A Unifying Perspective on Language Model Representations: From Filler-Role Structure to Mechanistic Interpretability

Large language models (LLMs) are built from structured high-dimensional objects such as token representations, weights, adaptation updates, caches, and activations, whose multilinear structure is underexploited by the conventional matrix-centric view. Tensor decompositions and tensor networks provide a principled algebraic language for this structure, yet the literature often treats them as isolated compression mechanisms. This survey organizes tensor methods for LLMs through two complementary views: a seven-stage lifecycle taxonomy covering tokenization, embeddings, pre-training, adaptation, compression, inference, and interpretability, and a component view covering embeddings, attention, and feed-forward networks. We provide unified notation and theoretical foundations, analyze tensorization strategies for individual Transformer components, and compare methods at each lifecycle stage while making differences in evaluation protocols and model scales explicit. We further connect tensor methods to neighboring efficiency techniques and probabilistic tensor networks. Finally, we synthesize open challenges and introduce $ρ_{\rm gap}$, a metric for the compression-realization gap between theoretical memory reduction and measured system-level speedup. By treating tensorization as a common structural principle, the survey provides a structured entry point to tensorized language models and clarifies when parameter savings can plausibly translate into memory efficiency, computational efficiency, or interpretability. The GitHub page dedicated to this paper is accessible at this https URL.

Interpretability is often treated as a tax on capability: language models are trained as opaque systems, then explained after the fact, with methods whose reliability is difficult to establish. In this work, we challenge this premise. Rather than reverse-engineering a model, we make interpretability a constraint of the training pipeline, optimized alongside the language modeling objective. Across three orders of magnitude of compute, on both autoregressive and diffusion language models, interpretability scales with capability rather than against it. Surprisingly, model representations become more disentangled and aligned with human-understandable concepts with scale. We instantiate the training-time recipe with Steerling-8B, a diffusion language model with a causal attention mask. For any group of generated tokens, Steerling-8B attributes the output to relevant input tokens, human-understandable concepts, and training data. This enables closed-loop intervention: diagnose an output through its concept or feature attribution, retrieve similar training data, and correct the behavior through concept steering without retraining. Steerling-8B remains competitive with open peer models trained on substantially 2-16x more compute, suggesting a different scaling paradigm: interpretability can be designed into training, and it improves with scale.

Mechanistic interpretability aims to decompose neural network computations into human-understandable features, yet progress is limited by the absence of ground-truth units to evaluate against. We address this with a Sparse Transformer (ST): a 5-layer language model trained on TinyStories whose wide, TopK-sparse MLP forces neuron specialization. We show that ST neurons are highly interpretable: they outperform a loss-matched dense transformer by 43% on AutoInterp, and circuits of a median of 12 neurons suffice to reproduce individual model predictions. This testbed allows us to directly compare feature learning methods: Transcoder, which approximates the MLP input-output mapping, recovers ST's neuron vectors with 52.6% higher cosine similarity than Sparse Autoencoder, which only reconstructs outputs. Furthermore, the ST enables a controlled study of polysemanticity: distilling its sparse MLP into a dense counterpart reveals how compression leads to feature superposition. These results show how a known reference basis sharpens evaluation and understanding, a role we hope the ST can serve for the field.