Does Representation Matter? Exploring Intermediate Layers in Large Language Models

Understanding what defines a good representation in large language models (LLMs) is fundamental to both theoretical understanding and practical applications. In this paper, we investigate the quality of intermediate representations in various LLM architectures, including Transformers and State Space Models (SSMs). We find that intermediate layers often yield more informative representations for downstream tasks than the final layers. To measure the representation quality, we adapt and apply a suite of metrics - such as prompt entropy, curvature, and augmentation-invariance - originally proposed in other contexts. Our empirical study reveals significant architectural differences, how representations evolve throughout training, and how factors like input randomness and prompt length affect each layer. Notably, we observe a bimodal pattern in the entropy of some intermediate layers and consider potential explanations tied to training data. Overall, our results illuminate the internal mechanics of LLMs and guide strategies for architectural optimization and training.

Rate-In: Information-Driven Adaptive Dropout Rates for Improved Inference-Time Uncertainty Estimation

Accurate uncertainty estimation is crucial for deploying neural networks in risk-sensitive applications such as medical diagnosis. Monte Carlo Dropout is a widely used technique for approximating predictive uncertainty by performing stochastic forward passes with dropout during inference. However, using static dropout rates across all layers and inputs can lead to suboptimal uncertainty estimates, as it fails to adapt to the varying characteristics of individual inputs and network layers. Existing approaches optimize dropout rates during training using labeled data, resulting in fixed inference-time parameters that cannot adjust to new data distributions, compromising uncertainty estimates in Monte Carlo simulations. In this paper, we propose Rate-In, an algorithm that dynamically adjusts dropout rates during inference by quantifying the information loss induced by dropout in each layer's feature maps. By treating dropout as controlled noise injection and leveraging information-theoretic principles, Rate-In adapts dropout rates per layer and per input instance without requiring ground truth labels. By quantifying the functional information loss in feature maps, we adaptively tune dropout rates to maintain perceptual quality across diverse medical imaging tasks and architectural configurations. Our extensive empirical study on synthetic data and real-world medical imaging tasks demonstrates that Rate-In improves calibration and sharpens uncertainty estimates compared to fixed or heuristic dropout rates without compromising predictive performance. Rate-In offers a practical, unsupervised, inference-time approach to optimizing dropout for more reliable predictive uncertainty estimation in critical applications.

Seq-VCR: Preventing Collapse in Intermediate Transformer Representations for Enhanced Reasoning

Decoder-only Transformers often struggle with complex reasoning tasks, particularly arithmetic reasoning requiring multiple sequential operations. In this work, we identify representation collapse in the model's intermediate layers as a key factor limiting their reasoning capabilities. To address this, we propose Sequential Variance-Covariance Regularization (Seq-VCR), which enhances the entropy of intermediate representations and prevents collapse. Combined with dummy pause tokens as substitutes for chain-of-thought (CoT) tokens, our method significantly improves performance in arithmetic reasoning problems. In the challenging $5 \times 5$ integer multiplication task, our approach achieves $99.5\%$ exact match accuracy, outperforming models of the same size (which yield $0\%$ accuracy) and GPT-4 with five-shot CoT prompting ($44\%$). We also demonstrate superior results on arithmetic expression and longest increasing subsequence (LIS) datasets. Our findings highlight the importance of preventing intermediate layer representation collapse to enhance the reasoning capabilities of Transformers and show that Seq-VCR offers an effective solution without requiring explicit CoT supervision.

Learning to Compress: Local Rank and Information Compression in Deep Neural Networks

Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.

LiveBench: A Challenging, Contamination-Free LLM Benchmark

Test set contamination, wherein test data from a benchmark ends up in a newer model's training set, is a well-documented obstacle for fair LLM evaluation and can quickly render benchmarks obsolete. To mitigate this, many recent benchmarks crowdsource new prompts and evaluations from human or LLM judges; however, these can introduce significant biases, and break down when scoring hard questions. In this work, we introduce a new benchmark for LLMs designed to be immune to both test set contamination and the pitfalls of LLM judging and human crowdsourcing. We release LiveBench, the first benchmark that (1) contains frequently-updated questions from recent information sources, (2) scores answers automatically according to objective ground-truth values, and (3) contains a wide variety of challenging tasks, spanning math, coding, reasoning, language, instruction following, and data analysis. To achieve this, LiveBench contains questions that are based on recently-released math competitions, arXiv papers, news articles, and datasets, and it contains harder, contamination-free versions of tasks from previous benchmarks such as Big-Bench Hard, AMPS, and IFEval. We evaluate many prominent closed-source models, as well as dozens of open-source models ranging from 0.5B to 110B in size. LiveBench is difficult, with top models achieving below 65% accuracy. We release all questions, code, and model answers. Questions will be added and updated on a monthly basis, and we will release new tasks and harder versions of tasks over time so that LiveBench can distinguish between the capabilities of LLMs as they improve in the future. We welcome community engagement and collaboration for expanding the benchmark tasks and models.

Just How Flexible are Neural Networks in Practice?

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.

Towards an Improved Understanding and Utilization of Maximum Manifold Capacity Representations

Maximum Manifold Capacity Representations (MMCR) is a recent multi-view self-supervised learning (MVSSL) method that matches or surpasses other leading MVSSL methods. MMCR is intriguing because it does not fit neatly into any of the commonplace MVSSL lineages, instead originating from a statistical mechanical perspective on the linear separability of data manifolds. In this paper, we seek to improve our understanding and our utilization of MMCR. To better understand MMCR, we leverage tools from high dimensional probability to demonstrate that MMCR incentivizes alignment and uniformity of learned embeddings. We then leverage tools from information theory to show that such embeddings maximize a well-known lower bound on mutual information between views, thereby connecting the geometric perspective of MMCR to the information-theoretic perspective commonly discussed in MVSSL. To better utilize MMCR, we mathematically predict and experimentally confirm non-monotonic changes in the pretraining loss akin to double descent but with respect to atypical hyperparameters. We also discover compute scaling laws that enable predicting the pretraining loss as a function of gradients steps, batch size, embedding dimension and number of views. We then show that MMCR, originally applied to image data, is performant on multimodal image-text data. By more deeply understanding the theoretical and empirical behavior of MMCR, our work reveals insights on improving MVSSL methods.

The Entropy Enigma: Success and Failure of Entropy Minimization

Entropy minimization (EM) is frequently used to increase the accuracy of classification models when they're faced with new data at test time. EM is a self-supervised learning method that optimizes classifiers to assign even higher probabilities to their top predicted classes. In this paper, we analyze why EM works when adapting a model for a few steps and why it eventually fails after adapting for many steps. We show that, at first, EM causes the model to embed test images close to training images, thereby increasing model accuracy. After many steps of optimization, EM makes the model embed test images far away from the embeddings of training images, which results in a degradation of accuracy. Building upon our insights, we present a method for solving a practical problem: estimating a model's accuracy on a given arbitrary dataset without having access to its labels. Our method estimates accuracy by looking at how the embeddings of input images change as the model is optimized to minimize entropy. Experiments on 23 challenging datasets show that our method sets the SoTA with a mean absolute error of $5.75\%$, an improvement of $29.62\%$ over the previous SoTA on this task. Our code is available at https://github.com/oripress/EntropyEnigma

Simplifying Neural Network Training Under Class Imbalance

Real-world datasets are often highly class-imbalanced, which can adversely impact the performance of deep learning models. The majority of research on training neural networks under class imbalance has focused on specialized loss functions, sampling techniques, or two-stage training procedures. Notably, we demonstrate that simply tuning existing components of standard deep learning pipelines, such as the batch size, data augmentation, optimizer, and label smoothing, can achieve state-of-the-art performance without any such specialized class imbalance methods. We also provide key prescriptions and considerations for training under class imbalance, and an understanding of why imbalance methods succeed or fail.

Sudden Drops in the Loss: Syntax Acquisition, Phase Transitions, and Simplicity Bias in MLMs

Most interpretability research in NLP focuses on understanding the behavior and features of a fully trained model. However, certain insights into model behavior may only be accessible by observing the trajectory of the training process. We present a case study of syntax acquisition in masked language models (MLMs) that demonstrates how analyzing the evolution of interpretable artifacts throughout training deepens our understanding of emergent behavior. In particular, we study Syntactic Attention Structure (SAS), a naturally emerging property of MLMs wherein specific Transformer heads tend to focus on specific syntactic relations. We identify a brief window in pretraining when models abruptly acquire SAS, concurrent with a steep drop in loss. This breakthrough precipitates the subsequent acquisition of linguistic capabilities. We then examine the causal role of SAS by manipulating SAS during training, and demonstrate that SAS is necessary for the development of grammatical capabilities. We further find that SAS competes with other beneficial traits during training, and that briefly suppressing SAS improves model quality. These findings offer an interpretation of a real-world example of both simplicity bias and breakthrough training dynamics.