# Attention as Conditioning: What Classical Learning Theory Predicts About Linear Transformers

arXiv: https://arxiv.org/abs/2508.08289 · HTML: https://mlsanity.com/paper/2508.08289/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 28 of 28)

- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kernel](https://mlsanity.com/paper/1908.11775/) (2019)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [Zoology: Measuring and Improving Recall in Efficient Language Models](https://mlsanity.com/paper/2312.04927/) (2023)
- [Using Fast Weights to Attend to the Recent Past](https://mlsanity.com/paper/1610.06258/) (2016)
- [Eagle and Finch: RWKV with Matrix-Valued States and Dynamic Recurrence](https://mlsanity.com/paper/2404.05892/) (2024)
- [Test-Time Training Done Right](https://mlsanity.com/paper/2505.23884/) (2025)
- [Toward Next-Generation Artificial Intelligence: Catalyzing the NeuroAI Revolution](https://mlsanity.com/paper/2210.08340/) (2022)
- [It's All Connected: A Journey Through Test-Time Memorization, Attentional Bias, Retention, and Online Optimization](https://mlsanity.com/paper/2504.13173/) (2025)
- [Relating transformers to models and neural representations of the hippocampal formation](https://mlsanity.com/paper/2112.04035/) (2021)
- [GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modeling](https://mlsanity.com/paper/2311.01927/) (2023)
- [Attention Approximates Sparse Distributed Memory](https://mlsanity.com/paper/2111.05498/) (2021)
- [Biological learning in key-value memory networks](https://mlsanity.com/paper/2110.13976/) (2021)

## Abstract (arXiv)

Attention is widely understood as an associative memory, but that description alone does not predict how the memory will behave. Predictive theories do exist, but in the literature on animal learning. We show that the state updates of the major linear-attention families are term-for-term identical with named models from a century of animal learning theory: linear attention implements Hebbian contiguity, DeltaNet implements Rescorla--Wagner error correction, and decay variants such as RetNet implement contiguity with a stimulus trace. This dictionary turns conditioning phenomena into testable statements about the in-context behavior of linear transformers, while distinguishing algebraic consequences from empirical measurements. Algebraically, it yields an exact closed form for Kamin blocking, verified in simulation to <10-7 across five learning rates. Empirically, it predicts a dissociation that survives training on generic in-context association: error-correcting attention exhibits cue competition, whereas contiguity-based attention does not. A single state also has two capacity regimes, with measured scaling exponents of 1.22 for faithful retrieval and 1.89 for identification, consistent with linear and near-quadratic predictions. Across the full head grid, retrieval error is governed primarily by total state size rather than its partition across heads, indicating that heads provide capacity rather than redundant copies. We also prove no spontaneous recovery for the analyzed single-state recurrences under cue-orthogonal retention trials; with a never-presented-cue control and probes within the trained positional range, we likewise find no recovery in trained models. Finally, we introduce PH-attention, a Pearce--Hall-inspired rule with an explicit feature-indexed associability state that yields cue-dependent learning rates and is absent from the token-computed gates we compare.