Daily Papers

Even when massively overparameterized, deep neural networks show a remarkable ability to generalize. Research on this phenomenon has focused on generalization within distribution, via smooth interpolation. Yet in some settings neural networks also learn to extrapolate to data far beyond the bounds of the original training set, sometimes even allowing for infinite generalization, implying that an algorithm capable of solving the task has been learned. Here we undertake a case study of the learning dynamics of recurrent neural networks (RNNs) trained on the streaming parity task in order to develop an effective theory of algorithm development. The streaming parity task is a simple but nonlinear task defined on sequences up to arbitrary length. We show that, with sufficient finite training experience, RNNs exhibit a phase transition to perfect infinite generalization. Using an effective theory for the representational dynamics, we find an implicit representational merger effect which can be interpreted as the construction of a finite automaton that reproduces the task. Overall, our results disclose one mechanism by which neural networks can generalize infinitely from finite training experience.

This paper studies the emergence of interpretable categorical features within large language models (LLMs), analyzing their behavior across training checkpoints (time), transformer layers (space), and varying model sizes (scale). Using sparse autoencoders for mechanistic interpretability, we identify when and where specific semantic concepts emerge within neural activations. Results indicate clear temporal and scale-specific thresholds for feature emergence across multiple domains. Notably, spatial analysis reveals unexpected semantic reactivation, with early-layer features re-emerging at later layers, challenging standard assumptions about representational dynamics in transformer models.

Transformers have found extensive applications across various domains due to the powerful fitting capabilities. This success can be partially attributed to their inherent nonlinearity. Thus, in addition to the ReLU function employed in the original transformer architecture, researchers have explored alternative modules such as GeLU and SwishGLU to enhance nonlinearity and thereby augment representational capacity. In this paper, we propose a novel category of polynomial composition activations (PolyCom), designed to optimize the dynamics of transformers. Theoretically, we provide a comprehensive mathematical analysis of PolyCom, highlighting its enhanced expressivity and efficacy relative to other activation functions. Notably, we demonstrate that networks incorporating PolyCom achieve the optimal approximation rate, indicating that PolyCom networks require minimal parameters to approximate general smooth functions in Sobolev spaces. We conduct empirical experiments on the pre-training configurations of large language models (LLMs), including both dense and sparse architectures. By substituting conventional activation functions with PolyCom, we enable LLMs to capture higher-order interactions within the data, thus improving performance metrics in terms of accuracy and convergence rates. Extensive experimental results demonstrate the effectiveness of our method, showing substantial improvements over other activation functions. Code is available at https://github.com/BryceZhuo/PolyCom.

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

As Vision Transformers (ViTs) become standard vision backbones, a mechanistic account of their computational phenomenology is essential. Despite architectural cues that hint at dynamical structure, there is no settled framework that interprets Transformer depth as a well-characterized flow. In this work, we introduce the Block-Recurrent Hypothesis (BRH), arguing that trained ViTs admit a block-recurrent depth structure such that the computation of the original L blocks can be accurately rewritten using only k ll L distinct blocks applied recurrently. Across diverse ViTs, between-layer representational similarity matrices suggest few contiguous phases. To determine whether these phases reflect genuinely reusable computation, we train block-recurrent surrogates of pretrained ViTs: Recurrent Approximations to Phase-structured TransfORmers (Raptor). In small-scale, we demonstrate that stochastic depth and training promote recurrent structure and subsequently correlate with our ability to accurately fit Raptor. We then provide an empirical existence proof for BRH by training a Raptor model to recover 96% of DINOv2 ImageNet-1k linear probe accuracy in only 2 blocks at equivalent computational cost. Finally, we leverage our hypothesis to develop a program of Dynamical Interpretability. We find i) directional convergence into class-dependent angular basins with self-correcting trajectories under small perturbations, ii) token-specific dynamics, where cls executes sharp late reorientations while patch tokens exhibit strong late-stage coherence toward their mean direction, and iii) a collapse to low rank updates in late depth, consistent with convergence to low-dimensional attractors. Altogether, we find a compact recurrent program emerges along ViT depth, pointing to a low-complexity normative solution that enables these models to be studied through principled dynamical systems analysis.

In this work, we study how multi-head latent attention (MLA), a popular strategy for compressing key/value memory, affects a transformer's internal capacity during pretraining. Using a lightweight suite of Marchenko-Pastur (MP) diagnostics, we analyze the spectrum of the W_{Q}W_{K}^top gram matrix throughout training, comparing three variants: the standard multi-head attention (MHA) baseline, MLA-PreRoPE with rotary applied before compression, and MLA-Decoupled, which shares a single rotary sub-vector across all heads. Our random matrix analysis reveals three key findings: i) capacity bottlenecks emerge locally: both MHA and MLA-PreRoPE exhibit sharp, early spikes in specific layers that persist and propagate, disrupting the balance between bulk and outlier directions; ii) these spikes coincide with rank collapse, concentrating the model's expressivity into narrow subspaces; iii) only the decoupled variant prevents this cascade, maintaining broad spectral support and suppressing outlier formation across layers. These results underscore that how rotary embeddings are applied is just as critical as where compression occurs. Sharing rotary components across heads mitigates spectral fragmentation and preserves representational capacity.

While contrastive approaches of self-supervised learning (SSL) learn representations by minimizing the distance between two augmented views of the same data point (positive pairs) and maximizing views from different data points (negative pairs), recent non-contrastive SSL (e.g., BYOL and SimSiam) show remarkable performance {\it without} negative pairs, with an extra learnable predictor and a stop-gradient operation. A fundamental question arises: why do these methods not collapse into trivial representations? We answer this question via a simple theoretical study and propose a novel approach, DirectPred, that directly sets the linear predictor based on the statistics of its inputs, without gradient training. On ImageNet, it performs comparably with more complex two-layer non-linear predictors that employ BatchNorm and outperforms a linear predictor by 2.5% in 300-epoch training (and 5% in 60-epoch). DirectPred is motivated by our theoretical study of the nonlinear learning dynamics of non-contrastive SSL in simple linear networks. Our study yields conceptual insights into how non-contrastive SSL methods learn, how they avoid representational collapse, and how multiple factors, like predictor networks, stop-gradients, exponential moving averages, and weight decay all come into play. Our simple theory recapitulates the results of real-world ablation studies in both STL-10 and ImageNet. Code is released https://github.com/facebookresearch/luckmatters/tree/master/ssl.

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical systems. This paper addresses a fundamental problem associated with EDMD: a trade-off between representational capacity of the dictionary and over-fitting due to insufficient data. A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encoded state is used to learn a low-dimensional and highly informative Koopman-invariant subspace of observables. A method is also presented for balanced model reduction of over-specified EDMD systems in feature space. Nonlinear reconstruction using partially linear multi-kernel regression aims to improve reconstruction accuracy from the low-dimensional state when the data has complex but intrinsically low-dimensional structure. The techniques demonstrate the ability to identify Koopman eigenfunctions of the unforced Duffing equation, create accurate low-dimensional models of an unstable cylinder wake flow, and make short-time predictions of the chaotic Kuramoto-Sivashinsky equation.

Large Language Models (LLMs) often produce fluent yet factually incorrect statements-a phenomenon known as hallucination-posing serious risks in high-stakes domains. We present Layer-wise Semantic Dynamics (LSD), a geometric framework for hallucination detection that analyzes the evolution of hidden-state semantics across transformer layers. Unlike prior methods that rely on multiple sampling passes or external verification sources, LSD operates intrinsically within the model's representational space. Using margin-based contrastive learning, LSD aligns hidden activations with ground-truth embeddings derived from a factual encoder, revealing a distinct separation in semantic trajectories: factual responses preserve stable alignment, while hallucinations exhibit pronounced semantic drift across depth. Evaluated on the TruthfulQA and synthetic factual-hallucination datasets, LSD achieves an F1-score of 0.92, AUROC of 0.96, and clustering accuracy of 0.89, outperforming SelfCheckGPT and Semantic Entropy baselines while requiring only a single forward pass. This efficiency yields a 5-20x speedup over sampling-based methods without sacrificing precision or interpretability. LSD offers a scalable, model-agnostic mechanism for real-time hallucination monitoring and provides new insights into the geometry of factual consistency within large language models.

The development of foundation models for functional magnetic resonance imaging (fMRI) time series holds significant promise for predicting phenotypes related to disease and cognition. Current models, however, are often trained using a mask-and-reconstruct objective on small brain regions. This focus on low-level information leads to representations that are sensitive to noise and temporal fluctuations, necessitating extensive fine-tuning for downstream tasks. We introduce Brain-Semantoks, a self-supervised framework designed specifically to learn abstract representations of brain dynamics. Its architecture is built on two core innovations: a semantic tokenizer that aggregates noisy regional signals into robust tokens representing functional networks, and a self-distillation objective that enforces representational stability across time. We show that this objective is stabilized through a novel training curriculum, ensuring the model robustly learns meaningful features from low signal-to-noise time series. We demonstrate that learned representations enable strong performance on a variety of downstream tasks even when only using a linear probe. Furthermore, we provide comprehensive scaling analyses indicating more unlabeled data reliably results in out-of-distribution performance gains without domain adaptation.

Large language models exhibit uneven performance across languages, with substantial gaps between high- and low-resource languages. We present a framework for enhancing monolingual capabilities of LLMs in underrepresented languages while preserving their general-purpose performance through targeted fine-tuning of language-specific subnetworks. Our approach identifies language-specific neurons using Language Activation Probability Entropy and fine-tunes only the weights associated with these neurons, a dedicated subnetwork, on target-language data. Experiments on Llama-3.1-8B and Mistral-Nemo-12B across 12 mid- and low-resource languages demonstrate that our method consistently outperforms full fine-tuning, FFN-only fine-tuning, LoRA adaptation, and random subset fine-tuning baselines while efficiently updating only up to 1% of model parameters. Beyond performance improvements, we observe enhanced favorable training dynamics, cross-lingual representational alignment, and systematic weight update changes. To facilitate future research, we release language-specific neuron identifications for over 100 languages as well as our adaptation pipeline, offering a cost-effective pathway for adapting state-of-the-art models to underrepresented languages.

Many AI models trained on natural images develop representations that resemble those of the human brain. However, the factors that drive this brain-model similarity remain poorly understood. To disentangle how the model, training and data independently lead a neural network to develop brain-like representations, we trained a family of self-supervised vision transformers (DINOv3) that systematically varied these different factors. We compare their representations of images to those of the human brain recorded with both fMRI and MEG, providing high resolution in spatial and temporal analyses. We assess the brain-model similarity with three complementary metrics focusing on overall representational similarity, topographical organization, and temporal dynamics. We show that all three factors - model size, training amount, and image type - independently and interactively impact each of these brain similarity metrics. In particular, the largest DINOv3 models trained with the most human-centric images reach the highest brain-similarity. This emergence of brain-like representations in AI models follows a specific chronology during training: models first align with the early representations of the sensory cortices, and only align with the late and prefrontal representations of the brain with considerably more training. Finally, this developmental trajectory is indexed by both structural and functional properties of the human cortex: the representations that are acquired last by the models specifically align with the cortical areas with the largest developmental expansion, thickness, least myelination, and slowest timescales. Overall, these findings disentangle the interplay between architecture and experience in shaping how artificial neural networks come to see the world as humans do, thus offering a promising framework to understand how the human brain comes to represent its visual world.

Recent advancements in generative modeling have made it possible to generate high-quality content from context information, but a key question remains: how to teach models to know when to generate content? To answer this question, this study proposes a novel event generative model that draws its statistical intuition from marked temporal point processes, and offers a clean, flexible, and computationally efficient solution for a wide range of applications involving multi-dimensional marks. We aim to capture the distribution of the point process without explicitly specifying the conditional intensity or probability density. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including exceptional efficiency in learning the model and generating samples, as well as considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

Multimodal LLMs have reached remarkable levels of proficiency in understanding multimodal inputs, driving extensive research to develop increasingly powerful models. However, much less attention has been paid to understanding and explaining the underlying mechanisms of these models. Most existing explainability research examines these models only in their final states, overlooking the dynamic representational shifts that occur during training. In this work, we systematically analyze the evolution of hidden state representations to reveal how fine-tuning alters the internal structure of a model to specialize in new multimodal tasks. Using a concept-based approach, we map hidden states to interpretable visual and textual concepts, enabling us to trace changes in encoded concepts across modalities as training progresses. We also demonstrate the use of shift vectors to capture these concepts changes. These shift vectors allow us to recover fine-tuned concepts by shifting those in the original model. Finally, we explore the practical impact of our findings on model steering, showing that we can adjust multimodal LLMs behaviors without any training, such as modifying answer types, captions style, or biasing the model toward specific responses. Our work sheds light on how multimodal representations evolve through fine-tuning and offers a new perspective for interpreting model adaptation in multimodal tasks. The code for this project is publicly available at https://github.com/mshukor/xl-vlms.