# Attention Sinks Are Provably Necessary in Softmax Transformers: Evidence from Trigger-Conditional Tasks

arXiv: https://arxiv.org/abs/2603.11487 · HTML: https://mlsanity.com/paper/2603.11487/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 60 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [When Attention Sink Emerges in Language Models: An Empirical View](https://mlsanity.com/paper/2410.10781/) (2024)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [Why do LLMs attend to the first token?](https://mlsanity.com/paper/2504.02732/) (2025)
- [Unveiling and Harnessing Hidden Attention Sinks: Enhancing Large Language Models without Training through Attention Calibration](https://mlsanity.com/paper/2406.15765/) (2024)
- [Spectral Filters, Dark Signals, and Attention Sinks](https://mlsanity.com/paper/2402.09221/) (2024)
- [Active-Dormant Attention Heads: Mechanistically Demystifying Extreme-Token Phenomena in LLMs](https://mlsanity.com/paper/2410.13835/) (2024)
- [Seeing Clearly by Layer Two: Enhancing Attention Heads to Alleviate Hallucination in LVLMs](https://mlsanity.com/paper/2411.09968/) (2024)
- [Attention Sinks and Compression Valleys in LLMs are Two Sides of the Same Coin](https://mlsanity.com/paper/2510.06477/) (2025)
- [Massive Values in Self-Attention Modules are the Key to Contextual Knowledge Understanding](https://mlsanity.com/paper/2502.01563/) (2025)
- [Softmax is not Enough (for Sharp Size Generalisation)](https://mlsanity.com/paper/2410.01104/) (2024)
- [Prefixing Attention Sinks can Mitigate Activation Outliers for Large Language Model Quantization](https://mlsanity.com/paper/2406.12016/) (2024)
- [Sumformer: Universal Approximation for Efficient Transformers](https://mlsanity.com/paper/2307.02301/) (2023)
- [What are you sinking? A geometric approach on attention sink](https://mlsanity.com/paper/2508.02546/) (2025)
- [The Spike, the Sparse and the Sink: Anatomy of Massive Activations and Attention Sinks](https://mlsanity.com/paper/2603.05498/) (2026)
- [A Unified View of Attention and Residual Sinks: Outlier-Driven Rescaling is Essential for Transformer Training](https://mlsanity.com/paper/2601.22966/) (2026)
- [Softpick: No Attention Sink, No Massive Activations with Rectified Softmax](https://mlsanity.com/paper/2504.20966/) (2025)
- [Normalized Attention Without Probability Cage](https://mlsanity.com/paper/2005.09561/) (2020)
- [Attention Sinks in Diffusion Language Models](https://mlsanity.com/paper/2510.15731/) (2025)
- [Attention Sinks: A 'Catch, Tag, Release' Mechanism for Embeddings](https://mlsanity.com/paper/2502.00919/) (2025)
- [Mirage in the Eyes: Hallucination Attack on Multi-modal Large Language Models with Only Attention Sink](https://mlsanity.com/paper/2501.15269/) (2025)
- [Mitigating Attention Sinks and Massive Activations in Audio-Visual Speech Recognition with LLMs](https://mlsanity.com/paper/2510.22603/) (2025)

## Built on by (most cited first, 11 of 11)

- [Attention Sink in Transformers: A Survey on Utilization, Interpretation, and Mitigation](https://mlsanity.com/paper/2604.10098/) (2026)
- [Irminsul: MLA-Native Position-Independent Caching for Agentic LLM Serving](https://mlsanity.com/paper/2605.05696/) (2026)
- [Attention Sinks in Diffusion Transformers: A Causal Analysis](https://mlsanity.com/paper/2605.09313/) (2026)
- [Attention Sinks and Outliers in Attention Residuals](https://mlsanity.com/paper/2605.17887/) (2026)
- [Sink vs. diagonal patterns as mechanisms for attention switch and oversmoothing prevention](https://mlsanity.com/paper/2605.08453/) (2026)
- [Massive Activations Are Architecturally Robust: A Controlled Scratch/Commitment Residual Stream Test](https://mlsanity.com/paper/2606.20743/) (2026)
- [The Geometric Cost of Normalization: Affine Bounds on the Bayesian Complexity of Neural Networks](https://mlsanity.com/paper/2603.27432/) (2026)
- [A Mechanistic Account of Attention Sinks in GPT-2: One Circuit, Broader Implications for Mitigation](https://mlsanity.com/paper/2604.14722/) (2026)
- [Mechanistically Interpretable Neural Encoding Reveals Fine-Grained Functional Selectivity in Human Visual Cortex](https://mlsanity.com/paper/2605.16468/) (2026)
- [From Attention Masks to Inert Zero-Vector Tokens: OAttention and O-Closure for Token Dynamics](https://mlsanity.com/paper/2608.21174/) (2026)
- [Abstention and Noise Filtering: Two Missing Primitives of Softmax Attention](https://mlsanity.com/paper/2609.22005/) (2026)

## Abstract (arXiv)

Transformers often display an attention sink: probability mass concentrates on a fixed, content-agnostic position. Are sinks a byproduct of the optimization/training regime? Or are they sometimes functionally necessary in softmax Transformers? We prove that, in some settings, it is the latter: computing a simple trigger-conditional behavior necessarily induces a sink in softmax self-attention models. Our results formalize a familiar intuition: normalization over a probability simplex must force attention to collapse onto a stable anchor to realize a default state (e.g., when the model needs to ignore the input). We instantiate this with a concrete task: when a designated trigger token appears, the model must return the average of all preceding token representations, and otherwise output zero, a task which mirrors the functionality of attention heads in the wild (Barbero et al., 2025; Guo et al., 2024). We also prove that non-normalized ReLU attention can solve the same task without any sink, confirming that the normalization constraint is the fundamental driver of sink behavior. Experiments validate our predictions and demonstrate they extend beyond the theoretically analyzed setting: softmax models develop strong sinks while ReLU attention eliminates them in both single-head and multi-head variants.