# Spectral Filters, Dark Signals, and Attention Sinks

arXiv: https://arxiv.org/abs/2402.09221 · HTML: https://mlsanity.com/paper/2402.09221/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [CCNet: Extracting High Quality Monolingual Datasets from Web Crawl Data](https://mlsanity.com/paper/1911.00359/) (2019)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Information-Theoretic Probing with Minimum Description Length](https://mlsanity.com/paper/2003.12298/) (2020)
- [Information-Theoretic Probing for Linguistic Structure](https://mlsanity.com/paper/2004.03061/) (2020)
- [Analyzing Transformers in Embedding Space](https://mlsanity.com/paper/2209.02535/) (2022)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [Jump to Conclusions: Short-Cutting Transformers With Linear Transformations](https://mlsanity.com/paper/2303.09435/) (2023)
- [Neurons in Large Language Models: Dead, N-gram, Positional](https://mlsanity.com/paper/2309.04827/) (2023)

## Built on by (most cited first, 30 of 56)

- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Do Llamas Work in English? On the Latent Language of Multilingual Transformers](https://mlsanity.com/paper/2402.10588/) (2024)
- [When Attention Sink Emerges in Language Models: An Empirical View](https://mlsanity.com/paper/2410.10781/) (2024)
- [See What You Are Told: Visual Attention Sink in Large Multimodal Models](https://mlsanity.com/paper/2503.03321/) (2025)
- [Why do LLMs attend to the first token?](https://mlsanity.com/paper/2504.02732/) (2025)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [Information Flow Routes: Automatically Interpreting Language Models at Scale](https://mlsanity.com/paper/2403.00824/) (2024)
- [A Simple and Effective L2 Norm-Based Strategy for KV Cache Compression](https://mlsanity.com/paper/2406.11430/) (2024)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [Confidence Regulation Neurons in Language Models](https://mlsanity.com/paper/2406.16254/) (2024)
- [Attention Sinks and Compression Valleys in LLMs are Two Sides of the Same Coin](https://mlsanity.com/paper/2510.06477/) (2025)
- [Mitigating Overthinking in Large Reasoning Models via Manifold Steering](https://mlsanity.com/paper/2505.22411/) (2025)
- [Multimodal Chain of Continuous Thought for Latent-Space Reasoning in Vision-Language Models](https://mlsanity.com/paper/2508.12587/) (2025)
- [What are you sinking? A geometric approach on attention sink](https://mlsanity.com/paper/2508.02546/) (2025)
- [Locate, Steer, and Improve: A Practical Survey of Actionable Mechanistic Interpretability in Large Language Models](https://mlsanity.com/paper/2601.14004/) (2026)
- [Transferring Linear Features Across Language Models With Model Stitching](https://mlsanity.com/paper/2506.06609/) (2025)
- [To Sink or Not to Sink: Visual Information Pathways in Large Vision-Language Models](https://mlsanity.com/paper/2510.08510/) (2025)
- [Attention Sinks in Diffusion Language Models](https://mlsanity.com/paper/2510.15731/) (2025)
- [Dense SAE Latents Are Features, Not Bugs](https://mlsanity.com/paper/2506.15679/) (2025)
- [Mitigating Attention Sinks and Massive Activations in Audio-Visual Speech Recognition with LLMs](https://mlsanity.com/paper/2510.22603/) (2025)
- [Attention Sinks Are Provably Necessary in Softmax Transformers: Evidence from Trigger-Conditional Tasks](https://mlsanity.com/paper/2603.11487/) (2026)
- [More Expressive Attention with Negative Weights](https://mlsanity.com/paper/2411.07176/) (2024)
- [Calibration Across Layers: Understanding Calibration Evolution in LLMs](https://mlsanity.com/paper/2511.00280/) (2025)
- [OrthoRank: Token Selection via Sink Token Orthogonality for Efficient LLM inference](https://mlsanity.com/paper/2507.03865/) (2025)
- [Don't Deceive Me: Mitigating Gaslighting through Attention Reallocation in LMMs](https://mlsanity.com/paper/2504.09456/) (2025)
- [Frame Representation Hypothesis: Multi-Token LLM Interpretability and Concept-Guided Text Generation](https://mlsanity.com/paper/2412.07334/) (2024)
- [All for One: LLMs Solve Mental Math at the Last Token With Information Transferred From Other Tokens](https://mlsanity.com/paper/2509.09650/) (2025)
- [Why Attention Patterns Exist: A Unifying Temporal Perspective Analysis](https://mlsanity.com/paper/2601.21709/) (2026)
- [On the Existence and Behavior of Secondary Attention Sinks](https://mlsanity.com/paper/2512.22213/) (2025)
- [Surgery: Mitigating Harmful Fine-Tuning for Large Language Models via Attention Sink](https://mlsanity.com/paper/2602.05228/) (2026)

## Abstract (arXiv)

Projecting intermediate representations onto the vocabulary is an increasingly popular interpretation tool for transformer-based LLMs, also known as the logit lens. We propose a quantitative extension to this approach and define spectral filters on intermediate representations based on partitioning the singular vectors of the vocabulary embedding and unembedding matrices into bands. We find that the signals exchanged in the tail end of the spectrum are responsible for attention sinking (Xiao et al. 2023), of which we provide an explanation. We find that the loss of pretrained models can be kept low despite suppressing sizable parts of the embedding spectrum in a layer-dependent way, as long as attention sinking is preserved. Finally, we discover that the representation of tokens that draw attention from many tokens have large projections on the tail end of the spectrum.