Independently trained neural models typically converge to incompatible latent representations, creating a fundamental barrier to highly modular AI systems. While Relative Representations (RR) address this by mapping absolute coordinates to a shared space defined by similarities to common anchor points, traditional implementations rely on randomly sampled anchors and cosine similarity, which frequently fail to capture the anisotropic geometries of modern architectures like Transformers. In this work, we propose a robust framework for cross-model communication based on two improvements. We learn anchors as robust semantic prototypes and utilize a geometry-aware similarity metric which preserves discriminative magnitude information and is invariant to affine shifts. Our approach demonstrates significant gains in performance and consistency across vision and language tasks. Notably, it enables nearly lossless information transfer and stable zero-shot communication even between highly heterogeneous architectures, such as small language models of varying scales.
The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of M≥3 models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.
Word embeddings are fundamental to natural language processing, yet traditional approaches represent each word with a single vector, creating representational bottlenecks for polysemous words and limiting semantic expressiveness. While multi-anchor representations have shown promise by representing words as combinations of multiple vectors, they have been limited to small-scale models due to computational inefficiency and lack of integration with modern transformer architectures. We introduce Adaptive Dictionary Embeddings (ADE), a framework that successfully scales multi-anchor word representations to large language models. ADE makes three key contributions: (1) Vocabulary Projection (VP), which transforms the costly two-stage anchor lookup into a single efficient matrix operation; (2) Grouped Positional Encoding (GPE), a novel positional encoding scheme where anchors of the same word share positional information, preserving semantic coherence while enabling anchor-level variation; and (3) context-aware anchor reweighting, which leverages self-attention to dynamically compose anchor contributions based on sequence context. We integrate these components into the Segment-Aware Transformer (SAT), which provides context-aware reweighting of anchor contributions at inference time. We evaluate ADE on AG News and DBpedia-14 text classification benchmarks. With 98.7% fewer trainable parameters than DeBERTa-v3-base, ADE surpasses DeBERTa on DBpedia-14 (98.06% vs. 97.80%) and approaches it on AG News (90.64% vs. 94.50%), while compressing the embedding layer over 40x -- demonstrating that multi-anchor representations are a practical and parameter-efficient alternative to single-vector embeddings in modern transformer architectures.
Representation alignment has emerged as an effective approach to improve Multimodal Large Language Models (MLLMs) by regularizing their internal representations toward those of an external vision encoder. However, existing methods typically align a fixed layer of the language backbone, overlooking the fine-grained structure of Transformer models. In this work, we propose Head-Wise Representation Alignment (HeRA), a method that enforces cross-modal alignment at the level of individual attention heads. Our approach is grounded in the Platonic Representation Hypothesis, focusing on preserving the topological structure of representations (i.e., their local neighborhood relationships) across modalities. Following the Mutual K-Nearest Neighbor (MKNN) alignment metric, we introduce a contrastive objective that acts as a differentiable proxy for matching local structures. HeRA applies this objective during multimodal training to specific attention heads in the LLM, selected by their alignment score according to the MKNN metric. Counterintuitively, we find that aligning the least aligned heads yields the largest gains. Extensive evaluations across multiple MLLMs and 18 benchmarks demonstrate that HeRA consistently improves performance on challenging vision-centric tasks and serves as an effective regularizer against visual hallucinations by naturally curbing the over-reliance on linguistic priors. Our code is publicly released.
Davide Caffagni, Alberto Compagnoni, Federico Melis +5