Understanding Generalization from Embedding Dimension and Distributional Convergence

Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned embeddings controls predictive performance for a fixed trained model. We show that population risk can be bounded by two factors: (i) the intrinsic dimension of the embedding distribution, which determines the convergence rate of empirical embedding distribution to the population distribution in Wasserstein distance, and (ii) the sensitivity of the downstream mapping from embeddings to predictions, characterized by Lipschitz constants. Together, these yield an embedding-dependent error bound that does not rely on parameter counts or hypothesis class complexity. At the final embedding layer, architectural sensitivity vanishes and the bound is dominated by embedding dimension, explaining its strong empirical correlation with generalization performance. Experiments across architectures and datasets validate the theory and demonstrate the utility of embedding-based diagnostics.

Local Intrinsic Dimension of Representations Predicts Alignment and Generalization in AI Models and Human Brain

Recent work has found that neural networks with stronger generalization tend to exhibit higher representational alignment with one another across architectures and training paradigms. In this work, we show that models with stronger generalization also align more strongly with human neural activity. Moreover, generalization performance, model--model alignment, and model--brain alignment are all significantly correlated with each other. We further show that these relationships can be explained by a single geometric property of learned representations: the local intrinsic dimension of embeddings. Lower local dimension is consistently associated with stronger model--model alignment, stronger model--brain alignment, and better generalization, whereas global dimension measures fail to capture these effects. Finally, we find that increasing model capacity and training data scale systematically reduces local intrinsic dimension, providing a geometric account of the benefits of scaling. Together, our results identify local intrinsic dimension as a unifying descriptor of representational convergence in artificial and biological systems.

AutoICE: Automatically Synthesizing Verifiable C Code via LLM-driven Evolution

Automatically synthesizing verifiable code from natural language requirements ensures software correctness and reliability while significantly lowering the barrier to adopting the techniques of formal methods. With the rise of large language models (LLMs), long-standing efforts at autoformalization have gained new momentum. However, existing approaches suffer from severe syntactic and semantic errors due to the scarcity of domain-specific pre-training corpora and often fail to formalize implicit knowledge effectively. In this paper, we propose AutoICE, an LLM-driven evolutionary search for synthesizing verifiable C code. It introduces the diverse individual initialization and the collaborative crossover to enable diverse iterative updates, thereby mitigating error propagation inherent in single-agent iterations. Besides, it employs the self-reflective mutation to facilitate the discovery of implicit knowledge. Evaluation results demonstrate the effectiveness of AutoICE: it successfully verifies $90.36$\% of code, outperforming the state-of-the-art (SOTA) approach. Besides, on a developer-friendly dataset variant, AutoICE achieves a $88.33$\% verification success rate, significantly surpassing the $65$\% success rate of the SOTA approach.

Scale-Invariance Drives Convergence in AI and Brain Representations

Despite variations in architecture and pretraining strategies, recent studies indicate that large-scale AI models often converge toward similar internal representations that also align with neural activity. We propose that scale-invariance, a fundamental structural principle in natural systems, is a key driver of this convergence. In this work, we propose a multi-scale analytical framework to quantify two core aspects of scale-invariance in AI representations: dimensional stability and structural similarity across scales. We further investigate whether these properties can predict alignment performance with functional Magnetic Resonance Imaging (fMRI) responses in the visual cortex. Our analysis reveals that embeddings with more consistent dimension and higher structural similarity across scales align better with fMRI data. Furthermore, we find that the manifold structure of fMRI data is more concentrated, with most features dissipating at smaller scales. Embeddings with similar scale patterns align more closely with fMRI data. We also show that larger pretraining datasets and the inclusion of language modalities enhance the scale-invariance properties of embeddings, further improving neural alignment. Our findings indicate that scale-invariance is a fundamental structural principle that bridges artificial and biological representations, providing a new framework for evaluating the structural quality of human-like AI systems.

Synthesizing Images on Perceptual Boundaries of ANNs for Uncovering and Manipulating Human Perceptual Variability

Human decision-making in cognitive tasks and daily life exhibits considerable variability, shaped by factors such as task difficulty, individual preferences, and personal experiences. Understanding this variability across individuals is essential for uncovering the perceptual and decision-making mechanisms that humans rely on when faced with uncertainty and ambiguity. We present a computational framework BAM (Boundary Alignment & Manipulation framework) that combines perceptual boundary sampling in ANNs and human behavioral experiments to systematically investigate this phenomenon. Our perceptual boundary sampling algorithm generates stimuli along ANN decision boundaries that intrinsically induce significant perceptual variability. The efficacy of these stimuli is empirically validated through large-scale behavioral experiments involving 246 participants across 116,715 trials, culminating in the variMNIST dataset containing 19,943 systematically annotated images. Through personalized model alignment and adversarial generation, we establish a reliable method for simultaneously predicting and manipulating the divergent perceptual decisions of pairs of participants. This work bridges the gap between computational models and human individual difference research, providing new tools for personalized perception analysis.