How LLMs Learn: Tracing Internal Representations with Sparse Autoencoders

Large Language Models (LLMs) demonstrate remarkable multilingual capabilities and broad knowledge. However, the internal mechanisms underlying the development of these capabilities remain poorly understood. To investigate this, we analyze how the information encoded in LLMs' internal representations evolves during the training process. Specifically, we train sparse autoencoders at multiple checkpoints of the model and systematically compare the interpretative results across these stages. Our findings suggest that LLMs initially acquire language-specific knowledge independently, followed by cross-linguistic correspondences. Moreover, we observe that after mastering token-level knowledge, the model transitions to learning higher-level, abstract concepts, indicating the development of more conceptual understanding.

Syntactic Learnability of Echo State Neural Language Models at Scale

What is a neural model with minimum architectural complexity that exhibits reasonable language learning capability? To explore such a simple but sufficient neural language model, we revisit a basic reservoir computing (RC) model, Echo State Network (ESN), a restricted class of simple Recurrent Neural Networks. Our experiments showed that ESN with a large hidden state is comparable or superior to Transformer in grammaticality judgment tasks when trained with about 100M words, suggesting that architectures as complex as that of Transformer may not always be necessary for syntactic learning.

Rectifying Belief Space via Unlearning to Harness LLMs' Reasoning

Large language models (LLMs) can exhibit advanced reasoning yet still generate incorrect answers. We hypothesize that such errors frequently stem from spurious beliefs, propositions the model internally considers true but are incorrect. To address this, we propose a method to rectify the belief space by suppressing these spurious beliefs while simultaneously enhancing true ones, thereby enabling more reliable inferences. Our approach first identifies the beliefs that lead to incorrect or correct answers by prompting the model to generate textual explanations, using our Forward-Backward Beam Search (FBBS). We then apply unlearning to suppress the identified spurious beliefs and enhance the true ones, effectively rectifying the model's belief space. Empirical results on multiple QA datasets and LLMs show that our method corrects previously misanswered questions without harming overall model performance. Furthermore, our approach yields improved generalization on unseen data, suggesting that rectifying a model's belief space is a promising direction for mitigating errors and enhancing overall reliability.

Number Representations in LLMs: A Computational Parallel to Human Perception

Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that numerical magnitudes are processed in a sublinear fashion rather than on a uniform linear scale. Inspired by this hypothesis, we investigate whether large language models (LLMs) exhibit a similar logarithmic-like structure in their internal numerical representations. By analyzing how numerical values are encoded across different layers of LLMs, we apply dimensionality reduction techniques such as PCA and PLS followed by geometric regression to uncover latent structures in the learned embeddings. Our findings reveal that the model's numerical representations exhibit sublinear spacing, with distances between values aligning with a logarithmic scale. This suggests that LLMs, much like humans, may encode numbers in a compressed, non-uniform manner.

Large Language Models Are Human-Like Internally

Recent cognitive modeling studies have reported that larger language models (LMs) exhibit a poorer fit to human reading behavior, leading to claims of their cognitive implausibility. In this paper, we revisit this argument through the lens of mechanistic interpretability and argue that prior conclusions were skewed by an exclusive focus on the final layers of LMs. Our analysis reveals that next-word probabilities derived from internal layers of larger LMs align with human sentence processing data as well as, or better than, those from smaller LMs. This alignment holds consistently across behavioral (self-paced reading times, gaze durations, MAZE task processing times) and neurophysiological (N400 brain potentials) measures, challenging earlier mixed results and suggesting that the cognitive plausibility of larger LMs has been underestimated. Furthermore, we first identify an intriguing relationship between LM layers and human measures: earlier layers correspond more closely with fast gaze durations, while later layers better align with relatively slower signals such as N400 potentials and MAZE processing times. Our work opens new avenues for interdisciplinary research at the intersection of mechanistic interpretability and cognitive modeling.

Automatic Feedback Generation for Short Answer Questions using Answer Diagnostic Graphs

Short-reading comprehension questions help students understand text structure but lack effective feedback. Students struggle to identify and correct errors, while manual feedback creation is labor-intensive. This highlights the need for automated feedback linking responses to a scoring rubric for deeper comprehension. Despite advances in Natural Language Processing (NLP), research has focused on automatic grading, with limited work on feedback generation. To address this, we propose a system that generates feedback for student responses. Our contributions are twofold. First, we introduce the first system for feedback on short-answer reading comprehension. These answers are derived from the text, requiring structural understanding. We propose an "answer diagnosis graph," integrating the text's logical structure with feedback templates. Using this graph and NLP techniques, we estimate students' comprehension and generate targeted feedback. Second, we evaluate our feedback through an experiment with Japanese high school students (n=39). They answered two 70-80 word questions and were divided into two groups with minimal academic differences. One received a model answer, the other system-generated feedback. Both re-answered the questions, and we compared score changes. A questionnaire assessed perceptions and motivation. Results showed no significant score improvement between groups, but system-generated feedback helped students identify errors and key points in the text. It also significantly increased motivation. However, further refinement is needed to enhance text structure understanding.

Weight-based Analysis of Detokenization in Language Models: Understanding the First Stage of Inference Without Inference

According to the stages-of-inference hypothesis, early layers of language models map their subword-tokenized input, which does not necessarily correspond to a linguistically meaningful segmentation, to more meaningful representations that form the model's ``inner vocabulary''. Prior analysis of this detokenization stage has predominantly relied on probing and interventions such as path patching, which involve selecting particular inputs, choosing a subset of components that will be patched, and then observing changes in model behavior. Here, we show that several important aspects of the detokenization stage can be understood purely by analyzing model weights, without performing any model inference steps. Specifically, we introduce an analytical decomposition of first-layer attention in GPT-2. Our decomposition yields interpretable terms that quantify the relative contributions of position-related, token-related, and mixed effects. By focusing on terms in this decomposition, we discover weight-based explanations of attention bias toward close tokens and attention for detokenization.

Think-to-Talk or Talk-to-Think? When LLMs Come Up with an Answer in Multi-Step Reasoning

This study investigates the internal reasoning mechanism of language models during symbolic multi-step reasoning, motivated by the question of whether chain-of-thought (CoT) outputs are faithful to the model's internals. Specifically, we inspect when they internally determine their answers, particularly before or after CoT begins, to determine whether models follow a post-hoc "think-to-talk" mode or a step-by-step "talk-to-think" mode of explanation. Through causal probing experiments in controlled arithmetic reasoning tasks, we found systematic internal reasoning patterns across models; for example, simple subproblems are solved before CoT begins, and more complicated multi-hop calculations are performed during CoT.

Repetition Neurons: How Do Language Models Produce Repetitions?

This paper introduces repetition neurons, regarded as skill neurons responsible for the repetition problem in text generation tasks. These neurons are progressively activated more strongly as repetition continues, indicating that they perceive repetition as a task to copy the previous context repeatedly, similar to in-context learning. We identify these repetition neurons by comparing activation values before and after the onset of repetition in texts generated by recent pre-trained language models. We analyze the repetition neurons in three English and one Japanese pre-trained language models and observe similar patterns across them.

The Geometry of Numerical Reasoning: Language Models Compare Numeric Properties in Linear Subspaces

This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding space when answering logical comparison questions (e.g., Was Cristiano born before Messi?). We first identified these subspaces using partial least squares regression, which effectively encodes the numerical attributes associated with the entities in comparison prompts. Further, we demonstrate causality by intervening in these subspaces to manipulate hidden states, thereby altering the LLM's comparison outcomes. Experimental results show that our findings hold for different numerical attributes, indicating that LLMs utilize the linearly encoded information for numerical reasoning.