve the desired position and force. Consequently, a human teleoperator can easily demonstrate a wide variety of loco-manipulation tasks. To the best of our knowledge, we provide the first deployment of learned whole-body force control in legged manipulators, paving the way for more versatile and adaptable legged robots.

KAN: Kolmogorov-Arnold Networks
Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y. Hou, Max Tegmark
[ arXiv:2404.19756 | code ]

Abstract Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving todays deep learning models which rely heavily on MLPs.

PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation
Tianyuan Zhang, Hong-Xing Yu, Rundi Wu, Brandon Y. Feng, Changxi Zheng, Noah Snavely, Jiajun Wu, William T. Freeman
[ arXiv:2404.13026 | code ]

Abstract Realistic object interactions are crucial for creating immersive virtual experiences, yet synthesizing realistic 3D object dynamics in response to novel interactions remains a significant challenge. Unlike unconditional or text-conditioned dynamics generation, action-conditioned dynamics requires perceiving the physical material properties of objects and grounding the 3D motion prediction on these properties, such as object stiffness. However, estimating physical material properties is an open problem due to the lack of material ground-truth data, as measuring these properties for real objects is highly difficult. We present PhysDreamer, a physics-based approach that endows static 3D objects with interactive dynamics by leveraging the object dynamics priors learned by video generation models. By distilling these priors, PhysDreamer enables the synthesis of realistic object responses to novel interactions, such as external forces or agent manipulations. We demonstrate our approach on diverse examples of elastic objects and evaluate the realism of the synthesized interactions through a user study. PhysDreamer takes a step towards more engaging and realistic virtual experiences by enabling static 3D objects to dynamically respond to interactive stimuli in a physically plausible manner.

Feature Splatting: Language-Driven Physics-Based Scene Synthesis and Editing
Ri-Zhao Qiu, Ge Yang, Weijia Zeng, Xiaolong Wang
[ arXiv:2404.01223 | code ]

Abstract Scene representations using 3D Gaussian primitives have produced excellent results in modeling the appearance of static and dynamic 3D scenes. Many graphics applications, however, demand the ability to manipulate both the appearance and the physical properties of objects. We introduce Feature Splatting, an approach that unifies physics-based dynamic scene synthesis with rich semantics from vision language foundation models that are grounded by natural language. Our first contribution is a way to distill high-quality, object-centric vision-language features into 3D Gaussians, that enables semi-automatic scene decomposition using text queries. Our second contribution is a way to synthesize physics-based dynamics from an otherwise static scene using a particle-based simulator, in which material properties are assigned automatically via text queries. We ablate key techniques used in this pipeline, to illustrate the challenge and opportunities in using feature-carrying 3D Gaussians as a unified format for appearance, geometry, material properties and semantics grounded on natural language. Project website: https://feature-splatting.github.io/

Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data
Matthias Gerstgrasser, Rylan Schaeffer, Apratim Dey, Rafael Rafailov, Henry Sleight, John Hughes, Tomasz Korbak, Rajashree Agrawal, Dhruv Pai, Andrey Gromov, Daniel A. Roberts, Diyi Yang, David L. Donoho, Sanmi Koyejo
[ arXiv:2404.01413 ]

Abstract The proliferation of generative models, combined with pretraining on web-scale data, raises a timely question: what happens when these models are trained on their own generated outputs? Recent investigations into model-data feedback loops discovered that such loops can lead to model collapse, a phenomenon where performance progressively degrades with each model-fitting iteration until the latest model becomes useless. However, several recent papers studying model collapse assumed that new data replace old data over time rather than assuming data accumulate over time. In this paper, we compare these two settings and show that accumulating data prevents model collapse. We begin by studying an analytically tractable setup in which a sequence of linear models are fit to the previous models predictions. Previous work showed if data are replaced, the test error increases linearly with the number of model-fitting iterations; we extend this result by proving that if data instead accumulate, the test error has a finite upper bound independent of the number of iterations. We next empirically test whether accumulating data similarly prevents model collapse by pretraining sequences of language models on text corpora. We confirm that replacing data does indeed cause model collapse, then demonstrate that accumulating data prevents model collapse; these results hold across a range of model sizes, architectures and hyperparameters. We further show that similar results hold for other deep generative models on real data: diffusion models for molecule generation and variational autoencoders for image generation. Our work provides consistent theoretical and empirical evidence that data accumulation mitigates model collapse.

The Unreasonable Ineffectiveness of the Deeper Layers
Andrey Gromov, Kushal Tirumala, Hassan Shapourian, Paolo Glorioso, Daniel A. Roberts
[ arXiv:2403.17887 ]

Abstract We empirically study a simple layer-pruning strategy for popular families of open-weight pretrained LLMs, finding minimal degradation of performance on different question-answering benchmarks until after a large fraction (up to half) of the layers are removed. To prune these models, we identify the optimal block of layers to prune by considering similarity across layers; then, to "heal" the damage, we perform a small amount of finetuning. In particular, we use parameter-efficient finetuning (PEFT) methods, specifically quantization and Low Rank Adapters (QLoRA), such that each of our experiments can be performed on a single A100 GPU. From a practical perspective, these results suggest that layer pruning methods can complement other PEFT strategies to further reduce computational resources of finetuning on the one hand, and can improve the memory and latency of inference on the other hand. From a scientific perspective, the robustness of these LLMs to the deletion of layers implies either that current pretraining methods are not properly leveraging the parameters in the deeper layers of the network or that the shallow layers play a critical role in storing knowledge.

FeatUp: A Model-Agnostic Framework for Features at Any Resolution
Stephanie Fu, Mark Hamilton, Laura Brandt, Axel Feldman, Zhoutong Zhang, William T. Freeman
[ arXiv:2403.10516 | code ]

Abstract Deep features are a cornerstone of computer vision research, capturing image semantics and enabling the community to solve downstream tasks even in the zero- or few-shot regime. However, these features often lack the spatial resolution to directly perform dense prediction tasks like segmentation and depth prediction because models aggressively pool information over large areas. In this work, we introduce FeatUp, a task- and model-agnostic framework to restore lost spatial information in deep features. We introduce two variants of FeatUp: one that guides features with high-resolution signal in a single forward pass, and one that fits an implicit model to a single image to reconstruct features at any resolution. Both approaches use a multi-view consistency loss with deep analogies to NeRFs. Our features retain their original semantics and can be swapped into existing applications to yield resolution and performance gains even without re-training. We show that FeatUp significantly outperforms other feature upsampling and image super-resolution approaches in class activation map generation, transfer learning for segmentation and depth prediction, and end-to-end training for semantic segmentation.

A Resource Model For Neural Scaling Law
Jinyeop Song, Ziming Liu, Max Tegmark, Jeff Gore
[ arXiv:2402.05164 ]

Abstract Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A task is usually composite hence can be decomposed into many subtasks, which compete for resources (measured by the number of neurons allocated to subtasks). On toy problems, we empirically find that: (1) The loss of a subtask is inversely proportional to its allocated neurons. (2) When multiple subtasks are present in a composite task, the resources acquired by each subtask uniformly grow as models get larger, keeping the ratios of acquired resources constants. We hypothesize these findings to be generally true and build a model to predict neural scaling laws for general composite tasks, which successfully replicates the neural scaling law of Chinchilla models reported in arXiv:2203.15556. We believe that the notion of resource used in this paper will be a useful tool for characterizing and diagnosing neural networks.

Opening the AI black box: program synthesis via mechanistic interpretability
Eric J. Michaud, Isaac Liao, Vedang Lad, Ziming Liu, Anish Mudide, Chloe Loughridge, Zifan Carl Guo, Tara Rezaei Kheirkhah, Mateja Vukelić, Max Tegmark
[ arXiv:2402.05110 | code ]

Abstract We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the learned algorithm into Python code. We test MIPS on a benchmark of 62 algorithmic tasks that can be learned by an RNN and find it highly complementary to GPT-4: MIPS solves 32 of them, including 13 that are not solved by GPT-4 (which also solves 30). MIPS uses an integer autoencoder to convert the RNN into a finite state machine, then applies Boolean or integer symbolic regression to capture the learned algorithm. As opposed to large language models, this program synthesis technique makes no use of (and is therefore not limited by) human training data such as algorithms and code from GitHub. We discuss opportunities and challenges for scaling up this approach to make machine-learned models more interpretable and trustworthy.

Generating Interpretable Networks using Hypernetworks
Isaac Liao, Ziming Liu, Max Tegmark
[ arXiv:2312.03051 ]

Abstract An essential goal in mechanistic interpretability to decode a network, i.e., to convert a neural network's raw weights to an interpretable algorithm. Given the difficulty of the decoding problem, progress has been made to understand the easier encoding problem, i.e., to convert an interpretable algorithm into network weights. Previous works focus on encoding existing algorithms into networks, which are interpretable by definition. However, focusing on encoding limits the possibility of discovering new algorithms that humans have never stumbled upon, but that are nevertheless interpretable. In this work, we explore the possibility of using hypernetworks to generate interpretable networks whose underlying algorithms are not yet known. The hypernetwork is carefully designed such that it can control network complexity, leading to a diverse family of interpretable algorithms ranked by their complexity. All of them are interpretable in hindsight, although some of them are less intuitive to humans, hence providing new insights regarding how to 'think' like a neural network. For the task of computing L1 norms, hypernetworks find three algorithms: (a) the double-sided algorithm, (b) the convexity algorithm, (c) the pudding algorithm, although only the first algorithm was expected by the authors before experiments. We automatically classify these algorithms and analyze how these algorithmic phases develop during training, as well as how they are affected by complexity control. Furthermore, we show that a trained hypernetwork can correctly construct models for input dimensions not seen in training, demonstrating systematic generalization.

One-step Diffusion with Distribution Matching Distillation
Tianwei Yin, Michaël Gharbi, Richard Zhang, Eli Shechtman, Fredo Durand, William T. Freeman, Taesung Park
[ arXiv:2311.18828 | code ]

Abstract Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on image quality. We enforce the one-step image generator match the diffusion model at distribution level, by minimizing an approximate KL divergence whose gradient can be expressed as the difference between 2 score functions, one of the target distribution and the other of the synthetic distribution being produced by our one-step generator. The score functions are parameterized as two diffusion models trained separately on each distribution. Combined with a simple regression loss matching the large-scale structure of the multi-step diffusion outputs, our method outperforms all published few-step diffusion approaches, reaching 2.62 FID on ImageNet 64x64 and 11.49 FID on zero-shot COCO-30k, comparable to Stable Diffusion but orders of magnitude faster. Utilizing FP16 inference, our model generates images at 20 FPS on modern hardware.

Growing Brains in Recurrent Neural Networks for Multiple Cognitive Tasks
Ziming Liu, Mikail Khona, Ila Fiete, Max Tegmark
NeurIPS 2023 Workshop NeurReps [ ]

Abstract Recurrent neural networks (RNNs) trained on a diverse ensemble of cognitive tasks, as described by Yang et al (2019); Khona et al. (2023), have been shown to exhibit functional modularity, where neurons organize into discrete functional clusters, each specialized for specific shared computational subtasks. However, these RNNs do not demonstrate anatomical modularity, where these functionally specialized clusters also have a distinct spatial organization. This contrasts with the human brain which has both functional and anatomical modularity. Is there a way to train RNNs to make them more like brains in this regard? We apply a recent machine learning method, brain-inspired modular training (BIMT), to encourage neural connectivity to be local in space. Consequently, hidden neuron organization of the RNN forms spatial structures reminiscent of those of the brain: spatial clusters which correspond to functional clusters. Compared to standard regularization and absence of regularization, BIMT exhibits superior performance by optimally balancing between task performance and sparsity. This balance is quantified both in terms of the number of active neurons and the cumulative wiring length. In addition to achieving brain-like organization in RNNs, our findings also suggest that BIMT holds promise for applications in neuromorphic computing and enhancing the interpretability of neural network architectures.

Symphony: Symmetry-Equivariant Point-Centered Spherical Harmonics for Molecule Generation
Ameya Daigavane, Song Kim, Mario Geiger, Tess Smidt
[ arXiv:2311.16199 | code ]

Abstract We present Symphony, an E(3)-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for molecules utilize rotationally invariant features to respect the 3D symmetries of molecules. In contrast, Symphony uses message-passing with higher-degree E(3)-equivariant features. This allows a novel representation of probability distributions via spherical harmonic signals to efficiently model the 3D geometry of molecules. We show that Symphony is able to accurately generate small molecules from the QM9 dataset, outperforming existing autoregressive models and approaching the performance of diffusion models.

Learning to See Physical Properties with Active Sensing Motor Policies
Gabriel B. Margolis, Xiang Fu, Yandong Ji, Pulkit Agrawal
[ arXiv:2311.01405 | code ]

Abstract Knowledge of terrain's physical properties inferred from color images can aid in making efficient robotic locomotion plans. However, unlike image classification, it is unintuitive for humans to label image patches with physical properties. Without labeled data, building a vision system that takes as input the observed terrain and predicts physical properties remains challenging. We present a method that overcomes this challenge by self-supervised labeling of images captured by robots during real-world traversal with physical property estimators trained in simulation. To ensure accurate labeling, we introduce Active Sensing Motor Policies (ASMP), which are trained to explore locomotion behaviors that increase the accuracy of estimating physical parameters. For instance, the quadruped robot learns to swipe its foot against the ground to estimate the friction coefficient accurately. We show that the visual system trained with a small amount of real-world traversal data accurately predicts physical parameters. The trained system is robust and works even with overhead images captured by a drone despite being trained on data collected by cameras attached to a quadruped robot walking on the ground.

Growing Brains: Co-emergence of Anatomical and Functional Modularity in Recurrent Neural Networks
Ziming Liu, Mikail Khona, Ila R. Fiete, Max Tegmark
[ arXiv:2310.07711 ]

Abstract Recurrent neural networks (RNNs) trained on compositional tasks can exhibit functional modularity, in which neurons can be clustered by activity similarity and participation in shared computational subtasks. Unlike brains, these RNNs do not exhibit anatomical modularity, in which functional clustering is correlated with strong recurrent coupling and spatial localization of functional clusters. Contrasting with functional modularity, which can be ephemerally dependent on the input, anatomically modular networks form a robust substrate for solving the same subtasks in the future. To examine whether it is possible to grow brain-like anatomical modularity, we apply a recent machine learning method, brain-inspired modular training (BIMT), to a network being trained to solve a set of compositional cognitive tasks. We find that functional and anatomical clustering emerge together, such that functionally similar neurons also become spatially localized and interconnected. Moreover, compared to standard L1 or no regularization settings, the model exhibits superior performance by optimally balancing task performance and network sparsity. In addition to achieving brain-like organization in RNNs, our findings also suggest that BIMT holds promise for applications in neuromorphic computing and enhancing the interpretability of neural network architectures.

The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets
Samuel Marks, Max Tegmark
[ arXiv:2310.06824 | code ]

Abstract Large Language Models (LLMs) have impressive capabilities, but are also prone to outputting falsehoods. Recent work has developed techniques for inferring whether a LLM is telling the truth by training probes on the LLM's internal activations. However, this line of work is controversial, with some authors pointing out failures of these probes to generalize in basic ways, among other conceptual issues. In this work, we curate high-quality datasets of true/false statements and use them to study in detail the structure of LLM representations of truth, drawing on three lines of evidence: 1. Visualizations of LLM true/false statement representations, which reveal clear linear structure. 2. Transfer experiments in which probes trained on one dataset generalize to different datasets. 3. Causal evidence obtained by surgically intervening in a LLM's forward pass, causing it to treat false statements as true and vice versa. Overall, we present evidence that language models linearly represent the truth or falsehood of factual statements. We also introduce a novel technique, mass-mean probing, which generalizes better and is more causally implicated in model outputs than other probing techniques.

Grokking as Compression: A Nonlinear Complexity Perspective
Ziming Liu, Ziqian Zhong, Max Tegmark
[ arXiv:2310.05918 ]

Abstract We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network complexity, which is a generalized version of linear region number for ReLU networks. LMN can nicely characterize neural network compression before generalization. Although the L2 norm has been a popular choice for characterizing model complexity, we argue in favor of LMN for a number of reasons: (1) LMN can be naturally interpreted as information/computation, while L2 cannot. (2) In the compression phase, LMN has linear relations with test losses, while L2 is correlated with test losses in a complicated nonlinear way. (3) LMN also reveals an intriguing phenomenon of the XOR network switching between two generalization solutions, while L2 does not. Besides explaining grokking, we argue that LMN is a promising candidate as the neural network version of the Kolmogorov complexity since it explicitly considers local or conditioned linear computations aligned with the nature of modern artificial neural networks.

Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution
Rui Wang, Elyssa Hofgard, Han Gao, Robin Walters, Tess E. Smidt
[ arXiv:2310.02299 ]

Abstract Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic structures. Thus, identifying sources of asymmetry is an important tool for understanding physical systems. In this paper, we focus on learning asymmetries of data using relaxed group convolutions. We provide both theoretical and empirical evidence that this flexible convolution technique allows the model to maintain the highest level of equivariance that is consistent with data and discover the subtle symmetry-breaking factors in various physical systems. We employ various relaxed group convolution architectures to uncover various symmetry-breaking factors that are interpretable and physically meaningful in different physical systems, including the phase transition of crystal structure, the isotropy and homogeneity breaking in turbulent flow, and the time-reversal symmetry breaking in pendulum systems.

Language Models Represent Space and Time
Wes Gurnee, Max Tegmark
[ arXiv:2310.02207 | code ]

Abstract The capabilities of large language models (LLMs) have sparked debate over whether such systems just learn an enormous collection of superficial statistics or a set of more coherent and grounded representations that reflect the real world. We find evidence for the latter by analyzing the learned representations of three spatial datasets (world, US, NYC places) and three temporal datasets (historical figures, artworks, news headlines) in the Llama-2 family of models. We discover that LLMs learn linear representations of space and time across multiple scales. These representations are robust to prompting variations and unified across different entity types (e.g. cities and landmarks). In addition, we identify individual 'space neurons' and 'time neurons' that reliably encode spatial and temporal coordinates. While further investigation is needed, our results suggest modern LLMs learn rich spatiotemporal representations of the real world and possess basic ingredients of a world model.

A Neural Scaling Law from Lottery Ticket Ensembling
Ziming Liu, Max Tegmark
[ arXiv:2310.02258 ]

Abstract Neural scaling laws (NSL) refer to the phenomenon where model performance improves with scale. Sharma & Kaplan analyzed NSL using approximation theory and predict that MSE losses decay as N−α, α=4/d, where N is the number of model parameters, and d is the intrinsic input dimension. Although their theory works well for some cases (e.g., ReLU networks), we surprisingly find that a simple 1D problem y=x2 manifests a different scaling law (α=1) from their predictions (α=4). We opened the neural networks and found that the new scaling law originates from lottery ticket ensembling: a wider network on average has more 'lottery tickets', which are ensembled to reduce the variance of outputs. We support the ensembling mechanism by mechanistically interpreting single neural networks, as well as studying them statistically. We attribute the N−1 scaling law to the 'central limit theorem' of lottery tickets. Finally, we discuss its potential implications for large language models and statistical physics-type theories of learning.

Mitigating Confirmation Bias in Semi-supervised Learning via Efficient Bayesian Model Averaging
Charlotte Loh, Rumen Dangovski, Shivchander Sudalairaj, Seungwook Han, Ligong Han, Leonid Karlinsky, Marin Soljacic, Akash Srivastava
Transactions on Machine Learning Research 2023, Submission number 1013 [ | code ]

Abstract State-of-the-art (SOTA) semi-supervised learning (SSL) methods have been highly successful in leveraging a mix of labeled and unlabeled data, often via self-training or pseudo-labeling. During pseudo-labeling, the model's predictions on unlabeled data are used for training and may result in confirmation bias where the model reinforces its own mistakes. In this work, we show that SOTA SSL methods often suffer from confirmation bias and demonstrate that this is often a result of using a poorly calibrated classifier for pseudo labeling. We introduce BaM-SSL, an efficient Bayesian Model averaging technique that improves uncertainty quantification in SSL methods with limited computational or memory overhead. We demonstrate that BaM-SSL mitigates confirmation bias in SOTA SSL methods across standard vision benchmarks of CIFAR-10, CIFAR-100, giving up to 16% improvement in test accuracy on the CIFAR-100 with 400 labels benchmark. Furthermore, we also demonstrate their effectiveness in additional realistic and challenging problems, such as class-imbalanced datasets and in photonics science.

Distilled Feature Fields Enable Few-Shot Language-Guided Manipulation
William Shen, Ge Yang, Alan Yu, Jansen Wong, Leslie Pack Kaelbling, Phillip Isola
[ arXiv:2308.07931 | code ]

Abstract Self-supervised and language-supervised image models contain rich knowledge of the world that is important for generalization. Many robotic tasks, however, require a detailed understanding of 3D geometry, which is often lacking in 2D image features. This work bridges this 2D-to-3D gap for robotic manipulation by leveraging distilled feature fields to combine accurate 3D geometry with rich semantics from 2D foundation models. We present a few-shot learning method for 6-DOF grasping and placing that harnesses these strong spatial and semantic priors to achieve in-the-wild generalization to unseen objects. Using features distilled from a vision-language model, CLIP, we present a way to designate novel objects for manipulation via free-text natural language, and demonstrate its ability to generalize to unseen expressions and novel categories of objects.

Polarization Multi-Image Synthesis with Birefringent Metasurfaces
Dean Hazineh, Soon Wei Daniel Lim, Qi Guo, Federico Capasso, Todd Zickler
IEEE International Conference on Computational Photography (ICCP), 2023 [ arXiv:2307.08106 | code ]

Abstract Optical metasurfaces composed of precisely engineered nanostructures have gained significant attention for their ability to manipulate light and implement distinct functionalities based on the properties of the incident field. Computational imaging systems have started harnessing this capability to produce sets of coded measurements that benefit certain tasks when paired with digital post-processing. Inspired by these works, we introduce a new system that uses a birefringent metasurface with a polarizer-mosaicked photosensor to capture four optically-coded measurements in a single exposure. We apply this system to the task of incoherent opto-electronic filtering, where digital spatial-filtering operations are replaced by simpler, per-pixel sums across the four polarization channels, independent of the spatial filter size. In contrast to previous work on incoherent opto-electronic filtering that can realize only one spatial filter, our approach can realize a continuous family of filters from a single capture, with filters being selected from the family by adjusting the post-capture digital summation weights. To find a metasurface that can realize a set of user-specified spatial filters, we introduce a form of gradient descent with a novel regularizer that encourages light efficiency and a high signal-to-noise ratio. We demonstrate several examples in simulation and with fabricated prototypes, including some with spatial filters that have prescribed variations with respect to depth and wavelength.

The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks
Ziqian Zhong, Ziming Liu, Max Tegmark, Jacob Andreas
[ arXiv:2306.17844 | code ]

Abstract Do neural networks, trained on well-understood algorithmic tasks, reliably rediscover known algorithms for solving those tasks? Several recent studies, on tasks ranging from group arithmetic to in-context linear regression, have suggested that the answer is yes. Using modular addition as a prototypical problem, we show that algorithm discovery in neural networks is sometimes more complex. Small changes to model hyperparameters and initializations can induce the discovery of qualitatively different algorithms from a fixed training set, and even parallel implementations of multiple such algorithms. Some networks trained to perform modular addition implement a familiar Clock algorithm; others implement a previously undescribed, less intuitive, but comprehensible procedure which we term the Pizza algorithm, or a variety of even more complex procedures. Our results show that even simple learning problems can admit a surprising diversity of solutions, motivating the development of new tools for characterizing the behavior of neural networks across their algorithmic phase space.

Discovering New Interpretable Conservation Laws as Sparse Invariants
Ziming Liu, Patrick Obin Sturm, Saketh Bharadwaj, Sam Silva, Max Tegmark
[ arXiv:2305.19525 ]

Abstract Discovering conservation laws for a given dynamical system is important but challenging. In a theorist setup (differential equations and basis functions are both known), we propose the Sparse Invariant Detector (SID), an algorithm that auto-discovers conservation laws from differential equations. Its algorithmic simplicity allows robustness and interpretability of the discovered conserved quantities. We show that SID is able to rediscover known and even discover new conservation laws in a variety of systems. For two examples in fluid mechanics and atmospheric chemistry, SID discovers 14 and 3 conserved quantities, respectively, where only 12 and 2 were previously known to domain experts.

Learning Linear Groups in Neural Networks
Emmanouil Theodosis, Karim Helwani, Demba Ba
[ arXiv:2305.18552 ]

Abstract Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a priori specification of the desired symmetries. We present a neural network architecture, Linear Group Networks (LGNs), for learning linear groups acting on the weight space of neural networks. Linear groups are desirable due to their inherent interpretability, as they can be represented as finite matrices. LGNs learn groups without any supervision or knowledge of the hidden symmetries in the data and the groups can be mapped to well known operations in machine learning. We use LGNs to learn groups on multiple datasets while considering different downstream tasks; we demonstrate that the linear group structure depends on both the data distribution and the considered task.

Machine Learning for Quantum-Enhanced Gravitational-Wave Observatories
Chris Whittle, Ge Yang, Matthew Evans, Lisa Barsotti
Physical Review D, Volume 108, Article 043034 [ arXiv:2305.13780 ]

Abstract Machine learning has become an effective tool for processing the extensive data sets produced by large physics experiments. Gravitational-wave detectors are now listening to the universe with quantum-enhanced sensitivity, accomplished with the injection of squeezed vacuum states. Squeezed state preparation and injection is operationally complicated, as well as highly sensitive to environmental fluctuations and variations in the interferometer state. Achieving and maintaining optimal squeezing levels is a challenging problem and will require development of new techniques to reach the lofty targets set by design goals for future observing runs and next-generation detectors. We use machine learning techniques to predict the squeezing level during the third observing run of the Laser Interferometer Gravitational-Wave Observatory (LIGO) based on auxiliary data streams, and offer interpretations of our models to identify and quantify salient sources of squeezing degradation. The development of these techniques lays the groundwork for future efforts to optimize squeezed state injection in gravitational-wave detectors, with the goal of enabling closed-loop control of the squeezer subsystem by an agent based on machine learning.

Materialistic: Selecting Similar Materials in Images
Prafull Sharma, Julien Philip, Michael Gharbi, Bill Freeman, Fredo Durand, Valentin Deschaintre
ACM Transactions on Graphics, 2023, Volume 42, Issue 4 [ arXiv:2305.13291 ]

Abstract Separating an image into meaningful underlying components is a crucial first step for both editing and understanding images. We present a method capable of selecting the regions of a photograph exhibiting the same material as an artist-chosen area. Our proposed approach is robust to shading, specular highlights, and cast shadows, enabling selection in real images. As we do not rely on semantic segmentation (different woods or metal should not be selected together), we formulate the problem as a similarity-based grouping problem based on a user-provided image location. In particular, we propose to leverage the unsupervised DINO features coupled with a proposed Cross-Similarity module and an MLP head to extract material similarities in an image. We train our model on a new synthetic image dataset, that we release. We show that our method generalizes well to real-world images. We carefully analyze our model's behavior on varying material properties and lighting. Additionally, we evaluate it against a hand-annotated benchmark of 50 real photographs. We further demonstrate our model on a set of applications, including material editing, in-video selection, and retrieval of object photographs with similar materials.

Dynamic Sparse Training with Structured Sparsity
Mike Lasby, Anna Golubeva, Utku Evci, Mihai Nica, Yani Ioannou
[ arXiv:2305.02299 ]

Abstract Dynamic Sparse Training (DST) methods achieve state-of-the-art results in sparse neural network training, matching the generalization of dense models while enabling sparse training and inference. Although the resulting models are highly sparse and theoretically cheaper to train, achieving speedups with unstructured sparsity on real-world hardware is challenging. In this work, we propose a sparse-to-sparse DST method to learn a variant of structured N:M sparsity by imposing a constant fan-in constraint. We demonstrate with both a theoretical analysis and empirical results: state-of-the-art spare-to-sparse structured DST performance on a variety of network architectures, a condensed representation with a reduced parameter and memory footprint, and reduced inference time compared to dense models with a naive PyTorch CPU implementation of the condensed representation.

Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretability
Ziming Liu, Eric Gan, Max Tegmark
[ arXiv:2305.08746 ]

Abstract We introduce Brain-Inspired Modular Training (BIMT), a method for making neural networks more modular and interpretable. Inspired by brains, BIMT embeds neurons in a geometric space and augments the loss function with a cost proportional to the length of each neuron connection. We demonstrate that BIMT discovers useful modular neural networks for many simple tasks, revealing compositional structures in symbolic formulas, interpretable decision boundaries and features for classification, and mathematical structure in algorithmic datasets. The ability to directly see modules with the naked eye can complement current mechanistic interpretability strategies such as probes, interventions or staring at all weights.

GenPhys: From Physical Processes to Generative Models
Ziming Liu, Di Luo, Yilun Xu, Tommi Jaakkola, Max Tegmark
[ arXiv:2304.02637 ]

Abstract Since diffusion models (DM) and the more recent Poisson flow generative models (PFGM) are inspired by physical processes, it is reasonable to ask: Can physical processes offer additional new generative models? We show that the answer is yes. We introduce a general family, Generative Models from Physical Processes (GenPhys), where we translate partial differential equations (PDEs) describing physical processes to generative models. We show that generative models can be constructed from s-generative PDEs (s for smooth). GenPhys subsume the two existing generative models (DM and PFGM) and even give rise to new families of generative models, e.g., "Yukawa Generative Models" inspired from weak interactions. On the other hand, some physical processes by default do not belong to the GenPhys family, e.g., the wave equation and the Schrödinger equation, but could be made into the GenPhys family with some modifications. Our goal with GenPhys is to explore and expand the design space of generative models.

DribbleBot: Dynamic Legged Manipulation in the Wild
Yandong Ji, Gabriel B. Margolis, Pulkit Agrawal
[ arXiv:2304.01159 | code ]

Abstract DribbleBot (Dexterous Ball Manipulation with a Legged Robot) is a legged robotic system that can dribble a soccer ball under the same real-world conditions as humans (i.e., in-the-wild). We adopt the paradigm of training policies in simulation using reinforcement learning and transferring them into the real world. We overcome critical challenges of accounting for variable ball motion dynamics on different terrains and perceiving the ball using body-mounted cameras under the constraints of onboard computing. Our results provide evidence that current quadruped platforms are well-suited for studying dynamic whole-body control problems involving simultaneous locomotion and manipulation directly from sensory observations.

Neural Volumetric Memory for Visual Locomotion Control
Ruihan Yang, Ge Yang, Xiaolong Wang
[ arXiv:2304.01201 ]

Abstract Legged robots have the potential to expand the reach of autonomy beyond paved roads. In this work, we consider the difficult problem of locomotion on challenging terrains using a single forward-facing depth camera. Due to the partial observability of the problem, the robot has to rely on past observations to infer the terrain currently beneath it. To solve this problem, we follow the paradigm in computer vision that explicitly models the 3D geometry of the scene and propose Neural Volumetric Memory (NVM), a geometric memory architecture that explicitly accounts for the SE(3) equivariance of the 3D world. NVM aggregates feature volumes from multiple camera views by first bringing them back to the ego-centric frame of the robot. We test the learned visual-locomotion policy on a physical robot and show that our approach, which explicitly introduces geometric priors during training, offers superior performance than more naïve methods. We also include ablation studies and show that the representations stored in the neural volumetric memory capture sufficient geometric information to reconstruct the scene.

Noisy dynamical systems evolve error correcting codes and modularity
Trevor McCourt, Ila R. Fiete, Isaac L. Chuang
[ arXiv:2303.14448 | code ]

Abstract There is an intimate connection between life (as we know it) and fault tolerance. Despite residing in the stochastic and complex physical world, biological systems execute functions that allow them to survive and thrive by maintaining their physical integrity. At the same time, biological systems are strikingly modular: parts responsible for different functions tend to be physically separate and easily distinguishable. In this work, through experiments in Boolean networks, we show that the simultaneous presence of fault tolerance and modularity in biological systems is no coincidence. Rather, it is a typical co-occurrence in dynamic systems undergoing adaptive evolution in noisy environments. From this, we deduce the principle of error correction enhanced evolvability: systems possessing error-correcting codes are more effectively improved by evolution than those without. Noise creates the evolutionary pressure to develop initial error-correcting codes, suggesting it plays a larger role in the evolution of complex structures than previously thought.

The Quantization Model of Neural Scaling
Eric J. Michaud, Ziming Liu, Uzay Girit, Max Tegmark
[ arXiv:2303.13506 | code ]

Abstract We propose the Quantization Model of neural scaling laws, explaining both the observed power law dropoff of loss with model and data size, and also the sudden emergence of new capabilities with scale. We derive this model from what we call the Quantization Hypothesis, where learned network capabilities are quantized into discrete chunks (quanta). We show that when quanta are learned in order of decreasing use frequency, then a power law in use frequencies explains observed power law scaling of loss. We validate this prediction on toy datasets, then study how scaling curves decompose for large language models. Using language model internals, we auto-discover diverse model capabilities (quanta) and find tentative evidence that the distribution over corresponding subproblems in the prediction of natural text is compatible with the power law predicted from the neural scaling exponent as predicted from our theory.

Multi-Symmetry Ensembles: Improving Diversity and Generalization via Opposing Symmetries
Charlotte Loh, Seungwook Han, Shivchander Sudalairaj, Rumen Dangovski, Kai Xu, Florian Wenzel, Marin Soljacic, Akash Srivastava
[ arXiv:2303.02484 | code ]

Abstract Deep ensembles (DE) have been successful in improving model performance by learning diverse members via the stochasticity of random initialization. While recent works have attempted to promote further diversity in DE via hyperparameters or regularizing loss functions, these methods primarily still rely on a stochastic approach to explore the hypothesis space. In this work, we present Multi-Symmetry Ensembles (MSE), a framework for constructing diverse ensembles by capturing the multiplicity of hypotheses along symmetry axes, which explore the hypothesis space beyond stochastic perturbations of model weights and hyperparameters. We leverage recent advances in contrastive representation learning to create models that separately capture opposing hypotheses of invariant and equivariant functional classes and present a simple ensembling approach to efficiently combine appropriate hypotheses for a given task. We show that MSE effectively captures the multiplicity of conflicting hypotheses that is often required in large, diverse datasets like ImageNet. As a result of their inherent diversity, MSE improves classification performance, uncertainty quantification, and generalization across a series of transfer tasks.

PFGM++: Unlocking the Potential of Physics-Inspired Generative Models
Yilun Xu, Ziming Liu, Yonglong Tian, Shangyuan Tong, Max Tegmark, Tommi Jaakkola
[ arXiv:2302.04265 | code ]

Abstract We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N+D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D=1 and to diffusion models when D→∞. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D→∞) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64×64 datasets, with FID scores of 1.91/2.43 when D=2048/128. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at this https URL

Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior
Gabriel B Margolis, Pulkit Agrawal
[ arXiv:2212.03238 | code ]

Abstract Learned locomotion policies can rapidly adapt to diverse environments similar to those experienced during training but lack a mechanism for fast tuning when they fail in an out-of-distribution test environment. This necessitates a slow and iterative cycle of reward and environment redesign to achieve good performance on a new task. As an alternative, we propose learning a single policy that encodes a structured family of locomotion strategies that solve training tasks in different ways, resulting in Multiplicity of Behavior (MoB). Different strategies generalize differently and can be chosen in real-time for new tasks or environments, bypassing the need for time-consuming retraining. We release a fast, robust open-source MoB locomotion controller, Walk These Ways, that can execute diverse gaits with variable footswing, posture, and speed, unlocking diverse downstream tasks: crouching, hopping, high-speed running, stair traversal, bracing against shoves, rhythmic dance, and more.

Learning Integrable Dynamics with Action-Angle Networks
Ameya Daigavane, Arthur Kosmala, Miles Cranmer, Tess Smidt, Shirley Ho
[ arXiv:2211.15338 | code ]

Abstract Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned simulators typically predict the evolution of the system in a step-by-step manner with numerical integration techniques. However, such models often suffer from instability over long roll-outs due to the accumulation of both estimation and integration error at each prediction step. Here, we propose an alternative construction for learned physical simulators that are inspired by the concept of action-angle coordinates from classical mechanics for describing integrable systems. We propose Action-Angle Networks, which learn a nonlinear transformation from input coordinates to the action-angle space, where evolution of the system is linear. Unlike traditional learned simulators, Action-Angle Networks do not employ any higher-order numerical integration methods, making them extremely efficient at modelling the dynamics of integrable physical systems.

Visual Dexterity: In-Hand Reorientation of Novel and Complex Object Shapes
Tao Chen, Megha Tippur, Siyang Wu, Vikash Kumar, Edward Adelson, Pulkit Agrawal
Science Robotics, 2023, Volume 8, Issue 84 [ arXiv:2211.11744 | code ]

Abstract In-hand object reorientation is necessary for performing many dexterous manipulation tasks, such as tool use in less structured environments that remain beyond the reach of current robots. Prior works built reorientation systems assuming one or many of the following: reorienting only specific objects with simple shapes, limited range of reorientation, slow or quasistatic manipulation, simulation-only results, the need for specialized and costly sensor suites, and other constraints which make the system infeasible for real-world deployment. We present a general object reorientation controller that does not make these assumptions. It uses readings from a single commodity depth camera to dynamically reorient complex and new object shapes by any rotation in real-time, with the median reorientation time being close to seven seconds. The controller is trained using reinforcement learning in simulation and evaluated in the real world on new object shapes not used for training, including the most challenging scenario of reorienting objects held in the air by a downward-facing hand that must counteract gravity during reorientation. Our hardware platform only uses open-source components that cost less than five thousand dollars. Although we demonstrate the ability to overcome assumptions in prior work, there is ample scope for improving absolute performance. For instance, the challenging duck-shaped object not used for training was dropped in 56 percent of the trials. When it was not dropped, our controller reoriented the object within 0.4 radians (23 degrees) 75 percent of the time. Videos are available at: this https URL.

A Solvable Model of Neural Scaling Laws
Alexander Maloney, Daniel A. Roberts, James Sully
[ arXiv:2210.16859 ]

Abstract Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model -- a joint generative data model and random feature model -- that captures this neural scaling phenomenology. By solving this model in the dual limit of large training set size and large number of parameters, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws, (ii) the way nonlinear feature maps, such as those provided by neural networks, enable scaling laws when trained on these datasets, (iii) the optimality of the equiparameterization scaling of training sets and parameters, and (iv) whether such scaling laws can break down and how they behave when they do. Key findings are the manner in which the power laws that occur in the statistics of natural datasets are extended by nonlinear random feature maps and then translated into power-law scalings of the test loss and how the finite extent of the data's spectral power law causes the model's performance to plateau.

Precision Machine Learning
Eric J. Michaud, Ziming Liu, Max Tegmark
Entropy, 2023, 25(1) [ arXiv:2210.13447 | code ]

Abstract We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with increasing parameters and data. We find that neural networks can often outperform classical approximation methods on high-dimensional examples, by auto-discovering and exploiting modular structures therein. However, neural networks trained with common optimizers are less powerful for low-dimensional cases, which motivates us to study the unique properties of neural network loss landscapes and the corresponding optimization challenges that arise in the high precision regime. To address the optimization issue in low dimensions, we develop training tricks which enable us to train neural networks to extremely low loss, close to the limits allowed by numerical precision.

Omnigrok: Grokking Beyond Algorithmic Data
Ziming Liu, Eric J. Michaud, Max Tegmark
[ arXiv:2210.01117 | code ]

Abstract Grokking, the unusual phenomenon for algorithmic datasets where generalization happens long after overfitting the training data, has remained elusive. We aim to understand grokking by analyzing the loss landscapes of neural networks, identifying the mismatch between training and test losses as the cause for grokking. We refer to this as the "LU mechanism" because training and test losses (against model weight norm) typically resemble "L" and "U", respectively. This simple mechanism can nicely explain many aspects of grokking: data size dependence, weight decay dependence, the emergence of representations, etc. Guided by the intuitive picture, we are able to induce grokking on tasks involving images, language and molecules. In the reverse direction, we are able to eliminate grokking for algorithmic datasets. We attribute the dramatic nature of grokking for algorithmic datasets to representation learning.

Poisson Flow Generative Models
Yilun Xu, Ziming Liu, Max Tegmark, Tommi Jaakkola
[ arXiv:2209.11178 | code ]

Abstract We propose a new "Poisson flow" generative model (PFGM) that maps a uniform distribution on a high-dimensional hemisphere into any data distribution. We interpret the data points as electrical charges on the z=0 hyperplane in a space augmented with an additional dimension z, generating a high-dimensional electric field (the gradient of the solution to Poisson equation). We prove that if these charges flow upward along electric field lines, their initial distribution in the z=0 plane transforms into a distribution on the hemisphere of radius r that becomes uniform in the r→∞ limit. To learn the bijective transformation, we estimate the normalized field in the augmented space. For sampling, we devise a backward ODE that is anchored by the physically meaningful additional dimension: the samples hit the unaugmented data manifold when the z reaches zero. Experimentally, PFGM achieves current state-of-the-art performance among the normalizing flow models on CIFAR-10, with an Inception score of 9.68 and a FID score of 2.48. It also performs on par with the state-of-the-art SDE approaches while offering 10× to 20× acceleration on image generation tasks. Additionally, PFGM appears more tolerant of estimation errors on a weaker network architecture and robust to the step size in the Euler method.

Bounding generalization error with input compression: An empirical study with infinite-width networks
Angus Galloway, Anna Golubeva, Mahmoud Salem, Mihai Nica, Yani Ioannou, Graham W. Taylor
[ arXiv:2207.09408 ]

Abstract Estimating the Generalization Error (GE) of Deep Neural Networks (DNNs) is an important task that often relies on availability of held-out data. The ability to better predict GE based on a single training set may yield overarching DNN design principles to reduce a reliance on trial-and-error, along with other performance assessment advantages. In search of a quantity relevant to GE, we investigate the Mutual Information (MI) between the input and final layer representations, using the infinite-width DNN limit to bound MI. An existing input compression-based GE bound is used to link MI and GE. To the best of our knowledge, this represents the first empirical study of this bound. In our attempt to empirically falsify the theoretical bound, we find that it is often tight for best-performing models. Furthermore, it detects randomization of training labels in many cases, reflects test-time perturbation robustness, and works well given only few training samples. These results are promising given that input compression is broadly applicable where MI can be estimated with confidence.

Deep Learning and Symbolic Regression for Discovering Parametric Equations
Michael Zhang, Samuel Kim, Peter Y. Lu, Marin Soljačić
IEEE Journals, 2023, PubMed ID 37721885 [ arXiv:2207.00529 ]

Abstract Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and dimensionality of the systems that it can analyze. Deep learning on the other hand has transformed machine learning in its ability to analyze extremely complex and high-dimensional datasets. We propose a neural network architecture to extend symbolic regression to parametric systems where some coefficient may vary but the structure of the underlying governing equation remains constant. We demonstrate our method on various analytic expressions, ODEs, and PDEs with varying coefficients and show that it extrapolates well outside of the training domain. The neural network-based architecture can also integrate with other deep learning architectures so that it can analyze high-dimensional data while being trained end-to-end. To this end we integrate our architecture with convolutional neural networks to analyze 1D images of varying spring systems.

Toward a more accurate 3D atlas of C. elegans neurons
Michael Skuhersky, Tailin Wu, Eviatar Yemini, Amin Nejatbakhsh, Edward Boyden & Max Tegmark
BMC Bioinformatics, Volume 23, Article 195 [ ]

Abstract Determining cell identity in volumetric images of tagged neuronal nuclei is an ongoing challenge in contemporary neuroscience. Frequently, cell identity is determined by aligning and matching tags to an “atlas” of labeled neuronal positions and other identifying characteristics. Previous analyses of such C. elegans datasets have been hampered by the limited accuracy of such atlases, especially for neurons present in the ventral nerve cord, and also by time-consuming manual elements of the alignment process.

Stable Object Reorientation using Contact Plane Registration
Richard Li, Carlos Esteves, Ameesh Makadia, Pulkit Agrawal
International Conference on Robotics and Automation 2022 [ ]

Abstract We present a system for accurately predicting stable orientations for diverse rigid objects. We propose to overcome the critical issue of modelling multimodality in the space of rotations by using a conditional generative model to accurately classify contact surfaces. Our system is capable of operating from noisy and partially-observed pointcloud observations captured by real world depth cameras. Our method substantially outperforms the current state-of-the-art systems on a simulated stacking task requiring highly accurate rotations, and demonstrates strong sim2real zero-shot transfer results across a variety of unseen objects on a real world reorientation task.

Towards Understanding Grokking: An Effective Theory of Representation Learning
Ziming Liu, Ouail Kitouni, Niklas Nolte, Eric J. Michaud, Max Tegmark, Mike Williams
[ arXiv:2205.10343 ]

Abstract We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a 'Goldilocks zone' (including comprehension and grokking) between memorization and confusion. Compared to the comprehension phase, the grokking phase stays closer to the memorization phase, leading to delayed generalization. The Goldilocks phase is reminiscent of 'intelligence from starvation' in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

Rapid Locomotion via Reinforcement Learning
Gabriel B. Margolis, Ge Yang, Kartik Paigwar, Tao Chen, Pulkit Agrawal
[ arXiv:2205.02824 ]

Abstract Agile maneuvers such as sprinting and high-speed turning in the wild are challenging for legged robots. We present an end-to-end learned controller that achieves record agility for the MIT Mini Cheetah, sustaining speeds up to 3.9m/s. This system runs and turns fast on natural terrains like grass, ice, and gravel and responds robustly to disturbances. Our controller is a neural network trained in simulation via reinforcement learning and transferred to the real world. The two key components are (i) an adaptive curriculum on velocity commands and (ii) an online system identification strategy for sim-to-real transfer leveraged from prior work. Videos of the robot’s behaviors are available at https://agility.csail.mit.edu/.

DiffCSE: Difference-based Contrastive Learning for Sentence Embeddings
Yung-Sung Chuang, Rumen Dangovski, Hongyin Luo, Yang Zhang, Shiyu Chang, Marin Soljačić, Shang-Wen Li, Wen-tau Yin, Yoon Kim, James Glass
[ arXiv:2204.10298 ]

Abstract We propose DiffCSE, an unsupervised contrastive learning framework for learning sentence embeddings. DiffCSE learns sentence embeddings that are sensitive to the difference between the original sentence and an edited sentence, where the edited sentence is obtained by stochastically masking out the original sentence and then sampling from a masked language model. We show that DiffSCE is an instance of equivariant contrastive learning (Dangovski et al., 2021), which generalizes contrastive learning and learns representations that are insensitive to certain types of augmentations and sensitive to other "harmful" types of augmentations. Our experiments show that DiffCSE achieves state-of-the-art results among unsupervised sentence representation learning methods, outperforming unsupervised SimCSE by 2.3 absolute points on semantic textual similarity tasks.

Pareto-optimal clustering with the primal deterministic information bottleneck
Andrew K. Tan, Max Tegmark, Isaac L. Chuang
Entropy, 2022, 24(6) [ arXiv:2204.02489 ]

Abstract At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the Deterministic Information Bottleneck (DIB) formulation of lossy compression, which can be interpreted as a clustering problem. To this end, we introduce the {\it primal} DIB problem, which we show results in a much richer frontier than its previously studied dual counterpart. We present an algorithm for mapping out the Pareto frontier of the primal DIB trade-off that is also applicable to most other two-objective clustering problems. We study general properties of the Pareto frontier, and give both analytic and numerical evidence for logarithmic sparsity of the frontier in general. We provide evidence that our algorithm has polynomial scaling despite the super-exponential search space; and additionally propose a modification to the algorithm that can be used where sampling noise is expected to be significant. Finally, we use our algorithm to map the DIB frontier of three different tasks: compressing the English alphabet, extracting informative color classes from natural images, and compressing a group theory inspired dataset, revealing interesting features of frontier, and demonstrating how the structure of the frontier can be used for model selection with a focus on points previously hidden by the cloak of the convex hull.

AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations
Ziming Liu, Varun Madhavan, Max Tegmark
Physical Review E, 2022, Volume 106, Article 045307 [ arXiv:2203.12610 ]

Abstract We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schrödinger equation.

Unsupervised Semantic Segmentation by Distilling Feature Correspondences
Mark Hamilton, Zhoutong Zhang, Bharath Hariharan, Noah Snavely, William T. Freeman
[ arXiv:2203.08414 ]

Abstract Unsupervised semantic segmentation aims to discover and localize semantically meaningful categories within image corpora without any form of annotation. To solve this task, algorithms must produce features for every pixel that are both semantically meaningful and compact enough to form distinct clusters. Unlike previous works which achieve this with a single end-to-end framework, we propose to separate feature learning from cluster compactification. Empirically, we show that current unsupervised feature learning frameworks already generate dense features whose correlations are semantically consistent. This observation motivates us to design STEGO (Self-supervised Transformer with Energy-based Graph Optimization), a novel framework that distills unsupervised features into high-quality discrete semantic labels. At the core of STEGO is a novel contrastive loss function that encourages features to form compact clusters while preserving their relationships across the corpora. STEGO yields a significant improvement over the prior state of the art, on both the CocoStuff (+14 mIoU) and Cityscapes (+9 mIoU) semantic segmentation challenges.

Categorical Representation Learning and RG flow operators for algorithmic classifiers
Artan Sheshmani, Yizhuang You, Wenbo Fu, Ahmadreza Azizi
Machine Learning Science and Technology, Volume 4, Number 1, Article 015012 [ arXiv:2203.07975 ]

Abstract Following the earlier formalism of the categorical representation learning (arXiv:2103.14770) by the first two authors, we discuss the construction of the RG-flow based categorifier. Borrowing ideas from theory of renormalization group flows (RG) in quantum field theory, holographic duality, and hyperbolic geometry, and mixing them with neural ODE's, we construct a new algorithmic natural language processing (NLP) architecture, called the RG-flow categorifier or for short the RG categorifier, which is capable of data classification and generation in all layers. We apply our algorithmic platform to biomedical data sets and show its performance in the field of sequence-to-function mapping. In particular we apply the RG categorifier to particular genomic sequences of flu viruses and show how our technology is capable of extracting the information from given genomic sequences, find their hidden symmetries and dominant features, classify them and use the trained data to make stochastic prediction of new plausible generated sequences associated with new set of viruses which could avoid the human immune system. The content of the current article is part of the recent US patent application submitted by first two authors (U.S. Patent Application No.: 63/313.504).

Biological error correction codes generate fault-tolerant neural networks
Alexander Zlokapa, Andrew K. Tan, John M. Martyn, Max Tegmark, Isaac L. Chuang
Physical Review E, 2024, Volume 110, Issue 5 [ arXiv:2202.12887 ]

Abstract It has been an open question in deep learning if fault-tolerant computation is possible: can arbitrarily reliable computation be achieved using only unreliable neurons? In the mammalian cortex, analog error correction codes known as grid codes have been observed to protect states against neural spiking noise, but their role in information processing is unclear. Here, we use these biological codes to show that a universal fault-tolerant neural network can be achieved if the faultiness of each neuron lies below a sharp threshold, which we find coincides in order of magnitude with noise observed in biological neurons. The discovery of a sharp phase transition from faulty to fault-tolerant neural computation opens a path towards understanding noisy analog systems in artificial intelligence and neuroscience.

Cracking the Quantum Scaling Limit with Machine Learned Electron Densities
Joshua A. Rackers, Lucas Tecot, Mario Geiger, Tess E. Smidt
[ arXiv:2201.03726 ]

Abstract A long-standing goal of science is to accurately solve the Schrödinger equation for large molecular systems. The poor scaling of current quantum chemistry algorithms on classical computers imposes an effective limit of about a few dozen atoms for which we can calculate molecular electronic structure. We present a machine learning (ML) method to break through this scaling limit and make quantum chemistry calculations of very large systems possible. We show that Euclidean Neural Networks can be trained to predict the electron density with high fidelity from limited data. Learning the electron density allows us to train a machine learning model on small systems and make accurate predictions on large ones. We show that this ML electron density model can break through the quantum scaling limit and calculate the electron density of systems of thousands of atoms with quantum accuracy.

Invariance Through Latent Alignment
Takuma Yoneda, Ge Yang, Matthew R. Walter, Bradly Stadie
[ arXiv:2112.08526 ]

Abstract A robot's deployment environment often involves perceptual changes that differ from what it has experienced during training. Standard practices such as data augmentation attempt to bridge this gap by augmenting source images in an effort to extend the support of the training distribution to better cover what the agent might experience at test time. In many cases, however, it is impossible to know test-time distribution-shift a priori, making these schemes infeasible. In this paper, we introduce a general approach, called Invariance Through Latent Alignment (ILA), that improves the test-time performance of a visuomotor control policy in deployment environments with unknown perceptual variations. ILA performs unsupervised adaptation at deployment-time by matching the distribution of latent features on the target domain to the agent's prior experience, without relying on paired data. Although simple, we show that this idea leads to surprising improvements on a variety of challenging adaptation scenarios, including changes in lighting conditions, the content in the scene, and camera poses. We present results on calibrated control benchmarks in simulation -- the distractor control suite -- and a physical robot under a sim-to-real setup.

Neural Descriptor Fields: SE(3) Equivariant Object Representations for Manipulation
Anthony Simeonov, Yilun Du, Andrea Tagliasacchi, Joshua B. Tenenbaum, Alberto Rodriguez, Pulkit Agrawal, Vincent Sitzmann
International Conference on Robotics and Automation 2022 [ arXiv:2112.05124 | code ]

Abstract We present Neural Descriptor Fields (NDFs), an object representation that encodes both points and relative poses between an object and a target (such as a robot gripper or a rack used for hanging) via category-level descriptors. We employ this representation for object manipulation, where given a task demonstration, we want to repeat the same task on a new object instance from the same category. We propose to achieve this objective by searching (via optimization) for the pose whose descriptor matches that observed in the demonstration. NDFs are conveniently trained in a self-supervised fashion via a 3D auto-encoding task that does not rely on expert-labeled keypoints. Further, NDFs are SE(3)-equivariant, guaranteeing performance that generalizes across all possible 3D object translations and rotations. We demonstrate learning of manipulation tasks from few (5-10) demonstrations both in simulation and on a real robot. Our performance generalizes across both object instances and 6-DoF object poses, and significantly outperforms a recent baseline that relies on 2D descriptors.

Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields
Dor Verbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T. Barron, Pratul P. Srinivasan
2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition [ arXiv:2112.03907 ]

Abstract Neural Radiance Fields (NeRF) is a popular view synthesis technique that represents a scene as a continuous volumetric function, parameterized by multilayer perceptrons that provide the volume density and view-dependent emitted radiance at each location. While NeRF-based techniques excel at representing fine geometric structures with smoothly varying view-dependent appearance, they often fail to accurately capture and reproduce the appearance of glossy surfaces. We address this limitation by introducing Ref-NeRF, which replaces NeRF's parameterization of view-dependent outgoing radiance with a representation of reflected radiance and structures this function using a collection of spatially-varying scene properties. We show that together with a regularizer on normal vectors, our model significantly improves the realism and accuracy of specular reflections. Furthermore, we show that our model's internal representation of outgoing radiance is interpretable and useful for scene editing.

Equivariant Contrastive Learning
Rumen Dangovski, Li Jing, Charlotte Loh, Seungwook Han, Akash Srivastava, Brian Cheung, Pulkit Agrawal, Marin Soljačić
[ arXiv:2111.00899 ]

Abstract In state-of-the-art self-supervised learning (SSL) pre-training produces semantically good representations by encouraging them to be invariant under meaningful transformations prescribed from human knowledge. In fact, the property of invariance is a trivial instance of a broader class called equivariance, which can be intuitively understood as the property that representations transform according to the way the inputs transform. Here, we show that rather than using only invariance, pre-training that encourages non-trivial equivariance to some transformations, while maintaining invariance to other transformations, can be used to improve the semantic quality of representations. Specifically, we extend popular SSL methods to a more general framework which we name Equivariant Self-Supervised Learning (E-SSL). In E-SSL, a simple additional pre-training objective encourages equivariance by predicting the transformations applied to the input. We demonstrate E-SSL's effectiveness empirically on several popular computer vision benchmarks. Furthermore, we demonstrate usefulness of E-SSL for applications beyond computer vision; in particular, we show its utility on regression problems in photonics science. We will release our code.

Mixture Model Auto-Encoders: Deep Clustering through Dictionary Learning
Alexander Lin, Andrew H. Song, Demba Ba
ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022, pp. 3368-3372 [ arXiv:2110.04683 ]

Abstract State-of-the-art approaches for clustering high-dimensional data utilize deep auto-encoder architectures. Many of these networks require a large number of parameters and suffer from a lack of interpretability, due to the black-box nature of the auto-encoders. We introduce Mixture Model Auto-Encoders (MixMate), a novel architecture that clusters data by performing inference on a generative model. Derived from the perspective of sparse dictionary learning and mixture models, MixMate comprises several auto-encoders, each tasked with reconstructing data in a distinct cluster, while enforcing sparsity in the latent space. Through experiments on various image datasets, we show that MixMate achieves competitive performance compared to state-of-the-art deep clustering algorithms, while using orders of magnitude fewer parameters.

Observation of enhanced free-electron radiation from photonic flatband resonancesg
Yi Yang, Charles Roques-Carmes, Steven E. Kooi, Haoning Tang, Justin Beroz, Eric Mazur, Ido Kaminer, John D. Joannopoulos, Marin Soljačić
Nature, 2023 [ arXiv:2110.03550 ]

Abstract Flatbands emerge from a myriad of structures such as Landau levels, Lieb and Kagome lattices, linegraphs, and more recently moire superlattices. They enable unique properties including slow light in photonics, correlated phases in electronics, and supercollimation in both systems. Despite these intense parallel efforts, flatbands have never been shown to affect the core light-matter interaction between electrons and photons, which is limited by a dimensionality mismatch. Here, we reveal that a photonic flatband can overcome this mismatch between localized electrons and extended photons and thus remarkably boost their light-matter interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the radiation emission from free electrons by tuning their trajectory and velocity. In particular, we record a 100-fold radiation enhancement from the conventional diffraction-enabled Smith-Purcell radiation, and show the potential of our approach to achieve 106-fold enhancements and beyond. The enhancement also enables us to perform polarization shaping of free electron radiation from multiple flatbands and demonstrate an approach to measure photonic bands via angle-resolved electron-beam measurements. Our results suggest flatbands as ideal test beds for strong light-electron interaction in various systems, with particular relevance for efficient and compact free-electron light sources and accelerators.

Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning
Ziming Liu, Yunyue Chen, Yuanqi Du, Max Tegmark
[ arXiv:2109.13901 ]

Abstract Integrating physical inductive biases into machine learning can improve model generalizability. We generalize the successful paradigm of physics-informed learning (PIL) into a more general framework that also includes what we term physics-augmented learning (PAL). PIL and PAL complement each other by handling discriminative and generative properties, respectively. In numerical experiments, we show that PAL performs well on examples where PIL is inapplicable or inefficient.

Overcoming the Spectral Bias of Neural Value Approximation
Ge Yang, Anurag Ajay, Pulkit Agrawal
ICLR 2022 Conference Proceedings [ arXiv:2206.04672 ]

Abstract Value approximation using deep neural networks is at the heart of off-policy deep reinforcement learning, and is often the primary module that provides learning signals to the rest of the algorithm. While multi-layer perceptron networks are universal function approximators, recent works in neural kernel regression suggest the presence of a \textit{spectral bias}, where fitting high-frequency components of the value function requires exponentially more gradient update steps than the low-frequency ones. In this work, we re-examine off-policy reinforcement learning through the lens of kernel regression and propose to overcome such bias via a composite neural tangent kernel. With just a single line-change, our approach, the Fourier feature networks (FFN) produce state-of-the-art performance on challenging continuous control domains with only a fraction of the compute. Faster convergence and better off-policy stability also make it possible to remove the target network without suffering catastrophic divergences, which further reduces TD(0)'s estimation bias on a few tasks. Code and analysis available at https://geyang.github.io/ffn.

Machine-Learning media bias
Samantha D’Alonzo, Max Tegmark
PLOS ONE, 2022, Volume 17, Issue 8, Article e0271947 [ arXiv:2109.00024 ]

Abstract We present an automated method for measuring media bias. Inferring which newspaper published a given article, based only on the frequencies with which it uses different phrases, leads to a conditional probability distribution whose analysis lets us automatically map newspapers and phrases into a bias space. By analyzing roughly a million articles from roughly a hundred newspapers for bias in dozens of news topics, our method maps newspapers into a two-dimensional bias landscape that agrees well with previous bias classifications based on human judgement. One dimension can be interpreted as traditional left-right bias, the other as establishment bias. This means that although news bias is inherently political, its measurement need not be.

What You Can Learn by Staring at a Blank Wall
Prafull Sharma, Miika Aittala, Yoav Y. Schechner, Antonio Torralba, Gregory W. Wornell, William T. Freeman, Fredo Durand
[ arXiv:2108.13027 ]

Abstract We present a passive non-line-of-sight method that infers the number of people or activity of a person from the observation of a blank wall in an unknown room. Our technique analyzes complex imperceptible changes in indirect illumination in a video of the wall to reveal a signal that is correlated with motion in the hidden part of a scene. We use this signal to classify between zero, one, or two moving people, or the activity of a person in the hidden scene. We train two convolutional neural networks using data collected from 20 different scenes, and achieve an accuracy of ≈94% for both tasks in unseen test environments and real-time online settings. Unlike other passive non-line-of-sight methods, the technique does not rely on known occluders or controllable light sources, and generalizes to unknown rooms with no re-calibration. We analyze the generalization and robustness of our method with both real and synthetic data, and study the effect of the scene parameters on the signal quality.

Discovering Sparse Interpretable Dynamics from Partial Observations
Peter Y. Lu, Joan Ariño, Marin Soljačić
Communications Physics, 2022, Vol 5, Article 206 [ arXiv:2107.10879 ]

Abstract Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We propose a machine learning framework for discovering these governing equations using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. Our tests show that this method can successfully reconstruct the full system state and identify the underlying dynamics for a variety of ODE and PDE systems.

QuanTaichi: A Compiler for Quantized Simulations
Yuanming Hu, Jiafeng Liu, Xuanda Yang, Mingkuan Xu, Ye Kuang, Weiwei Xu, Qiang Dai, William Freeman, Fredo Durand
ACM Transactions on Graphics, Volume 4, Article 182 [ ]

Abstract High-resolution simulations can deliver great visual quality, but they are often limited by available memory, especially on GPUs. We present a compiler for physical simulation that can achieve both high performance and significantly reduced memory costs, by enabling flexible and aggressive quantization. Low-precision ("quantized") numerical data types are used and packed to represent simulation states, leading to reduced memory space and bandwidth consumption. Quantized simulation allows higher resolution simulation with less memory, which is especially attractive on GPUs. Implementing a quantized simulator that has high performance and packs the data tightly for aggressive storage reduction would be extremely labor-intensive and error-prone using a traditional programming language. To make the creation of quantized simulation practical, we have developed a new set of language abstractions and a compilation system. A suite of tailored domain-specific optimizations ensure quantized simulators often run as fast as the full-precision simulators, despite the overhead of encoding-decoding the packed quantized data types. Our programming language and compiler, based on Taichi, allow developers to effortlessly switch between different full-precision and quantized simulators, to explore the full design space of quantization schemes, and ultimately to achieve a good balance between space and precision. The creation of quantized simulation with our system has large benefits in terms of memory consumption and performance, on a variety of hardware, from mobile devices to workstations with high-end GPUs. We can simulate with levels of resolution that were previously only achievable on systems with much more memory, such as multiple GPUs. For example, on a single GPU, we can simulate a Game of Life with 20 billion cells (8x compression per pixel), an Eulerian fluid system with 421 million active voxels (1.6x compression per voxel), and a hybrid Eulerian-Lagrangian elastic object simulation with 235 million particles (1.7x compression per particle). At the same time, quantized simulations create physically plausible results. Our quantization techniques are complementary to existing acceleration approaches of physical simulation: they can be used in combination with these existing approaches, such as sparse data structures, for even higher scalability and performance.

Learning Task Informed Abstractions
Xiang Fu, Ge Yang, Pulkit Agrawal, Tommi Jaakkola
Proceedings of the 38th International Conference on Machine Learning, 2021, PMLR 139 [ arXiv:2106.15612 | code ]

Abstract Current model-based reinforcement learning methods struggle when operating from complex visual scenes due to their inability to prioritize task-relevant features. To mitigate this problem, we propose learning Task Informed Abstractions (TIA) that explicitly separates reward-correlated visual features from distractors. For learning TIA, we introduce the formalism of Task Informed MDP (TiMDP) that is realized by training two models that learn visual features via cooperative reconstruction, but one model is adversarially dissociated from the reward signal. Empirical evaluation shows that TIA leads to significant performance gains over state-of-the-art methods on many visual control tasks where natural and unconstrained visual distractions pose a formidable challenge.

The Principles of Deep Learning Theory
Daniel A. Roberts, Sho Yaida, Boris Hanin
Cambridge University Press (Book), 2022 [ arXiv:2106.10165 ]

Abstract This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Toward Automatic Interpretation of 3D Plots
Laura E. Brandt, William T. Freeman
[ arXiv:2106.07627 ]

Abstract This paper explores the challenge of teaching a machine how to reverse-engineer the grid-marked surfaces used to represent data in 3D surface plots of two-variable functions. These are common in scientific and economic publications; and humans can often interpret them with ease, quickly gleaning general shape and curvature information from the simple collection of curves. While machines have no such visual intuition, they do have the potential to accurately extract the more detailed quantitative data that guided the surface's construction. We approach this problem by synthesizing a new dataset of 3D grid-marked surfaces (SurfaceGrid) and training a deep neural net to estimate their shape. Our algorithm successfully recovers shape information from synthetic 3D surface plots that have had axes and shading information removed, been rendered with a variety of grid types, and viewed from a range of viewpoints.

Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering
Vincent Sitzmann, Semon Rezchikov, William T. Freeman, Joshua B. Tenenbaum, Fredo Durand
[ arXiv:2106.02634 ]

Abstract Inferring representations of 3D scenes from 2D observations is a fundamental problem of computer graphics, computer vision, and artificial intelligence. Emerging 3D-structured neural scene representations are a promising approach to 3D scene understanding. In this work, we propose a novel neural scene representation, Light Field Networks or LFNs, which represent both geometry and appearance of the underlying 3D scene in a 360-degree, four-dimensional light field parameterized via a neural implicit representation. Rendering a ray from an LFN requires only a *single* network evaluation, as opposed to hundreds of evaluations per ray for ray-marching or volumetric based renderers in 3D-structured neural scene representations. In the setting of simple scenes, we leverage meta-learning to learn a prior over LFNs that enables multi-view consistent light field reconstruction from as little as a single image observation. This results in dramatic reductions in time and memory complexity, and enables real-time rendering. The cost of storing a 360-degree light field via an LFN is two orders of magnitude lower than conventional methods such as the Lumigraph. Utilizing the analytical differentiability of neural implicit representations and a novel parameterization of light space, we further demonstrate the extraction of sparse depth maps from LFNs.

Covariance-Free Sparse Bayesian Learning
Alexander Lin, Andrew H. Song, Berkin Bilgic, Demba Ba
IEEE Transactions on Signal Processing, volume 70 [ arXiv:2105.10439 ]

Abstract Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. The most popular inference algorithms for SBL exhibit prohibitively large computational costs for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new method for accelerating SBL inference -- named covariance-free expectation maximization (CoFEM) -- that avoids explicit computation of the covariance matrix. CoFEM solves multiple linear systems to obtain unbiased estimates of the posterior statistics needed by SBL. This is accomplished by exploiting innovations from numerical linear algebra such as preconditioned conjugate gradient and a little-known diagonal estimation rule. For a large class of compressed sensing matrices, we provide theoretical justifications for why our method scales well in high-dimensional settings. Through simulations, we show that CoFEM can be up to thousands of times faster than existing baselines without sacrificing coding accuracy. Through applications to calcium imaging deconvolution and multi-contrast MRI reconstruction, we show that CoFEM enables SBL to tractably tackle high-dimensional sparse coding problems of practical interest.

Scalable and Flexible Deep Bayesian Optimization with Auxiliary Information for Scientific Problems
Samuel Kim, Peter Y. Lu, Charlotte Loh, Jamie Smith, Jasper Snoek, Marin Soljačić
Transactions on Machine Learning Research, September 2022 [ arXiv:2104.11667 ]

Abstract Bayesian optimization (BO) is a popular paradigm for global optimization of expensive black-box functions, but there are many domains where the function is not completely black-box. The data may have some known structure, e.g. symmetries, and the data generation process can yield useful intermediate or auxiliary information in addition to the value of the optimization objective. However, surrogate models traditionally employed in BO, such as Gaussian Processes (GPs), scale poorly with dataset size and struggle to incorporate known structure or auxiliary information. Instead, we propose performing BO on complex, structured problems by using Bayesian Neural Networks (BNNs), a class of scalable surrogate models that have the representation power and flexibility to handle structured data and exploit auxiliary information. We demonstrate BO on a number of realistic problems in physics and chemistry, including topology optimization of photonic crystal materials using convolutional neural networks, and chemical property optimization of molecules using graph neural networks. On these complex tasks, we show that BNNs often outperform GPs as surrogate models for BO in terms of both sampling efficiency and computational cost.

Why is AI hard and Physics simple?
Daniel A. Roberts
[ arXiv:2104.00008 ]

Abstract We discuss why AI is hard and why physics is simple. We discuss how physical intuition and the approach of theoretical physics can be brought to bear on the field of artificial intelligence and specifically machine learning. We suggest that the underlying project of machine learning and the underlying project of physics are strongly coupled through the principle of sparsity, and we call upon theoretical physicists to work on AI as physicists. As a first step in that direction, we discuss an upcoming book on the principles of deep learning theory that attempts to realize this approach.

Deep learning: a statistical viewpoint
Peter L. Bartlett, Andrea Montanari, and Alexander Rakhlin
[ arXiv:2103.09177 ]

Abstract The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

On the Minimal Error of Empirical Risk Minimization
Gil Kur, Alexander Rakhlin
[ arXiv:2102.12066 ]

Abstract RWe study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting to simplicity of the model generating the data. In the fixed design setting, we show that the error is governed by the global complexity of the entire class. In contrast, in random design, ERM may only adapt to simpler models if the local neighborhoods around the regression function are nearly as complex as the class itself, a somewhat counter-intuitive conclusion. We provide sharp lower bounds for performance of ERM for both Donsker and non-Donsker classes. We also discuss our results through the lens of recent studies on interpolation in overparameterized models.

Field of Junctions: Extracting Boundary Structure at Low SNR
Dor Verbin, Todd Zickler
IEEE/CVF International Conference on Computer Vision, 2021 [ arXiv:2011.13866 ]

Abstract We introduce a bottom-up model for simultaneously finding many boundary elements in an image, including contours, corners and junctions. The model explains boundary shape in each small patch using a 'generalized M-junction' comprising M angles and a freely-moving vertex. Images are analyzed using non-convex optimization to cooperatively find M+2 junction values at every location, with spatial consistency being enforced by a novel regularizer that reduces curvature while preserving corners and junctions. The resulting 'field of junctions' is simultaneously a contour detector, corner/junction detector, and boundary-aware smoothing of regional appearance. Notably, its unified analysis of contours, corners, junctions and uniform regions allows it to succeed at high noise levels, where other methods for segmentation and boundary detection fail.

AI Feynman: a Physics-Inspired Method for Symbolic Regression
Silviu-Marian Udrescu, Max Tegmark
Sciences Advances, 2020, 6:easy2631 [ arXiv:1905.11481 ]

Abstract A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult test set, we improve the state of the art success rate from 15% to 90%.

This project is supported by National Science Foundation under Cooperative Agreement PHY-2019786. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.