StructLens: A Structural Lens for Language Models via Maximum Spanning Trees

Finding human-interpretable directions in language-model activations is important for understanding and controlling model behavior. These directions are usually discovered through indirect learning objectives such as sparse reconstruction, but it remains unclear what existing statistical structure distinguishes interpretable directions and whether that structure can be used directly for feature discovery. We find that non-Gaussianity provides such a signature: projection distributions of natural-text residual-stream activations along sparse autoencoder (SAE) decoder directions are substantially more non-Gaussian than those along random directions, with most contexts forming a concentrated background and recurring patterns often occupying one tail. This raises a natural question: if interpretable directions tend to have non-Gaussian projection distributions, can we discover them by searching for non-Gaussian directions directly in activation space, without training another sparse dictionary? To test this hypothesis, we introduce ICA Lens, a practical workflow for efficient discovery, reliable annotation, and faithful evaluation of non-Gaussian directions in LLM residual-stream activations. Across GPT-2 Small, Gemma 2 2B, and Qwen 3.5 9B Base, we find that: (1) the recovered non-Gaussian directions capture coherent lexical, syntactic, and semantic patterns under both human and LLM-based evaluation; (2) non-Gaussianity is positively associated with both human-label confidence and automated interpretability; and (3) the resulting coordinates are competitive with SAEs across interpretability, sparse reconstruction, concept prediction, and targeted probe perturbation, while fitting in minutes per layer and using 7-43 times less memory. These results show that non-Gaussianity is a direct unsupervised signal for discovering interpretable and useful structure in activations.

Structured pruning reduces LLM inference costs by removing model components to produce smaller dense models. However, existing methods can cause reasoning performance to collapse on long-form reasoning tasks such as AIME. We propose LayerTrim, a training-free structured pruning method that identifies redundant decoder layers and selectively trims their MLP features while preserving attention and decoder depth. LayerTrim is the first training-free structured pruning method designed to preserve long-form reasoning without gradients or recovery training. Across three reasoning language models and five benchmarks, LayerTrim outperforms existing structured pruning methods in most evaluated settings, improving average accuracy by up to 21.4 percentage points over RESP. On Qwen3-14B, LayerTrim achieves 1.24$\times$ faster prefill and 19.7% lower peak GPU memory than the dense model, while better preserving reasoning ability. It also achieves the shortest average generation length among evaluated pruned models, while retaining the highest average accuracy. These results demonstrate that LayerTrim improves reasoning efficiency through both structural compression and reduced token generation.

Hidden states change substantially across the layers of modern language models, but most layer-wise analyses focus on one aspect of that change. We propose Layer-wise Representation Dynamics (LRD), a framework with three layer-wise measurement families: Frenet (Grassmann speed and curvature) for global subspace motion, Neighborhood Retention Score (NRS) for local nearest-neighbor retention, and Graph Filtration Mutual Information (GFMI) for alignment with the final layer. Applying LRD to 31 models (encoder-based and decoder-based embedders, plus base LLMs) on 30 MTEB tasks reveals architectural and task-level differences that are not apparent from final-layer representations alone. We then use LRD for two applications: label-free model selection and inference-time layer pruning. For selection, all three model-level scores correlate positively with downstream MTEB performance, with end-to-end subspace displacement (d_{0,L}) the strongest, and the same direction holds on a smaller base-LLM MMLU panel. For pruning, GFMI is the only measurement-guided rule that beats Random at the 15% and 20% budgets and has the best median change at every budget. Frenet is effective only at the lightest budget, while NRS does not transfer from model selection to pruning. These results show that layer-wise structure provides signal for both interpretation and deployment decisions.