TensorLens: End-to-End Transformer Analysis via High-Order Attention Tensors

TL;DR

TensorLens introduces a comprehensive high-order tensor representation of transformer models, capturing all components and enabling advanced interpretability and analysis beyond traditional attention head methods.

Contribution

It provides the first unified, input-dependent linear operator formulation of transformers using a high-order attention tensor, integrating all model components.

Findings

Richer representations than previous attention-aggregation methods

Effective for interpretability and model understanding

Empirically validated on transformer models

Abstract

Attention matrices are fundamental to transformer research, supporting a broad range of applications including interpretability, visualization, manipulation, and distillation. Yet, most existing analyses focus on individual attention heads or layers, failing to account for the model's global behavior. While prior efforts have extended attention formulations across multiple heads via averaging and matrix multiplications or incorporated components such as normalization and FFNs, a unified and complete representation that encapsulates all transformer blocks is still lacking. We address this gap by introducing TensorLens, a novel formulation that captures the entire transformer as a single, input-dependent linear operator expressed through a high-order attention-interaction tensor. This tensor jointly encodes attention, FFNs, activations, normalizations, and residual connections, offering a theoretically coherent and expressive linear representation of the model's computation. TensorLens is theoretically grounded and our empirical validation shows that it yields richer representations than previous attention-aggregation methods. Our experiments demonstrate that the attention tensor can serve as a powerful foundation for developing tools aimed at interpretability and model understanding. Our code is attached as a supplementary.