Ila Fiete

Andrew Kirjner, Jason Yim, Raman Samusevich et al.

The ability to engineer novel proteins with higher fitness for a desired property would be revolutionary for biotechnology and medicine. Modeling the combinatorially large space of sequences is infeasible; prior methods often constrain optimization to a small mutational radius, but this drastically limits the design space. Instead of heuristics, we propose smoothing the fitness landscape to facilitate protein optimization. First, we formulate protein fitness as a graph signal then use Tikunov regularization to smooth the fitness landscape. We find optimizing in this smoothed landscape leads to improved performance across multiple methods in the GFP and AAV benchmarks. Second, we achieve state-of-the-art results utilizing discrete energy-based models and MCMC in the smoothed landscape. Our method, called Gibbs sampling with Graph-based Smoothing (GGS), demonstrates a unique ability to achieve 2.5 fold fitness improvement (with in-silico evaluation) over its training set. GGS demonstrates potential to optimize proteins in the limited data regime. Code: https://github.com/kirjner/GGS

Jaedong Hwang, Zhang-Wei Hong, Eric Chen et al. · mit

Animals and robots navigate through environments by building and refining maps of space. These maps enable functions including navigation back to home, planning, search and foraging. Here, we use observations from neuroscience, specifically the observed fragmentation of grid cell map in compartmentalized spaces, to propose and apply the concept of Fragmentation-and-Recall (FARMap) in the mapping of large spaces. Agents solve the mapping problem by building local maps via a surprisal-based clustering of space, which they use to set subgoals for spatial exploration. Agents build and use a local map to predict their observations; high surprisal leads to a "fragmentation event" that truncates the local map. At these events, the recent local map is placed into long-term memory (LTM) and a different local map is initialized. If observations at a fracture point match observations in one of the stored local maps, that map is recalled (and thus reused) from LTM. The fragmentation points induce a natural online clustering of the larger space, forming a set of intrinsic potential subgoals that are stored in LTM as a topological graph. Agents choose their next subgoal from the set of near and far potential subgoals from within the current local map or LTM, respectively. Thus, local maps guide exploration locally, while LTM promotes global exploration. We demonstrate that FARMap replicates the fragmentation points observed in animal studies. We evaluate FARMap on complex procedurally-generated spatial environments and realistic simulations to demonstrate that this mapping strategy much more rapidly covers the environment (number of agent steps and wall clock time) and is more efficient in active memory usage, without loss of performance. https://jd730.github.io/projects/FARMap/

Rylan Schaeffer, Gabrielle Kaili-May Liu, Yilun Du et al. · mit

Learning from a continuous stream of non-stationary data in an unsupervised manner is arguably one of the most common and most challenging settings facing intelligent agents. Here, we attack learning under all three conditions (unsupervised, streaming, non-stationary) in the context of clustering, also known as mixture modeling. We introduce a novel clustering algorithm that endows mixture models with the ability to create new clusters online, as demanded by the data, in a probabilistic, time-varying, and principled manner. To achieve this, we first define a novel stochastic process called the Dynamical Chinese Restaurant Process (Dynamical CRP), which is a non-exchangeable distribution over partitions of a set; next, we show that the Dynamical CRP provides a non-stationary prior over cluster assignments and yields an efficient streaming variational inference algorithm. We conclude with experiments showing that the Dynamical CRP can be applied on diverse synthetic and real data with Gaussian and non-Gaussian likelihoods.

Rylan Schaeffer, Mikail Khona, Zachary Robertson et al.

Double descent is a surprising phenomenon in machine learning, in which as the number of model parameters grows relative to the number of data, test error drops as models grow ever larger into the highly overparameterized (data undersampled) regime. This drop in test error flies against classical learning theory on overfitting and has arguably underpinned the success of large models in machine learning. This non-monotonic behavior of test loss depends on the number of data, the dimensionality of the data and the number of model parameters. Here, we briefly describe double descent, then provide an explanation of why double descent occurs in an informal and approachable manner, requiring only familiarity with linear algebra and introductory probability. We provide visual intuition using polynomial regression, then mathematically analyze double descent with ordinary linear regression and identify three interpretable factors that, when simultaneously all present, together create double descent. We demonstrate that double descent occurs on real data when using ordinary linear regression, then demonstrate that double descent does not occur when any of the three factors are ablated. We use this understanding to shed light on recent observations in nonlinear models concerning superposition and double descent. Code is publicly available.

Mitchell Ostrow, Adam Eisen, Leo Kozachkov et al.

How can we tell whether two neural networks utilize the same internal processes for a particular computation? This question is pertinent for multiple subfields of neuroscience and machine learning, including neuroAI, mechanistic interpretability, and brain-machine interfaces. Standard approaches for comparing neural networks focus on the spatial geometry of latent states. Yet in recurrent networks, computations are implemented at the level of dynamics, and two networks performing the same computation with equivalent dynamics need not exhibit the same geometry. To bridge this gap, we introduce a novel similarity metric that compares two systems at the level of their dynamics, called Dynamical Similarity Analysis (DSA). Our method incorporates two components: Using recent advances in data-driven dynamical systems theory, we learn a high-dimensional linear system that accurately captures core features of the original nonlinear dynamics. Next, we compare different systems passed through this embedding using a novel extension of Procrustes Analysis that accounts for how vector fields change under orthogonal transformation. In four case studies, we demonstrate that our method disentangles conjugate and non-conjugate recurrent neural networks (RNNs), while geometric methods fall short. We additionally show that our method can distinguish learning rules in an unsupervised manner. Our method opens the door to comparative analyses of the essential temporal structure of computation in neural circuits.

Rylan Schaeffer, Mikail Khona, Tzuhsuan Ma et al.

To solve the spatial problems of mapping, localization and navigation, the mammalian lineage has developed striking spatial representations. One important spatial representation is the Nobel-prize winning grid cells: neurons that represent self-location, a local and aperiodic quantity, with seemingly bizarre non-local and spatially periodic activity patterns of a few discrete periods. Why has the mammalian lineage learnt this peculiar grid representation? Mathematical analysis suggests that this multi-periodic representation has excellent properties as an algebraic code with high capacity and intrinsic error-correction, but to date, there is no satisfactory synthesis of core principles that lead to multi-modular grid cells in deep recurrent neural networks. In this work, we begin by identifying key insights from four families of approaches to answering the grid cell question: coding theory, dynamical systems, function optimization and supervised deep learning. We then leverage our insights to propose a new approach that combines the strengths of all four approaches. Our approach is a self-supervised learning (SSL) framework - including data, data augmentations, loss functions and a network architecture - motivated from a normative perspective, without access to supervised position information or engineering of particular readout representations as needed in previous approaches. We show that multiple grid cell modules can emerge in networks trained on our SSL framework and that the networks and emergent representations generalize well outside their training distribution. This work contains insights for neuroscientists interested in the origins of grid cells as well as machine learning researchers interested in novel SSL frameworks.

Qiyao Liang, Ziming Liu, Mitchell Ostrow et al.

Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set, demonstrating the ability to \textit{compositionally generalize}. Nonetheless, the precise mechanism of compositionality and how it is acquired through training remains elusive. Inspired by cognitive neuroscientific approaches, we consider a highly reduced setting to examine whether and when diffusion models learn semantically meaningful and factorized representations of composable features. We performed extensive controlled experiments on conditional Denoising Diffusion Probabilistic Models (DDPMs) trained to generate various forms of 2D Gaussian bump images. We found that the models learn factorized but not fully continuous manifold representations for encoding continuous features of variation underlying the data. With such representations, models demonstrate superior feature compositionality but limited ability to interpolate over unseen values of a given feature. Our experimental results further demonstrate that diffusion models can attain compositionality with few compositional examples, suggesting a more efficient way to train DDPMs. Finally, we connect manifold formation in diffusion models to percolation theory in physics, offering insight into the sudden onset of factorized representation learning. Our thorough toy experiments thus contribute a deeper understanding of how diffusion models capture compositional structure in data.

Ziming Liu, Mikail Khona, Ila R. Fiete et al.

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 $L_1$ 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.

Akhilan Boopathy, Sunshine Jiang, William Yue et al.

Modular neural networks outperform nonmodular neural networks on tasks ranging from visual question answering to robotics. These performance improvements are thought to be due to modular networks' superior ability to model the compositional and combinatorial structure of real-world problems. However, a theoretical explanation of how modularity improves generalizability, and how to leverage task modularity while training networks remains elusive. Using recent theoretical progress in explaining neural network generalization, we investigate how the amount of training data required to generalize on a task varies with the intrinsic dimensionality of a task's input. We show theoretically that when applied to modularly structured tasks, while nonmodular networks require an exponential number of samples with task dimensionality, modular networks' sample complexity is independent of task dimensionality: modular networks can generalize in high dimensions. We then develop a novel learning rule for modular networks to exploit this advantage and empirically show the improved generalization of the rule, both in- and out-of-distribution, on high-dimensional, modular tasks.

Jaedong Hwang, Zhang-Wei Hong, Eric Chen et al.

Deep reinforcement learning methods exhibit impressive performance on a range of tasks but still struggle on hard exploration tasks in large environments with sparse rewards. To address this, intrinsic rewards can be generated using forward model prediction errors that decrease as the environment becomes known, and incentivize an agent to explore novel states. While prediction-based intrinsic rewards can help agents solve hard exploration tasks, they can suffer from catastrophic forgetting and actually increase at visited states. We first examine the conditions and causes of catastrophic forgetting in grid world environments. We then propose a new method FARCuriosity, inspired by how humans and animals learn. The method depends on fragmentation and recall: an agent fragments an environment based on surprisal, and uses different local curiosity modules (prediction-based intrinsic reward functions) for each fragment so that modules are not trained on the entire environment. At each fragmentation event, the agent stores the current module in long-term memory (LTM) and either initializes a new module or recalls a previously stored module based on its match with the current state. With fragmentation and recall, FARCuriosity achieves less forgetting and better overall performance in games with varied and heterogeneous environments in the Atari benchmark suite of tasks. Thus, this work highlights the problem of catastrophic forgetting in prediction-based curiosity methods and proposes a solution.

Akhilan Boopathy, Ila Fiete

As neural networks continue to grow in size but datasets might not, it is vital to understand how much performance improvement can be expected: is it more important to scale network size or data volume? Thus, neural network scaling laws, which characterize how test error varies with network size and data volume, have become increasingly important. However, existing scaling laws are often applicable only in limited regimes and often do not incorporate or predict well-known phenomena such as double descent. Here, we present a novel theoretical characterization of how three factors -- model size, training time, and data volume -- interact to determine the performance of deep neural networks. We first establish a theoretical and empirical equivalence between scaling the size of a neural network and increasing its training time proportionally. Scale-time equivalence challenges the current practice, wherein large models are trained for small durations, and suggests that smaller models trained over extended periods could match their efficacy. It also leads to a novel method for predicting the performance of large-scale networks from small-scale networks trained for extended epochs, and vice versa. We next combine scale-time equivalence with a linear model analysis of double descent to obtain a unified theoretical scaling law, which we confirm with experiments across vision benchmarks and network architectures. These laws explain several previously unexplained phenomena: reduced data requirements for generalization in larger models, heightened sensitivity to label noise in overparameterized models, and instances where increasing model scale does not necessarily enhance performance. Our findings hold significant implications for the practical deployment of neural networks, offering a more accessible and efficient path to training and fine-tuning large models.

Samuel J. Gershman, Ila Fiete, Kazuki Irie

Classical models of memory in psychology and neuroscience rely on similarity-based retrieval of stored patterns, where similarity is a function of retrieval cues and the stored patterns. While parsimonious, these models do not allow distinct representations for storage and retrieval, despite their distinct computational demands. Key-value memory systems, in contrast, distinguish representations used for storage (values) and those used for retrieval (keys). This allows key-value memory systems to optimize simultaneously for fidelity in storage and discriminability in retrieval. We review the computational foundations of key-value memory, its role in modern machine learning systems, related ideas from psychology and neuroscience, applications to a number of empirical puzzles, and possible biological implementations.

Rylan Schaeffer, Nika Zahedi, Mikail Khona et al. · mit

Associative memory and probabilistic modeling are two fundamental topics in artificial intelligence. The first studies recurrent neural networks designed to denoise, complete and retrieve data, whereas the second studies learning and sampling from probability distributions. Based on the observation that associative memory's energy functions can be seen as probabilistic modeling's negative log likelihoods, we build a bridge between the two that enables useful flow of ideas in both directions. We showcase four examples: First, we propose new energy-based models that flexibly adapt their energy functions to new in-context datasets, an approach we term \textit{in-context learning of energy functions}. Second, we propose two new associative memory models: one that dynamically creates new memories as necessitated by the training data using Bayesian nonparametrics, and another that explicitly computes proportional memory assignments using the evidence lower bound. Third, using tools from associative memory, we analytically and numerically characterize the memory capacity of Gaussian kernel density estimators, a widespread tool in probababilistic modeling. Fourth, we study a widespread implementation choice in transformers -- normalization followed by self attention -- to show it performs clustering on the hypersphere. Altogether, this work urges further exchange of useful ideas between these two continents of artificial intelligence.

Jaedong Hwang, Kumar Tanmay, Seok-Jin Lee et al.

Large Language Models (LLMs) have achieved strong performance in domains like mathematics, factual question answering, and code generation, yet their ability to reason on these tasks in different languages remains underdeveloped. Especially for low-resource languages such as Swahili or Thai, LLMs can often misinterpret prompts or default to reasoning in English. This implicit bias toward high-resource languages undermines factual accuracy, interpretability, and trust. We propose M2A, a novel method that combines multi-scale multilingual alignment with language-consistency rewards on machine-translated questions, training models to reason directly and accurately in the target language. Furthermore, existing multilingual benchmarks only evaluate on final answers, overlooking whether reasoning occurs in the intended language. To close this gap, we introduce GeoFact-X, a geography-based multilingual factual reasoning benchmark together with reasoning traces in five languages: English, Hindi, Japanese, Swahili, and Thai. Our results show that M2A significantly enhances multilingual reasoning fidelity in both mathematical and factual reasoning tasks, highlighting that reasoning-aware multilingual reinforcement learning is crucial for robust cross-lingual generalization. https://jd730.github.io/projects/M2A_GeoFact-X

Akhilan Boopathy, Aneesh Muppidi, Peggy Yang et al.

State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in high-dimensional state spaces, these filters face challenges such as 'particle deprivation' which hinders accurate representation of the true posterior distribution. This paper introduces a novel resampling-free particle filter designed to mitigate particle deprivation by forgoing the traditional resampling step. This ensures a broader and more diverse particle set, especially vital in high-dimensional scenarios. Theoretically, our proposed filter is shown to offer a near-accurate representation of the desired posterior distribution in high-dimensional contexts. Empirically, the effectiveness of our approach is underscored through a high-dimensional synthetic state estimation task and a 6D pose estimation derived from videos. We posit that as robotic systems evolve with greater degrees of freedom, particle filters tailored for high-dimensional state spaces will be indispensable.

Qiyao Liang, Daoyuan Qian, Liu Ziyin et al.

Composition-the ability to generate myriad variations from finite means-is believed to underlie powerful generalization. However, compositional generalization remains a key challenge for deep learning. A widely held assumption is that learning disentangled (factorized) representations naturally supports this kind of extrapolation. Yet, empirical results are mixed, with many generative models failing to recognize and compose factors to generate out-of-distribution (OOD) samples. In this work, we investigate a controlled 2D Gaussian "bump" generation task with fully disentangled (x,y) inputs, demonstrating that standard generative architectures still fail in OOD regions when training with partial data, by re-entangling latent representations in subsequent layers. By examining the model's learned kernels and manifold geometry, we show that this failure reflects a "memorization" strategy for generation via data superposition rather than via composition of the true factorized features. We show that when models are forced-through architectural modifications with regularization or curated training data-to render the disentangled latents into the full-dimensional representational (pixel) space, they can be highly data-efficient and effective at composing in OOD regions. These findings underscore that disentangled latents in an abstract representation are insufficient and show that if models can represent disentangled factors directly in the output representational space, it can achieve robust compositional generalization.

Qiyao Liang, Ziming Liu, Ila Fiete

Diffusion models are capable of impressive feats of image generation with uncommon juxtapositions such as astronauts riding horses on the moon with properly placed shadows. These outputs indicate the ability to perform compositional generalization, but how do the models do so? We perform controlled experiments on conditional DDPMs learning to generate 2D spherical Gaussian bumps centered at specified $x$- and $y$-positions. Our results show that the emergence of semantically meaningful latent representations is key to achieving high performance. En route to successful performance over learning, the model traverses three distinct phases of latent representations: (phase A) no latent structure, (phase B) a 2D manifold of disordered states, and (phase C) a 2D ordered manifold. Corresponding to each of these phases, we identify qualitatively different generation behaviors: 1) multiple bumps are generated, 2) one bump is generated but at inaccurate $x$ and $y$ locations, 3) a bump is generated at the correct $x$ and y location. Furthermore, we show that even under imbalanced datasets where features ($x$- versus $y$-positions) are represented with skewed frequencies, the learning process for $x$ and $y$ is coupled rather than factorized, demonstrating that simple vanilla-flavored diffusion models cannot learn efficient representations in which localization in $x$ and $y$ are factorized into separate 1D tasks. These findings suggest the need for future work to find inductive biases that will push generative models to discover and exploit factorizable independent structures in their inputs, which will be required to vault these models into more data-efficient regimes.

Daoyuan Qian, Qiyao Liang, Ila Fiete

Circuits in the brain commonly exhibit modular architectures that factorise complex tasks, resulting in the ability to compositionally generalise and reduce catastrophic forgetting. In contrast, artificial neural networks (ANNs) appear to mix all processing, because modular solutions are difficult to find as they are vanishing subspaces in the space of possible solutions. Here, we draw inspiration from fault-tolerant computation and the Poisson-like firing of real neurons to show that activity-dependent neural noise, combined with nonlinear neural responses, drives the emergence of solutions that reflect an accurate understanding of modular tasks, corresponding to acquisition of a correct world model. We find that noise-driven modularisation can be recapitulated by a deterministic regulariser that multiplicatively combines weights and activations, revealing rich phenomenology not captured in linear networks or by standard regularisation methods. Though the emergence of modular structure requires sufficiently many training samples (exponential in the number of modular task dimensions), we show that pre-modularised ANNs exhibit superior noise-robustness and the ability to generalise and extrapolate well beyond training data, compared to ANNs without such inductive biases. Together, our work demonstrates a regulariser and architectures that could encourage modularity emergence to yield functional benefits.

Arman Behrad, Mitchell Ostrow, Mohammad Taha Fakharian et al.

To understand how neural systems process information, it is often essential to compare one circuit with another, one brain with another, or data with a model. Traditional similarity measures ignore the dynamical processes underlying neural representations. Dynamical similarity methods offer a framework to compare the temporal structure of dynamical systems by embedding their (possibly) nonlinear dynamics into a globally linear space and there computing conjugacy metrics. However, identifying the best embedding and computing these metrics can be computationally slow. Here we introduce fast Dynamical Similarity Analysis (fastDSA), which is computationally far more efficient than previous methods while maintaining their accuracy and robustness. FastDSA introduces two key components that boost efficiency: (1) automatic selection of the effective model order of the Hankel (delay) embedding from the data via a data-driven singular-value threshold that identifies the informative subspace and discards noise to lower computational cost without sacrificing signal, and (2) a novel optimization procedure and objective, which replaces the slow exact orthogonality constraint in finding a minimal distance between dynamics matrices with a lightweight process to keep the search close to the space of orthogonal transformations. We demonstrate that fastDSA is at least an order of magnitude faster than the previous methods. Furthermore, we demonstrate that fastDSA has the properties of its ancestor, including its invariances and sensitivities to system dynamics. FastDSA, therefore, provides a computationally efficient and accurate method for dynamical similarity analysis.

Akhilan Boopathy, Aneesh Muppidi, Peggy Yang et al.

Sequential learning in deep models often suffers from challenges such as catastrophic forgetting and loss of plasticity, largely due to the permutation dependence of gradient-based algorithms, where the order of training data impacts the learning outcome. In this work, we introduce a novel permutation-invariant learning framework based on high-dimensional particle filters. We theoretically demonstrate that particle filters are invariant to the sequential ordering of training minibatches or tasks, offering a principled solution to mitigate catastrophic forgetting and loss-of-plasticity. We develop an efficient particle filter for optimizing high-dimensional models, combining the strengths of Bayesian methods with gradient-based optimization. Through extensive experiments on continual supervised and reinforcement learning benchmarks, including SplitMNIST, SplitCIFAR100, and ProcGen, we empirically show that our method consistently improves performance, while reducing variance compared to standard baselines.

Jaedong Hwang, Brian Cheung, Zhang-Wei Hong et al.

Large-scale pretrained models are widely leveraged as foundations for learning new specialized tasks via fine-tuning, with the goal of maintaining the general performance of the model while allowing it to gain new skills. A valuable goal for all such models is robustness: the ability to perform well on out-of-distribution (OOD) tasks. We assess whether fine-tuning preserves the overall robustness of the pretrained model, and observed that models pretrained on large datasets exhibited strong catastrophic forgetting and loss of OOD generalization. To systematically assess robustness preservation in fine-tuned models, we propose the Robustness Inheritance Benchmark (ImageNet-RIB). The benchmark, which can be applied to any pretrained model, consists of a set of related but distinct OOD (downstream) tasks and involves fine-tuning on one of the OOD tasks in the set then testing on the rest. We find that though continual learning methods help, fine-tuning reduces robustness across pretrained models. Surprisingly, models pretrained on the largest and most diverse datasets (e.g., LAION-2B) exhibit both larger robustness losses and lower absolute robustness after fine-tuning on small datasets, relative to models pretrained on smaller datasets. These findings suggest that starting with the strongest foundation model is not necessarily the best approach for performance on specialist tasks. https://jd730.github.io/projects/ImageNet-RIB

Akhilan Boopathy, William Yue, Jaedong Hwang et al.

Much research in machine learning involves finding appropriate inductive biases (e.g. convolutional neural networks, momentum-based optimizers, transformers) to promote generalization on tasks. However, quantification of the amount of inductive bias associated with these architectures and hyperparameters has been limited. We propose a novel method for efficiently computing the inductive bias required for generalization on a task with a fixed training data budget; formally, this corresponds to the amount of information required to specify well-generalizing models within a specific hypothesis space of models. Our approach involves modeling the loss distribution of random hypotheses drawn from a hypothesis space to estimate the required inductive bias for a task relative to these hypotheses. Unlike prior work, our method provides a direct estimate of inductive bias without using bounds and is applicable to diverse hypothesis spaces. Moreover, we derive approximation error bounds for our estimation approach in terms of the number of sampled hypotheses. Consistent with prior results, our empirical results demonstrate that higher dimensional tasks require greater inductive bias. We show that relative to other expressive model classes, neural networks as a model class encode large amounts of inductive bias. Furthermore, our measure quantifies the relative difference in inductive bias between different neural network architectures. Our proposed inductive bias metric provides an information-theoretic interpretation of the benefits of specific model architectures for certain tasks and provides a quantitative guide to developing tasks requiring greater inductive bias, thereby encouraging the development of more powerful inductive biases.

Sunny Duan, Mikail Khona, Abhiram Iyer et al.

Frontier AI systems are making transformative impacts across society, but such benefits are not without costs: models trained on web-scale datasets containing personal and private data raise profound concerns about data privacy and security. Language models are trained on extensive corpora including potentially sensitive or proprietary information, and the risk of data leakage - where the model response reveals pieces of such information - remains inadequately understood. Prior work has investigated what factors drive memorization and have identified that sequence complexity and the number of repetitions drive memorization. Here, we focus on the evolution of memorization over training. We begin by reproducing findings that the probability of memorizing a sequence scales logarithmically with the number of times it is present in the data. We next show that sequences which are apparently not memorized after the first encounter can be "uncovered" throughout the course of training even without subsequent encounters, a phenomenon we term "latent memorization". The presence of latent memorization presents a challenge for data privacy as memorized sequences may be hidden at the final checkpoint of the model but remain easily recoverable. To this end, we develop a diagnostic test relying on the cross entropy loss to uncover latent memorized sequences with high accuracy.

Mitchell Ostrow, Adam Eisen, Ila Fiete

To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that unobserved variables can be recovered from the history of only a handful of observed variables. To test whether language models are effectively constructing delay embeddings, we measure the capacities of sequence models to reconstruct unobserved dynamics. We trained 1-layer transformer decoders and state-space sequence models on next-step prediction from noisy, partially-observed time series data. We found that each sequence layer can learn a viable embedding of the underlying system. However, state-space models have a stronger inductive bias than transformers-in particular, they more effectively reconstruct unobserved information at initialization, leading to more parameter-efficient models and lower error on dynamics tasks. Our work thus forges a novel connection between dynamical systems and deep learning sequence models via delay embedding theory.

Akhilan Boopathy, Kevin Liu, Jaedong Hwang et al.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

Sugandha Sharma, Sarthak Chandra, Ila R. Fiete

Content-addressable memory (CAM) networks, so-called because stored items can be recalled by partial or corrupted versions of the items, exhibit near-perfect recall of a small number of information-dense patterns below capacity and a 'memory cliff' beyond, such that inserting a single additional pattern results in catastrophic loss of all stored patterns. We propose a novel CAM architecture, Memory Scaffold with Heteroassociation (MESH), that factorizes the problems of internal attractor dynamics and association with external content to generate a CAM continuum without a memory cliff: Small numbers of patterns are stored with complete information recovery matching standard CAMs, while inserting more patterns still results in partial recall of every pattern, with a graceful trade-off between pattern number and pattern richness. Motivated by the architecture of the Entorhinal-Hippocampal memory circuit in the brain, MESH is a tripartite architecture with pairwise interactions that uses a predetermined set of internally stabilized states together with heteroassociation between the internal states and arbitrary external patterns. We show analytically and experimentally that for any number of stored patterns, MESH nearly saturates the total information bound (given by the number of synapses) for CAM networks, outperforming all existing CAM models.

Sugandha Sharma, Aidan Curtis, Marta Kryven et al.

Humans are expert explorers. Understanding the computational cognitive mechanisms that support this efficiency can advance the study of the human mind and enable more efficient exploration algorithms. We hypothesize that humans explore new environments efficiently by inferring the structure of unobserved spaces using spatial information collected from previously explored spaces. This cognitive process can be modeled computationally using program induction in a Hierarchical Bayesian framework that explicitly reasons about uncertainty with strong spatial priors. Using a new behavioral Map Induction Task, we demonstrate that this computational framework explains human exploration behavior better than non-inductive models and outperforms state-of-the-art planning algorithms when applied to a realistic spatial navigation domain.

Akhilan Boopathy, Ila Fiete

Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider NTK regime wide neural networks as a possible model of biological neural networks. Leveraging NTK theory, we show theoretically that gradient descent drives layerwise weight updates that are aligned with their input activity correlations weighted by error, and demonstrate empirically that the result also holds in finite-width wide networks. The alignment result allows us to formulate a family of biologically-motivated, backpropagation-free learning rules that are theoretically equivalent to backpropagation in infinite-width networks. We test these learning rules on benchmark problems in feedforward and recurrent neural networks and demonstrate, in wide networks, comparable performance to backpropagation. The proposed rules are particularly effective in low data regimes, which are common in biological learning settings.

Rishidev Chaudhuri, Ila Fiete

The brain must robustly store a large number of memories, corresponding to the many events encountered over a lifetime. However, the number of memory states in existing neural network models either grows weakly with network size or recall fails catastrophically with vanishingly little noise. We construct an associative content-addressable memory with exponentially many stable states and robust error-correction. The network possesses expander graph connectivity on a restricted Boltzmann machine architecture. The expansion property allows simple neural network dynamics to perform at par with modern error-correcting codes. Appropriate networks can be constructed with sparse random connections, glomerular nodes, and associative learning using low dynamic-range weights. Thus, sparse quasi-random structures---characteristic of important error-correcting codes---may provide for high-performance computation in artificial neural networks and the brain.