What Makes a Good Layer? Assessing the Layer-Wise Intrinsic Properties of Music Foundation Models

Music foundation models are commonly used as frozen audio feature extractors, yet selecting which layer to extract from remains largely heuristic. Current practice defaults to fixed depths or multi-layer fusion, with limited understanding of why certain layers transfer better across downstream tasks or how representation quality varies with depth and pre-training paradigm. We conduct a systematic layer-wise analysis of 12 music foundation models spanning three pre-training paradigms (masked modeling, autoregressive modeling, and contrastive learning), characterizing their hidden representations through intrinsic geometric and transformation-based properties. Correlating label-free representation-quality metrics with layer-wise performance across 15 downstream tasks, we find that several metrics track layer quality for genre classification, emotion recognition, automatic tagging, and beat tracking, albeit with varying strength across tasks and pre-training paradigms. However, all metrics fail on tonal tasks such as key estimation and chord recognition, indicating that no single property serves as a general proxy for representation quality across music information retrieval tasks. To address this gap, we introduce a pitch-transposition equivariance measure that captures properties missed by these standard metrics, providing a consistent indicator of tonal quality across model families. Finally, we show that intrinsic metrics can serve as effective proxies for layer selection, matching or outperforming trainable multi-layer fusion methods, particularly in limited-data settings.

Task- and dataset-specific information in protein language models

Protein language models (PLMs) have transferred the latest advances from natural language processing to computational biology. These models, trained on large corpora of protein sequence data, are widely used to translate amino acid sequences into latent-space embeddings, ready for use in diverse downstream tasks (DTs). By a common consensus, embeddings from the model's last layer are used, and the model's internal behavior remains poorly understood. We analyzed 13 PLMs across 15 DTs from 11 datasets to investigate the informativeness of embeddings created in intermediate PLM layers. We trained probe models on embeddings from each layer, compared their performance, and computed characteristics of the latent spaces they span to estimate the information they contain, and found that the last layers of PLMs rarely contained embeddings that led to the best results on downstream tasks. Furthermore, we identified a connection between DTs and the distribution across PLMs' layers of the relevant information to predict that task. For example, similarity between the pre-training objective and the objective of predicting properties of individual residues leads to a steady increase in understanding of such tasks across the layers of PLMs. On the other hand, for whole-protein tasks, we observe that the dataset, rather than the task itself, defines PLMs' ability to perform well on a DT. Embeddings from shallow layers of PLMs perform better for datasets that contain deep mutational scan (DMS) data, while datasets containing diverse natural proteins find most useful embeddings in the models' deeper layers. Additionally, we discover that the performance of PLMs drops significantly when tasks are introduced for artificial proteins.

MechLens: Late Crystallization of Factual Knowledge Explains Intervention Effectiveness in Language Models

Understanding where LLMs store factual knowledge is critical for hallucination mitigation. We systematically quantify Late Crystallization: factual knowledge does not gradually emerge across layers but "crystallizes" abruptly at the final layers. Across five model families (Pythia, Gemma, Qwen2.5, Llama-3.1, Mistral; 0.5--14B), 26.8%--93.4% of correct answers never enter top-10 predictions at any intermediate layer, with late emergence (>80% depth) consistent across architectures. Cross-scale (Qwen2.5-14B) and cross-benchmark (MMLU: 98.2%) results confirm generality; tuned lens rules out probe artifacts. A sentiment-classification control (0.5% for Qwen vs. 85.9% factual; 2.0% for Mistral vs. 26.8%) confirms the phenomenon is specific to factual recall. Late Crystallization yields a crystallization-guided intervention principle: CAA outperforms DoLa on moderate-crystallization models (Llama, Mistral; p<0.001), with a directionally consistent reversal on high-crystallization Qwen (+25.4% vs. +15.5% MC1, p=0.069). LayerNorm ablation shows crystallization is intrinsic to the residual stream; LN scaling (x1.2) yields +11.8% MC1 with zero inference overhead. We further reveal a Computability-Memorization Spectrum: computable knowledge crystallizes earlier (layer 22.1/28) than memorized facts (28.0/28). We release MechLens supporting five model families.

Dominant-Layer ZO: A Single Layer Dominates Zeroth-Order Fine-Tuning of LLMs

Zeroth-order (ZO) optimization enables memory-efficient fine-tuning of large language models (LLMs) using only forward passes, but it remains unclear how useful adaptation is distributed across layers. In this work, we reveal a surprising phenomenon: ZO fine-tuning is sharply dominated by a single decoding layer. Across multiple LLM families and downstream tasks, fine-tuning this dominant layer alone consistently matches or even exceeds full-model ZO fine-tuning. We further show that the dominant layer is task-agnostic but model-specific, and can be identified before training through a simple inference-only analysis of activation outliers. Specifically, the dominant layer consistently aligns with the first activation-outlier layer in the pre-trained model. To explain this phenomenon, we analyze how perturbation effects propagate under ZO optimization. We find that the dominant layer combines two key properties: high perturbation sensitivity and early placement in the residual stream, allowing perturbation-induced effects to propagate and accumulate through remaining subsequent decoding layers. As a result, this layer produces disproportionately strong and stable optimization signals under forward-only updates. Extensive experiments on LLaMA2-7B and Qwen3-8B across nine benchmarks show that dominant-layer ZO fine-tuning improves average performance over full-model MeZO and LoRA-based ZO fine-tuning while achieving up to 4.52$\times$ training speedup.