# Abstention and Noise Filtering: Two Missing Primitives of Softmax Attention

arXiv: https://arxiv.org/abs/2609.22005 · HTML: https://mlsanity.com/paper/2609.22005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 53 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 30 of 46)

- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [DynamicViT: Efficient Vision Transformers with Dynamic Token Sparsification](https://mlsanity.com/paper/2106.02034/) (2021)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [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)
- [Transformer Quality in Linear Time](https://mlsanity.com/paper/2202.10447/) (2022)
- [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)
- [Do Transformer Modifications Transfer Across Implementations and Applications?](https://mlsanity.com/paper/2102.11972/) (2021)
- [NormFormer: Improved Transformer Pretraining with Extra Normalization](https://mlsanity.com/paper/2110.09456/) (2021)
- [Active-Dormant Attention Heads: Mechanistically Demystifying Extreme-Token Phenomena in LLMs](https://mlsanity.com/paper/2410.13835/) (2024)
- [Forgetting Transformer: Softmax Attention with a Forget Gate](https://mlsanity.com/paper/2503.02130/) (2025)
- [Vision Transformers Don't Need Trained Registers](https://mlsanity.com/paper/2506.08010/) (2025)
- [Mathematical Models of Computation in Superposition](https://mlsanity.com/paper/2408.05451/) (2024)
- [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)
- [Selective Attention Improves Transformer](https://mlsanity.com/paper/2410.02703/) (2024)
- [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)
- [On the Complexity of Neural Computation in Superposition](https://mlsanity.com/paper/2409.15318/) (2024)
- [Attention Sinks Are Provably Necessary in Softmax Transformers: Evidence from Trigger-Conditional Tasks](https://mlsanity.com/paper/2603.11487/) (2026)
- [Attention Sink in Transformers: A Survey on Utilization, Interpretation, and Mitigation](https://mlsanity.com/paper/2604.10098/) (2026)
- [From Data Statistics to Feature Geometry: How Correlations Shape Superposition](https://mlsanity.com/paper/2603.09972/) (2026)
- [Value-State Gated Attention for Mitigating Extreme-Token Phenomena in Transformers](https://mlsanity.com/paper/2510.09017/) (2025)

## Abstract (arXiv)

Softmax attention has two structural gaps. A head cannot abstain, because its weights sum to one, so it outputs something even when nothing is relevant. Nor can it filter what it reads, because its output is a weighted average of value vectors, passing interference as faithfully as signal. We call these missing primitives abstention and noise filtering. Recent studies report that gating the value pathway improves pretraining but attribute the gain to different causes. We show that a value gate partly supplies both primitives, which unifies the reported causes as views of one gain. We give each primitive its own mechanism in matched models of 10M to 350M parameters and measure what each contributes. The gain from gating is almost entirely abstention at 10M, whereas by 350M filtering contributes as much as abstention, so what a study observes depends on its scale. The two benefits are largely additive, with a small overlap. A gate determined by each value alone leaves the attention sink in place, whereas a query-controlled mechanism removes it. Injecting interference into the value reads shows that abstention and filtering protect against it in distinguishable ways. The same patterns appear in pretrained models up to 20B parameters.