# When Does Depth Matter For In-Context Learning? Adaptive Inference in Deep Transformers

arXiv: https://arxiv.org/abs/2606.16694 · HTML: https://mlsanity.com/paper/2606.16694/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 61 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [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)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [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)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Key-Value Memory Networks for Directly Reading Documents](https://mlsanity.com/paper/1606.03126/) (2016)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [The emergence of clusters in self-attention dynamics](https://mlsanity.com/paper/2305.05465/) (2023)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [Towards a Neural Statistician](https://mlsanity.com/paper/1606.02185/) (2016)
- [The mechanistic basis of data dependence and abrupt learning in an in-context classification task](https://mlsanity.com/paper/2312.03002/) (2023)
- [Meta-learning of Sequential Strategies](https://mlsanity.com/paper/1905.03030/) (2019)
- [Which Attention Heads Matter for In-Context Learning?](https://mlsanity.com/paper/2502.14010/) (2025)

## Abstract (arXiv)

Transformers perform computations through many successive attention and feedforward blocks, allowing them to learn complex correlations between a large collection of coupled variables. When does stacking successive attention-feedforward computations over many layers provide a computational advantage over a single transformer block? We address this question by examining in-context learning in generalized linear attention transformers. We first introduce a general theory of distributed inference in such transformers, subject to constraints on communication and depth. We show that such systems can exploit internal representations (`function vectors') to infer a latent context variable at increasingly finer scales over its layers. For an in-context linear regression task, the theory predicts that while one-layer transformers without feedforward blocks are optimal for Gaussian priors over the context variable, multi-layer transformers are superior for non-Gaussian, tree-like priors. Trained linear attention transformers reproduce quantitative predictions from the theory. Using causal key-patching experiments, we verify that function vectors in intermediate layers mediate adaptive routing of information. Our results suggest that depth and feedforward blocks enable transformers to implement adaptive inference, and this is advantageous when the distribution over latent variables has hierarchical structure.