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

TL;DR

The paper investigates why artificial vision models and human visual cortex representations converge as models scale, proposing local intrinsic dimensionality as a unifying geometric descriptor. By jointly analyzing AI-AI and AI-Brain alignment across ConvNeXt, ResNet, ResMLP, and ViT models trained on varied data, the study shows that stronger generalization coincides with greater representational convergence, and that this convergence is tightly tied to lower local dimensionality in representations. Using NSD fMRI data and a PCA-based encoding framework, the authors demonstrate that local, not global, geometry predicts alignment and performance, and that scaling model capacity and data systematically reduces local dimensionality, enabling cross-architecture convergence at high performance. These results offer a geometric account for the benefits of scaling and provide a robust, architecture-agnostic descriptor linking brain alignment, inter-model similarity, and generalization with potential implications for interpretability and model design.

Abstract

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.

Figures (16)

• Figure 1: Motivation and overview of representational alignment. Higher-performing AI models exhibit more similar representations to each other and to human neural activity. These convergent representations are also locally low-dimensional, revealing simple geometric principles underlying cross-model and AI-brain alignment.
• Figure 2: Representational convergence links AI--Brain alignment, inter-model alignment, and generalization. (A) Whole-brain maps of AI--Brain alignment, showing strongest alignment in visual cortex. (B) Median alignment across cortical regions, normalized by noise ceiling; higher-level visual areas (e.g., EBA) reach up to $\sim$60% of ceiling. (C) Distributions of alignment scores across models for each region, revealing substantial inter-model variability. (D) Pairwise AI--AI alignment matrix, with models ordered by AI--Brain alignment; models with stronger brain alignment also exhibit stronger mutual alignment. (E) Distributions of AI--AI alignment within groups of models binned by ImageNet performance; higher-performing groups exhibit stronger inter-model alignment. (F) Pairwise correlations between AI--Brain alignment, AI--AI alignment, and generalization performance, showing that these measures are all positively associated across models.
• Figure 3: Intrinsic dimensionality and representational convergence. (A) Models are grouped into bins according to intrinsic dimensionality, and the distribution of within-group AI--AI alignment is shown for each bin; lower-dimensional models align more strongly with each other. (B) Intrinsic dimensionality is negatively correlated with AI--AI alignment measured relative to the generalization-optimal reference model. (C) Intrinsic dimensionality is negatively correlated with AI--Brain alignment in EBA. (D) Intrinsic dimensionality is negatively correlated with ImageNet-1K performance. Across all measures, lower intrinsic dimensionality consistently corresponds to stronger representational alignment and improved generalization.
• Figure 4: Alignment and generalization depend on local, not global, intrinsic geometry. (A) Intrinsic dimensionality estimated as a function of neighborhood size $K$, spanning local to global scales. (B) Visualization of local versus global embedding structure with matched sample sizes. (C) Correlations between intrinsic dimensionality and AI--AI alignment, AI--Brain alignment, and generalization across scales, with strongest effects at local scales. (D) Correlations computed within a fixed local neighborhood (1,000 nearest neighbors), remaining stable across a range of $K$. (E) Control analysis using random global subsampling with matched sample size, demonstrating that the observed effects are not driven by differences in data volume.
• Figure 5: Representational alignment generalizes across architectures. (A--C) Relationships between AI--AI alignment (measured relative to the generalization-optimal reference), AI--Brain alignment, and ImageNet-1K performance when models from all architectures are pooled. (D--F) Relationships between intrinsic dimensionality and AI--AI alignment, AI--Brain alignment, and generalization across architectures. (G) Pairwise AI--AI alignment matrix reveals family-level structure, with stronger alignment within architectural families than across families. (H) Average intrinsic dimensionality shows no systematic differences across architectures. (I) Correlations between generalization performance and AI--AI alignment across models from different architectures. (J) Correlations between AI--AI alignment and AI--Brain alignment across architectures.

Theorems & Definitions (2)

• Definition 4.1
• Definition 4.2