# CAST: Compositional Analysis via Spectral Tracking for Understanding Transformer Layer Functions

arXiv: https://arxiv.org/abs/2510.14262 · HTML: https://mlsanity.com/paper/2510.14262/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 48 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 27 of 27)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Revealing the Dark Secrets of BERT](https://mlsanity.com/paper/1908.08593/) (2019)
- [A Multiscale Visualization of Attention in the Transformer Model](https://mlsanity.com/paper/1906.05714/) (2019)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Analysis Methods in Neural Language Processing: A Survey](https://mlsanity.com/paper/1812.08951/) (2018)
- [Analyzing the Structure of Attention in a Transformer Language Model](https://mlsanity.com/paper/1906.04284/) (2019)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [Probing the Probing Paradigm: Does Probing Accuracy Entail Task Relevance?](https://mlsanity.com/paper/2005.00719/) (2020)
- [The Bottom-up Evolution of Representations in the Transformer: A Study with Machine Translation and Language Modeling Objectives](https://mlsanity.com/paper/1909.01380/) (2019)
- [The Shape of Learning: Anisotropy and Intrinsic Dimensions in Transformer-Based Models](https://mlsanity.com/paper/2311.05928/) (2023)
- [DirectProbe: Studying Representations without Classifiers](https://mlsanity.com/paper/2104.05904/) (2021)
- [AdaSVD: Adaptive Singular Value Decomposition for Large Language Models](https://mlsanity.com/paper/2502.01403/) (2025)
- [Joint Matrix Decomposition for Deep Convolutional Neural Networks Compression](https://mlsanity.com/paper/2107.04386/) (2021)
- [Exact Spectral Norm Regularization for Neural Networks](https://mlsanity.com/paper/2206.13581/) (2022)

## Built on by (most cited first, 2 of 2)

- [Dynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology](https://mlsanity.com/paper/2605.14258/) (2026)
- [Sparse Growing Transformer: Training-Time Sparse Depth Allocation via Progressive Attention Looping](https://mlsanity.com/paper/2603.23998/) (2026)

## Abstract (arXiv)

Large language models have achieved remarkable success but remain largely black boxes with poorly understood internal mechanisms. To address this limitation, many researchers have proposed various interpretability methods including mechanistic analysis, probing classifiers, and activation visualization, each providing valuable insights from different perspectives. Building upon this rich landscape of complementary approaches, we introduce CAST (Compositional Analysis via Spectral Tracking), a probe-free framework that contributes a novel perspective by analyzing transformer layer functions through direct transformation matrix estimation and comprehensive spectral analysis. CAST offers complementary insights to existing methods by estimating the realized transformation matrices for each layer using Moore-Penrose pseudoinverse and applying spectral analysis with six interpretable metrics characterizing layer behavior. Our analysis reveals distinct behaviors between encoder-only and decoder-only models, with decoder models exhibiting compression-expansion cycles while encoder models maintain consistent high-rank processing. Kernel analysis further demonstrates functional relationship patterns between layers, with CKA similarity matrices clearly partitioning layers into three phases: feature extraction, compression, and specialization.