Law of Neural Interaction: Depth-Width Shape, Interaction Efficiency, and Generalization

The guidance of scaling laws has increased the resource demands of modern large language models (LLMs), yet it remains questionable whether these models utilize resources effectively under a fixed budget. Previous research has proved superposition as a key contributor to loss. By leveraging the Neural Feature Ansatz, we extend superposition from parameter space to gradient space and define it as neural interaction. We find that under a fixed budget, good generalization is usually accompanied by efficient neural interactions, and the model can be placed in an efficient interaction interval by adjusting its depth-width ratio ($R_{D/W}$). In addition, as the budget scales up, the efficient interaction interval of the model remains relatively stable. By comparing existing small scale dense LLMs, we observe that models operating near this interval tend to perform better on the MMLU-Pro benchmark. Our findings reveal that the $R_{D/W}$ influences resource utilization efficiency and thereby affects generalization, providing insights into model shape initialization and the understanding of model generalization mechanisms. Code for Neural Interaction Law is available at: https://anonymous.4open.science/r/Neural_Interaction_Law-D788

Universal Activation Verbalizer: A Unified Framework for Cross-Model Activation Explanation

Activation verbalization explains hidden representations in natural language, but existing methods are mostly limited to self-explanation, where each model explains only its own activations. We introduce Universal Activation Verbalizer (UAV), a framework that uses a shared decoder to explain activations from heterogeneous donor models. UAV learns a lightweight adapter that converts donor activations into soft tokens in decoder's embedding space, and further supports adapter-only transfer by reusing a frozen decoder-side LoRA while training only a new adapter for another donor. Across classification, fact retrieval, and gist summarization, UAV remains competitive with strong self-explanation baselines while enabling cross-model verbalization across model families and scales. Ablations show that decoder-side tuning mainly improves task behavior, whereas the adapter provides the activation-grounded factual and semantic information needed for faithful explanations.

Farther the Shift, Sparser the Representation: Analyzing OOD Mechanisms in LLMs

In this work, we investigate how Large Language Models (LLMs) adapt their internal representations when encountering inputs of increasing difficulty, quantified as the degree of out-of-distribution (OOD) shift. We reveal a consistent and quantifiable phenomenon: as task difficulty increases, whether through harder reasoning questions, longer contexts, or adding answer choices, the last hidden states of LLMs become substantially sparser. In short, \textbf{\textit{the farther the shift, the sparser the representations}}. This sparsity--difficulty relation is observable across diverse models and domains, suggesting that language models respond to unfamiliar or complex inputs by concentrating computation into specialized subspaces in the last hidden state. Through a series of controlled analyses with a learning dynamic explanation, we demonstrate that this sparsity is not incidental but an adaptive mechanism for stabilizing reasoning under OOD. Leveraging this insight, we design \textit{Sparsity-Guided Curriculum In-Context Learning (SG-ICL)}, a strategy that explicitly uses representation sparsity to schedule few-shot demonstrations, leading to considerable performance enhancements. Our study provides new mechanistic insights into how LLMs internalize OOD challenges. The source code is available at the URL: https://github.com/MingyuJ666/sparsityLLM.

FinAnchor: Aligned Multi-Model Representations for Financial Prediction

Financial prediction from long documents involves significant challenges, as actionable signals are often sparse and obscured by noise, and the optimal LLM for generating embeddings varies across tasks and time periods. In this paper, we propose FinAnchor(Financial Anchored Representations), a lightweight framework that integrates embeddings from multiple LLMs without fine-tuning the underlying models. FinAnchor addresses the incompatibility of feature spaces by selecting an anchor embedding space and learning linear mappings to align representations from other models into this anchor. These aligned features are then aggregated to form a unified representation for downstream prediction. Across multiple financial NLP tasks, FinAnchor consistently outperforms strong single-model baselines and standard ensemble methods, demonstrating the effectiveness of anchoring heterogeneous representations for robust financial prediction.

AdaJudge: Adaptive Multi-Perspective Judging for Reward Modeling

Reward modeling is essential for aligning large language models with human preferences, yet predominant architectures rely on a static pooling strategy to condense sequences into scalar scores. This paradigm, however, suffers from two key limitations: a static inductive bias that misaligns with task-dependent preference signals, and a representational mismatch, as the backbone is optimized for generation rather than fine-grained discrimination. To address this, we propose AdaJudge, a unified framework that jointly adapts representation and aggregation. AdaJudge first refines backbone representations into a discrimination-oriented space via gated refinement blocks. It then replaces the static readout with an adaptive multi-view pooling module that dynamically routes and combines evidence. Extensive experiments on RM-Bench and JudgeBench show that AdaJudge outperforms strong off-the-shelf reward models and traditional pooling baselines.

NeuronScope: A Multi-Agent Framework for Explaining Polysemantic Neurons in Language Models

Neuron-level interpretation in large language models (LLMs) is fundamentally challenged by widespread polysemanticity, where individual neurons respond to multiple distinct semantic concepts. Existing single-pass interpretation methods struggle to faithfully capture such multi-concept behavior. In this work, we propose NeuronScope, a multi-agent framework that reformulates neuron interpretation as an iterative, activation-guided process. NeuronScope explicitly deconstructs neuron activations into atomic semantic components, clusters them into distinct semantic modes, and iteratively refines each explanation using neuron activation feedback. Experiments demonstrate that NeuronScope uncovers hidden polysemanticity and produces explanations with significantly higher activation correlation compared to single-pass baselines.

Rep2Text: Decoding Full Text from a Single LLM Token Representation

Large language models (LLMs) have achieved remarkable progress across diverse tasks, yet their internal mechanisms remain largely opaque. In this work, we address a fundamental question: to what extent can the original input text be recovered from a single last-token representation within an LLM? We propose Rep2Text, a novel framework for decoding full text from last-token representations. Rep2Text employs a trainable adapter that projects a target model's internal representations into the embedding space of a decoding language model, which then autoregressively reconstructs the input text. Experiments on various model combinations (Llama-3.1-8B, Gemma-7B, Mistral-7B-v0.1, Llama-3.2-3B) demonstrate that, on average, over half of the information in 16-token sequences can be recovered from this compressed representation while maintaining strong semantic integrity and coherence. Furthermore, our analysis reveals an information bottleneck effect: longer sequences exhibit decreased token-level recovery while preserving strong semantic integrity. Besides, our framework also demonstrates robust generalization to out-of-distribution medical data.

KnowThyself: An Agentic Assistant for LLM Interpretability

We develop KnowThyself, an agentic assistant that advances large language model (LLM) interpretability. Existing tools provide useful insights but remain fragmented and code-intensive. KnowThyself consolidates these capabilities into a chat-based interface, where users can upload models, pose natural language questions, and obtain interactive visualizations with guided explanations. At its core, an orchestrator LLM first reformulates user queries, an agent router further directs them to specialized modules, and the outputs are finally contextualized into coherent explanations. This design lowers technical barriers and provides an extensible platform for LLM inspection. By embedding the whole process into a conversational workflow, KnowThyself offers a robust foundation for accessible LLM interpretability.

AdaptiveK Sparse Autoencoders: Dynamic Sparsity Allocation for Interpretable LLM Representations

Understanding the internal representations of large language models (LLMs) remains a central challenge for interpretability research. Sparse autoencoders (SAEs) offer a promising solution by decomposing activations into interpretable features, but existing approaches rely on fixed sparsity constraints that fail to account for input complexity. We propose Adaptive Top K Sparse Autoencoders (AdaptiveK), a novel framework that dynamically adjusts sparsity levels based on the semantic complexity of each input. Leveraging linear probes, we demonstrate that context complexity is linearly encoded in LLM representations, and we use this signal to guide feature allocation during training. Experiments across three language models (Pythia-70M, Pythia-160M, and Gemma-2-2B) demonstrate that this complexity-driven adaptation significantly outperforms fixed-sparsity approaches on reconstruction fidelity, explained variance, and cosine similarity metrics while eliminating the computational burden of extensive hyperparameter tuning.

Attribution Explanations for Deep Neural Networks: A Theoretical Perspective

Attribution explanation is a typical approach for explaining deep neural networks (DNNs), inferring an importance or contribution score for each input variable to the final output. In recent years, numerous attribution methods have been developed to explain DNNs. However, a persistent concern remains unresolved, i.e., whether and which attribution methods faithfully reflect the actual contribution of input variables to the decision-making process. The faithfulness issue undermines the reliability and practical utility of attribution explanations. We argue that these concerns stem from three core challenges. First, difficulties arise in comparing attribution methods due to their unstructured heterogeneity, differences in heuristics, formulations, and implementations that lack a unified organization. Second, most methods lack solid theoretical underpinnings, with their rationales remaining absent, ambiguous, or unverified. Third, empirically evaluating faithfulness is challenging without ground truth. Recent theoretical advances provide a promising way to tackle these challenges, attracting increasing attention. We summarize these developments, with emphasis on three key directions: (i) Theoretical unification, which uncovers commonalities and differences among methods, enabling systematic comparisons; (ii) Theoretical rationale, clarifying the foundations of existing methods; (iii) Theoretical evaluation, rigorously proving whether methods satisfy faithfulness principles. Beyond a comprehensive review, we provide insights into how these studies help deepen theoretical understanding, inform method selection, and inspire new attribution methods. We conclude with a discussion of promising open problems for further work.