Hidenori Tanaka

Liu Ziyin, Ekdeep Singh Lubana, Masahito Ueda et al. · mit

Prevention of complete and dimensional collapse of representations has recently become a design principle for self-supervised learning (SSL). However, questions remain in our theoretical understanding: When do those collapses occur? What are the mechanisms and causes? We answer these questions by deriving and thoroughly analyzing an analytically tractable theory of SSL loss landscapes. In this theory, we identify the causes of the dimensional collapse and study the effect of normalization and bias. Finally, we leverage the interpretability afforded by the analytical theory to understand how dimensional collapse can be beneficial and what affects the robustness of SSL against data imbalance.

Samyak Jain, Robert Kirk, Ekdeep Singh Lubana et al.

Fine-tuning large pre-trained models has become the de facto strategy for developing both task-specific and general-purpose machine learning systems, including developing models that are safe to deploy. Despite its clear importance, there has been minimal work that explains how fine-tuning alters the underlying capabilities learned by a model during pretraining: does fine-tuning yield entirely novel capabilities or does it just modulate existing ones? We address this question empirically in synthetic, controlled settings where we can use mechanistic interpretability tools (e.g., network pruning and probing) to understand how the model's underlying capabilities are changing. We perform an extensive analysis of the effects of fine-tuning in these settings, and show that: (i) fine-tuning rarely alters the underlying model capabilities; (ii) a minimal transformation, which we call a 'wrapper', is typically learned on top of the underlying model capabilities, creating the illusion that they have been modified; and (iii) further fine-tuning on a task where such hidden capabilities are relevant leads to sample-efficient 'revival' of the capability, i.e., the model begins reusing these capability after only a few gradient steps. This indicates that practitioners can unintentionally remove a model's safety wrapper merely by fine-tuning it on a, e.g., superficially unrelated, downstream task. We additionally perform analysis on language models trained on the TinyStories dataset to support our claims in a more realistic setup.

Ekdeep Singh Lubana, Eric J. Bigelow, Robert P. Dick et al.

We study neural network loss landscapes through the lens of mode connectivity, the observation that minimizers of neural networks retrieved via training on a dataset are connected via simple paths of low loss. Specifically, we ask the following question: are minimizers that rely on different mechanisms for making their predictions connected via simple paths of low loss? We provide a definition of mechanistic similarity as shared invariances to input transformations and demonstrate that lack of linear connectivity between two models implies they use dissimilar mechanisms for making their predictions. Relevant to practice, this result helps us demonstrate that naive fine-tuning on a downstream dataset can fail to alter a model's mechanisms, e.g., fine-tuning can fail to eliminate a model's reliance on spurious attributes. Our analysis also motivates a method for targeted alteration of a model's mechanisms, named connectivity-based fine-tuning (CBFT), which we analyze using several synthetic datasets for the task of reducing a model's reliance on spurious attributes.

Maya Okawa, Ekdeep Singh Lubana, Robert P. Dick et al.

Modern generative models exhibit unprecedented capabilities to generate extremely realistic data. However, given the inherent compositionality of the real world, reliable use of these models in practical applications requires that they exhibit the capability to compose a novel set of concepts to generate outputs not seen in the training data set. Prior work demonstrates that recent diffusion models do exhibit intriguing compositional generalization abilities, but also fail unpredictably. Motivated by this, we perform a controlled study for understanding compositional generalization in conditional diffusion models in a synthetic setting, varying different attributes of the training data and measuring the model's ability to generate samples out-of-distribution. Our results show: (i) the order in which the ability to generate samples from a concept and compose them emerges is governed by the structure of the underlying data-generating process; (ii) performance on compositional tasks exhibits a sudden "emergence" due to multiplicative reliance on the performance of constituent tasks, partially explaining emergent phenomena seen in generative models; and (iii) composing concepts with lower frequency in the training data to generate out-of-distribution samples requires considerably more optimization steps compared to generating in-distribution samples. Overall, our study lays a foundation for understanding capabilities and compositionality in generative models from a data-centric perspective.

Ekdeep Singh Lubana, Kyogo Kawaguchi, Robert P. Dick et al.

Increase in data, size, or compute can lead to sudden learning of specific capabilities by a neural network -- a phenomenon often called "emergence''. Beyond scientific understanding, establishing the causal factors underlying such emergent capabilities is crucial to enable risk regulation frameworks for AI. In this work, we seek inspiration from study of emergent properties in other fields and propose a phenomenological definition for the concept in the context of neural networks. Our definition implicates the acquisition of general structures underlying the data-generating process as a cause of sudden performance growth for specific, narrower tasks. We empirically investigate this definition by proposing an experimental system grounded in a context-sensitive formal language and find that Transformers trained to perform tasks on top of strings from this language indeed exhibit emergent capabilities. Specifically, we show that once the language's underlying grammar and context-sensitivity inducing structures are learned by the model, performance on narrower tasks suddenly begins to improve. We then analogize our network's learning dynamics with the process of percolation on a bipartite graph, establishing a formal phase transition model that predicts the shift in the point of emergence observed in our experiments when changing the data structure. Overall, our experimental and theoretical frameworks yield a step towards better defining, characterizing, and predicting emergence in neural networks.

Eric J. Bigelow, Ekdeep Singh Lubana, Robert P. Dick et al.

Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

Rahul Ramesh, Ekdeep Singh Lubana, Mikail Khona et al.

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities, potentially yielding a combinatorial explosion of what operations it can perform on an input. Motivated by the above, we train autoregressive Transformer models on a synthetic data-generating process that involves compositions of a set of well-defined monolithic capabilities. Through a series of extensive and systematic experiments on this data-generating process, we show that: (1) autoregressive Transformers can learn compositional structures from small amounts of training data and generalize to exponentially or even combinatorially many functions; (2) generating intermediate outputs when composing functions is more effective for generalizing to new, unseen compositions than not generating any intermediate outputs (3) biases in the order of the compositions in the training data result in Transformers that fail to compose some combinations of functions; and (4) the attention layers select which capability to apply while the feed-forward layers execute the selected capability.

Eric Bigelow, Daniel Wurgaft, YingQiao Wang et al.

Large language models (LLMs) can be controlled at inference time through prompts (in-context learning) and internal activations (activation steering). Different accounts have been proposed to explain these methods, yet their common goal of controlling model behavior raises the question of whether these seemingly disparate methodologies can be seen as specific instances of a broader framework. Motivated by this, we develop a unifying, predictive account of LLM control from a Bayesian perspective. Specifically, we posit that both context- and activation-based interventions impact model behavior by altering its belief in latent concepts: steering operates by changing concept priors, while in-context learning leads to an accumulation of evidence. This results in a closed-form Bayesian model that is highly predictive of LLM behavior across context- and activation-based interventions in a set of domains inspired by prior work on many-shot in-context learning. This model helps us explain prior empirical phenomena - e.g., sigmoidal learning curves as in-context evidence accumulates - while predicting novel ones - e.g., additivity of both interventions in log-belief space, which results in distinct phases such that sudden and dramatic behavioral shifts can be induced by slightly changing intervention controls. Taken together, this work offers a unified account of prompt-based and activation-based control of LLM behavior, and a methodology for empirically predicting the effects of these interventions.

Kento Nishi, Raphael Tang, Karun Kumar et al.

Generative sequence models are often trained to plan motion in physical domains, from robotics to mechanical simulations. When constructing a dataset to train such a model, engineers may curate demonstrations to specify how trajectories should be distributed over a physical quantity like travel distance or mechanical energy. For example, a roboticist building a maze navigation agent might choose demonstrations whose travel distances cover a fixed range uniformly, hoping to constrain the agent's expected power usage. We find that standard deep learning can violate this intent: each generated trajectory can seem plausible on its own, but the aggregate distribution over the physical quantity is wrong. We call this failure physical misgeneralization, and develop an account of its mechanism. Using controlled synthetic tasks, we show that physical misgeneralization arises when local errors typical of the model class propagate through the physical measurement to shift the recovered distribution. We estimate these errors with a data deviation kernel, and we use it to predict which physical quantities gain or lose mass in both our synthetic and more applied maze navigation and double-pendulum motion tasks. Finally, our mechanistic interpretation helps identify which mitigation strategies are structurally promising, and we use it to propose a kernel-informed intervention.

Tian Qin, Core Francisco Park, Mujin Kwun et al.

Mathematical reasoning tasks have become prominent benchmarks for assessing the reasoning capabilities of LLMs, especially with reinforcement learning (RL) methods such as GRPO showing significant performance gains. However, accuracy metrics alone do not support fine-grained assessment of capabilities and fail to reveal which problem-solving skills have been internalized. To better understand these capabilities, we propose to decompose problem solving into fundamental capabilities: Plan (mapping questions to sequences of steps), Execute (correctly performing solution steps), and Verify (identifying the correctness of a solution). Empirically, we find that GRPO mainly enhances the execution skill-improving execution robustness on problems the model already knows how to solve-a phenomenon we call temperature distillation. More importantly, we show that RL-trained models struggle with fundamentally new problems, hitting a 'coverage wall' due to insufficient planning skills. To explore RL's impact more deeply, we construct a minimal, synthetic solution-tree navigation task as an analogy for mathematical problem-solving. This controlled setup replicates our empirical findings, confirming RL primarily boosts execution robustness. Importantly, in this setting, we identify conditions under which RL can potentially overcome the coverage wall through improved exploration and generalization to new solution paths. Our findings provide insights into the role of RL in enhancing LLM reasoning, expose key limitations, and suggest a path toward overcoming these barriers. Code is available at https://github.com/cfpark00/RL-Wall.

Core Francisco Park, Ekdeep Singh Lubana, Itamar Pres et al.

In-Context Learning (ICL) has significantly expanded the general-purpose nature of large language models, allowing them to adapt to novel tasks using merely the inputted context. This has motivated a series of papers that analyze tractable synthetic domains and postulate precise mechanisms that may underlie ICL. However, the use of relatively distinct setups that often lack a sequence modeling nature to them makes it unclear how general the reported insights from such studies are. Motivated by this, we propose a synthetic sequence modeling task that involves learning to simulate a finite mixture of Markov chains. As we show, models trained on this task reproduce most well-known results on ICL, hence offering a unified setting for studying the concept. Building on this setup, we demonstrate we can explain a model's behavior by decomposing it into four broad algorithms that combine a fuzzy retrieval vs. inference approach with either unigram or bigram statistics of the context. These algorithms engage in a competition dynamics to dominate model behavior, with the precise experimental conditions dictating which algorithm ends up superseding others: e.g., we find merely varying context size or amount of training yields (at times sharp) transitions between which algorithm dictates the model behavior, revealing a mechanism that explains the transient nature of ICL. In this sense, we argue ICL is best thought of as a mixture of different algorithms, each with its own peculiarities, instead of a monolithic capability. This also implies that making general claims about ICL that hold universally across all settings may be infeasible.

Hidenori Tanaka

Multi-agent systems powered by large language models (LLMs) are increasingly deployed in settings that shape consequential decisions, both directly and indirectly. Yet it remains unclear whether their outcomes reflect collective reasoning, systematic bias, or mere chance. Recent work has sharpened this question with naming games, showing that even when no individual agent favors any label a priori, populations rapidly break symmetry and reach consensus. Here, we reveal the mechanism by introducing a minimal model, Quantized Simplex Gossip (QSG), and trace the microscopic origin of this agreement to mutual in-context learning. In QSG, agents maintain internal belief states but learn from one another's sampled outputs, so one agent's arbitrary choice becomes the next agent's evidence and can compound toward agreement. By analogy with neutral evolution, we call this sampling-driven regime memetic drift. QSG predicts a crossover from a drift-dominated regime, where consensus is effectively a lottery, to a selection regime, where weak biases are amplified and shape the outcome. We derive scaling laws for drift-induced polarization as a function of population size, communication bandwidth, in-context adaptation rate, and agents' internal uncertainty, and we validate them in both QSG simulations and naming-game experiments with LLM populations. Together, these results provide a framework for studying the collective mechanisms of social representation formation in multi-agent systems.

Core Francisco Park, Andrew Lee, Ekdeep Singh Lubana et al.

Recent work has demonstrated that semantics specified by pretraining data influence how representations of different concepts are organized in a large language model (LLM). However, given the open-ended nature of LLMs, e.g., their ability to in-context learn, we can ask whether models alter these pretraining semantics to adopt alternative, context-specified ones. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, do models reorganize their representations in accordance with these novel semantics? To answer this question, we take inspiration from the theory of conceptual role semantics and define a toy "graph tracing" task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.) and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization from pretrained semantic representations to in-context representations aligned with the graph structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, providing evidence towards an implicit optimization process to infer context-specified semantics. Overall, our findings indicate scaling context-size can flexibly re-organize model representations, possibly unlocking novel capabilities.

Eric Bigelow, Ari Holtzman, Hidenori Tanaka et al.

Estimating uncertainty in Large Language Models (LLMs) is important for properly evaluating LLMs, and ensuring safety for users. However, prior approaches to uncertainty estimation focus on the final answer in generated text, ignoring intermediate steps that might dramatically impact the outcome. We hypothesize that there exist key forking tokens, such that re-sampling the system at those specific tokens, but not others, leads to very different outcomes. To test this empirically, we develop a novel approach to representing uncertainty dynamics across individual tokens of text generation, and applying statistical models to test our hypothesis. Our approach is highly flexible: it can be applied to any dataset and any LLM, without fine tuning or accessing model weights. We use our method to analyze LLM responses on 7 different tasks across 4 domains, spanning a wide range of typical use cases. We find many examples of forking tokens, including surprising ones such as punctuation marks, suggesting that LLMs are often just a single token away from saying something very different.

Mikail Khona, Maya Okawa, Jan Hula et al.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these protocols, the underlying mechanisms of stepwise inference have remained elusive. To address this, we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. Despite is simplicity, we find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy tradeoff in model generations as sampling temperature varies; (iii) a simplicity bias in the model's output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Kento Nishi, Rahul Ramesh, Maya Okawa et al.

Knowledge Editing (KE) algorithms alter models' weights to perform targeted updates to incorrect, outdated, or otherwise unwanted factual associations. However, recent work has shown that applying KE can adversely affect models' broader factual recall accuracy and diminish their reasoning abilities. Although these studies give insights into the potential harms of KE algorithms, e.g., performance evaluations on benchmarks, little is understood about why such destructive failures occur. Motivated by this, we define a novel synthetic task in which a Transformer is trained from scratch to internalize a "structured" knowledge graph. The structure enforces relationships between entities of the graph, such that editing a factual association has "trickling effects" on other entities (e.g., altering X's parent is Y to Z affects who X's siblings' parent is). Through evaluations of edited models on this task, we show that KE inadvertently affects representations of entities beyond the targeted one, distorting relevant structures that allow a model to infer unseen knowledge about an entity. We call this phenomenon representation shattering and demonstrate that it degrades models' factual recall and reasoning performance. We further corroborate our findings in naturalistic settings with pre-trained Llama and Mamba models as well. Overall, our work yields a precise mechanistic hypothesis to explain why KE has adverse effects on model abilities.

Daniel Wurgaft, Ekdeep Singh Lubana, Core Francisco Park et al.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

Fatih Dinc, Ege Cirakman, Yiqi Jiang et al.

\emph{Abrupt learning} is commonly observed in neural networks, where long plateaus in network performance are followed by rapid convergence to a desirable solution. Yet, despite its common occurrence, the complex interplay of task, network architecture, and learning rule has made it difficult to understand the underlying mechanisms. Here, we introduce a minimal dynamical system trained on a delayed-activation task and demonstrate analytically how even a one-dimensional system can exhibit abrupt learning through ghost points rather than bifurcations. Through our toy model, we show that the emergence of a ghost point destabilizes learning dynamics. We identify a critical learning rate that prevents learning through two distinct loss landscape features: a no-learning zone and an oscillatory minimum. Testing these predictions in recurrent neural networks (RNNs), we confirm that ghost points precede abrupt learning and accompany the destabilization of learning. We demonstrate two complementary remedies: lowering the model output confidence prevents the network from getting stuck in no-learning zones, while increasing trainable ranks beyond task requirements (\textit{i.e.}, adding sloppy parameters) provides more stable learning trajectories. Our model reveals a bifurcation-free mechanism for abrupt learning and illustrates the importance of both deliberate uncertainty and redundancy in stabilizing learning dynamics.

Core Francisco Park, Zechen Zhang, Hidenori Tanaka

Humans and intelligent animals can internalize new information and accurately internalize their implications to perform downstream tasks. While large language models (LLMs) can achieve this through in-context learning (ICL) when the information (news) is explicitly given as context, adequately integrating the information into model weights via fine-tuning remains challenging. In this paper, we introduce New News, a dataset composed of hypothetical yet plausible news spanning multiple domains (mathematics, coding, discoveries, leaderboards, events), accompanied by downstream evaluation questions whose correct answers critically depend on understanding and internalizing the news. First, we demonstrate a substantial gap between naive fine-tuning and in-context learning (FT-ICL gap) on our dataset. To address this gap, we explore a suite of self-play data generation protocols -- paraphrases, implications, and Self-QA -- designed to distill the knowledge processed by the model with context into the weights of the model, which we term System-2 Fine-tuning (Sys2-FT). We systematically evaluate ICL and Sys2-FT performance across data domains and model scales with the Qwen 2.5 family of models. Our results demonstrate that the Self-QA protocol of Sys2-FT significantly improves models' in-weight learning of the news while preserving general capabilities. Furthermore, we discover the contextual shadowing effect, where training with the news in context followed by its rephrases or QAs catastrophically degrades learning of the news. Finally, we show preliminary evidence of an emerging scaling law of Sys2-FT.

Keisuke Kawano, Takuro Kutsuna, Naoki Hayashi et al.

In many real-world settings--e.g., single-cell RNA sequencing, mobility sensing, and environmental monitoring--data are observed only as temporally aggregated snapshots collected over finite time windows, often with noisy or uncertain timestamps, and without access to continuous trajectories. We study the problem of estimating continuous-time dynamics from such snapshots. We present Continuous-Time Optimal Transport Flow (CT-OT Flow), a two-stage framework that (i) infers high-resolution time labels by aligning neighboring intervals via partial optimal transport (POT) and (ii) reconstructs a continuous-time data distribution through temporal kernel smoothing, from which we sample pairs of nearby times to train standard ODE/SDE models. Our formulation explicitly accounts for snapshot aggregation and time-label uncertainty and uses practical accelerations (screening and mini-batch POT), making it applicable to large datasets. Across synthetic benchmarks and two real datasets (scRNA-seq and typhoon tracks), CT-OT Flow reduces distributional and trajectory errors compared with OT-CFM, [SF]\(^{2}\)M, TrajectoryNet, MFM, and ENOT.

Rhys Gould, Hidenori Tanaka

Adaptive optimization algorithms, particularly Adam and its variant AdamW, are fundamental components of modern deep learning. However, their training dynamics lack comprehensive theoretical understanding, with limited insight into why common practices -- such as specific hyperparameter choices and normalization layers -- contribute to successful generalization. This work presents a continuous-time formulation of Adam and AdamW, facilitating a tractable analysis of training dynamics that can shed light on such practical questions. We theoretically derive a stable region for Adam's hyperparameters $(β, γ)$ that ensures bounded updates, empirically verifying these predictions by observing unstable exponential parameter growth outside of this stable region. Furthermore, we theoretically justify the success of normalization layers by uncovering an implicit meta-adaptive effect of scale-invariant architectural components. This insight leads to an explicit optimizer, $2$-Adam, which we generalize to $k$-Adam -- an optimizer that applies an adaptive normalization procedure $k$ times, encompassing Adam (corresponding to $k=1$) and Adam with a normalization layer (corresponding to $k=2$). Overall, our continuous-time formulation of Adam facilitates a principled analysis, offering deeper understanding of optimal hyperparameter choices and architectural decisions in modern deep learning.

Yongyi Yang, Hidenori Tanaka, Wei Hu

In-context learning (ICL) enables large language models (LLMs) to acquire new behaviors from the input sequence alone without any parameter updates. Recent studies have shown that ICL can surpass the original meaning learned in pretraining stage through internalizing the structure the data-generating process (DGP) of the prompt into the hidden representations. However, the mechanisms by which LLMs achieve this ability is left open. In this paper, we present the first rigorous explanation of such phenomena by introducing a unified framework of double convergence, where hidden representations converge both over context and across layers. This double convergence process leads to an implicit bias towards smooth (low-frequency) representations, which we prove analytically and verify empirically. Our theory explains several open empirical observations, including why learned representations exhibit globally structured but locally distorted geometry, and why their total energy decays without vanishing. Moreover, our theory predicts that ICL has an intrinsic robustness towards high-frequency noise, which we empirically confirm. These results provide new insights into the underlying mechanisms of ICL, and a theoretical foundation to study it that hopefully extends to more general data distributions and settings.

Bo Zhao, Maya Okawa, Eric J. Bigelow et al.

As large language models (LLMs) increasingly power conversational agents, understanding how they model users' emotional states is critical for ethical deployment. Inspired by emotion wheels -- a psychological framework that argues emotions organize hierarchically -- we analyze probabilistic dependencies between emotional states in model outputs. We find that LLMs naturally form hierarchical emotion trees that align with human psychological models, and larger models develop more complex hierarchies. We also uncover systematic biases in emotion recognition across socioeconomic personas, with compounding misclassifications for intersectional, underrepresented groups. Human studies reveal striking parallels, suggesting that LLMs internalize aspects of social perception. Beyond highlighting emergent emotional reasoning in LLMs, our results hint at the potential of using cognitively-grounded theories for developing better model evaluations.

Core Francisco Park, Maya Okawa, Andrew Lee et al.

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model's learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model's learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

Daniel Kunin, Javier Sagastuy-Brena, Lauren Gillespie et al.

In this work we explore the limiting dynamics of deep neural networks trained with stochastic gradient descent (SGD). As observed previously, long after performance has converged, networks continue to move through parameter space by a process of anomalous diffusion in which distance travelled grows as a power law in the number of gradient updates with a nontrivial exponent. We reveal an intricate interaction between the hyperparameters of optimization, the structure in the gradient noise, and the Hessian matrix at the end of training that explains this anomalous diffusion. To build this understanding, we first derive a continuous-time model for SGD with finite learning rates and batch sizes as an underdamped Langevin equation. We study this equation in the setting of linear regression, where we can derive exact, analytic expressions for the phase space dynamics of the parameters and their instantaneous velocities from initialization to stationarity. Using the Fokker-Planck equation, we show that the key ingredient driving these dynamics is not the original training loss, but rather the combination of a modified loss, which implicitly regularizes the velocity, and probability currents, which cause oscillations in phase space. We identify qualitative and quantitative predictions of this theory in the dynamics of a ResNet-18 model trained on ImageNet. Through the lens of statistical physics, we uncover a mechanistic origin for the anomalous limiting dynamics of deep neural networks trained with SGD.

Ekdeep Singh Lubana, Robert P. Dick, Hidenori Tanaka

Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning. Recent works have identified a multitude of beneficial properties in BatchNorm to explain its success. However, given the pursuit of alternative normalization layers, these properties need to be generalized so that any given layer's success/failure can be accurately predicted. In this work, we take a first step towards this goal by extending known properties of BatchNorm in randomly initialized deep neural networks (DNNs) to several recently proposed normalization layers. Our primary findings follow: (i) similar to BatchNorm, activations-based normalization layers can prevent exponential growth of activations in ResNets, but parametric techniques require explicit remedies; (ii) use of GroupNorm can ensure an informative forward propagation, with different samples being assigned dissimilar activations, but increasing group size results in increasingly indistinguishable activations for different samples, explaining slow convergence speed in models with LayerNorm; and (iii) small group sizes result in large gradient norm in earlier layers, hence explaining training instability issues in Instance Normalization and illustrating a speed-stability tradeoff in GroupNorm. Overall, our analysis reveals a unified set of mechanisms that underpin the success of normalization methods in deep learning, providing us with a compass to systematically explore the vast design space of DNN normalization layers.

Hidenori Tanaka, Daniel Kunin

In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry breaking is not well understood. Here, we develop a theoretical framework to study the "geometry of learning dynamics" in neural networks, and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. To build this understanding, we model the discrete learning dynamics of gradient descent using a continuous-time Lagrangian formulation, in which the learning rule corresponds to the kinetic energy and the loss function corresponds to the potential energy. Then, we identify "kinetic symmetry breaking" (KSB), the condition when the kinetic energy explicitly breaks the symmetry of the potential function. We generalize Noether's theorem known in physics to take into account KSB and derive the resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD). Finally, we apply NLD to neural networks with normalization layers and reveal how KSB introduces a mechanism of "implicit adaptive optimization", establishing an analogy between learning dynamics induced by normalization layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

Daniel Kunin, Javier Sagastuy-Brena, Surya Ganguli et al.

Understanding the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning. A central obstacle is that the motion of a network in high-dimensional parameter space undergoes discrete finite steps along complex stochastic gradients derived from real-world datasets. We circumvent this obstacle through a unifying theoretical framework based on intrinsic symmetries embedded in a network's architecture that are present for any dataset. We show that any such symmetry imposes stringent geometric constraints on gradients and Hessians, leading to an associated conservation law in the continuous-time limit of stochastic gradient descent (SGD), akin to Noether's theorem in physics. We further show that finite learning rates used in practice can actually break these symmetry induced conservation laws. We apply tools from finite difference methods to derive modified gradient flow, a differential equation that better approximates the numerical trajectory taken by SGD at finite learning rates. We combine modified gradient flow with our framework of symmetries to derive exact integral expressions for the dynamics of certain parameter combinations. We empirically validate our analytic expressions for learning dynamics on VGG-16 trained on Tiny ImageNet. Overall, by exploiting symmetry, our work demonstrates that we can analytically describe the learning dynamics of various parameter combinations at finite learning rates and batch sizes for state of the art architectures trained on any dataset.

Hidenori Tanaka, Daniel Kunin, Daniel L. K. Yamins et al.

Pruning the parameters of deep neural networks has generated intense interest due to potential savings in time, memory and energy both during training and at test time. Recent works have identified, through an expensive sequence of training and pruning cycles, the existence of winning lottery tickets or sparse trainable subnetworks at initialization. This raises a foundational question: can we identify highly sparse trainable subnetworks at initialization, without ever training, or indeed without ever looking at the data? We provide an affirmative answer to this question through theory driven algorithm design. We first mathematically formulate and experimentally verify a conservation law that explains why existing gradient-based pruning algorithms at initialization suffer from layer-collapse, the premature pruning of an entire layer rendering a network untrainable. This theory also elucidates how layer-collapse can be entirely avoided, motivating a novel pruning algorithm Iterative Synaptic Flow Pruning (SynFlow). This algorithm can be interpreted as preserving the total flow of synaptic strengths through the network at initialization subject to a sparsity constraint. Notably, this algorithm makes no reference to the training data and consistently competes with or outperforms existing state-of-the-art pruning algorithms at initialization over a range of models (VGG and ResNet), datasets (CIFAR-10/100 and Tiny ImageNet), and sparsity constraints (up to 99.99 percent). Thus our data-agnostic pruning algorithm challenges the existing paradigm that, at initialization, data must be used to quantify which synapses are important.

Hidenori Tanaka, Aran Nayebi, Niru Maheswaranathan et al.

Recently, deep feedforward neural networks have achieved considerable success in modeling biological sensory processing, in terms of reproducing the input-output map of sensory neurons. However, such models raise profound questions about the very nature of explanation in neuroscience. Are we simply replacing one complex system (a biological circuit) with another (a deep network), without understanding either? Moreover, beyond neural representations, are the deep network's computational mechanisms for generating neural responses the same as those in the brain? Without a systematic approach to extracting and understanding computational mechanisms from deep neural network models, it can be difficult both to assess the degree of utility of deep learning approaches in neuroscience, and to extract experimentally testable hypotheses from deep networks. We develop such a systematic approach by combining dimensionality reduction and modern attribution methods for determining the relative importance of interneurons for specific visual computations. We apply this approach to deep network models of the retina, revealing a conceptual understanding of how the retina acts as a predictive feature extractor that signals deviations from expectations for diverse spatiotemporal stimuli. For each stimulus, our extracted computational mechanisms are consistent with prior scientific literature, and in one case yields a new mechanistic hypothesis. Thus overall, this work not only yields insights into the computational mechanisms underlying the striking predictive capabilities of the retina, but also places the framework of deep networks as neuroscientific models on firmer theoretical foundations, by providing a new roadmap to go beyond comparing neural representations to extracting and understand computational mechanisms.