# Programs-of-Layers in LLMs through the Lens of Cortical Areas

arXiv: https://arxiv.org/abs/2609.31360 · HTML: https://mlsanity.com/paper/2609.31360/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 68 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [HippoRAG: Neurobiologically Inspired Long-Term Memory for Large Language Models](https://mlsanity.com/paper/2405.14831/) (2024)
- [BERT Loses Patience: Fast and Robust Inference with Early Exit](https://mlsanity.com/paper/2006.04152/) (2020)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [LaCo: Large Language Model Pruning via Layer Collapse](https://mlsanity.com/paper/2402.11187/) (2024)
- [Looped Transformers for Length Generalization](https://mlsanity.com/paper/2409.15647/) (2024)
- [DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving](https://mlsanity.com/paper/2407.13690/) (2024)
- [Deep Neural Networks Reveal a Gradient in the Complexity of Neural Representations across the Brain's Ventral Visual Pathway](https://mlsanity.com/paper/1411.6422/) (2014)
- [Coordination Among Neural Modules Through a Shared Global Workspace](https://mlsanity.com/paper/2103.01197/) (2021)
- [MoEUT: Mixture-of-Experts Universal Transformers](https://mlsanity.com/paper/2405.16039/) (2024)
- [Inner Thinking Transformer: Leveraging Dynamic Depth Scaling to Foster Adaptive Internal Thinking](https://mlsanity.com/paper/2502.13842/) (2025)
- [Transformer Layers as Painters](https://mlsanity.com/paper/2407.09298/) (2024)
- [Memory Layers at Scale](https://mlsanity.com/paper/2412.09764/) (2024)
- [Rosetta Neurons: Mining the Common Units in a Model Zoo](https://mlsanity.com/paper/2306.09346/) (2023)
- [Adaptive Layer-skipping in Pre-trained LLMs](https://mlsanity.com/paper/2503.23798/) (2025)
- [Continuous Thought Machines](https://mlsanity.com/paper/2505.05522/) (2025)
- [Block-Recurrent Dynamics in Vision Transformers](https://mlsanity.com/paper/2512.19941/) (2025)

## Built on by (most cited first, 1 of 1)

- [Input-Blind Controls Produce Substantial Oracle Headroom for Layer Programs in Multiple-Choice Evaluation](https://mlsanity.com/paper/2610.10368/) (2026)

## Abstract (arXiv)

Inference in LLMs is conventionally a fixed-depth, fixed-order forward pass through every layer, regardless of how difficult the input is. The human brain does not work this way: using the thalamus as a central hub, it routes information flexibly to all regions of the cortex according to demand. Li et al. (2026) recently showed, with a system they call program-of-layers (PoLar), that transformers can be given an analogous flexibility if their layers are treated as a library of functions rather than a fixed sequence. Performance improves over the standard forward pass when each input is dynamically routed through an adaptive sequence of skipped or repeated contiguous layer blocks. We reconstructed PoLar's diagnostic MCTS in more detail than the original paper and applied it across 5 models. We reproduced several of PoLar's findings: skipping outperformed the standard pass, repeating outperformed skipping, and combining both outperformed either alone. Shorter programs sufficed for easier questions, while harder questions required more layer repeats. However, we failed to replicate the main claim regarding their learned router for single-shot inference: its top-ranked prediction consistently collapsed back to the standard pass, even though its top-k predicted programs, taken together, did show a real accuracy gain. Beyond reproduction, we find that a small number of generic programs are enough to solve most of the questions. We also provide a much deeper analysis of these programs' structure and robustness: for example, we found that programs that correct errors are highly brittle: undoing even a single edit inside a program typically breaks the correction. Connecting this to the brain's routing mechanisms, PoLar mirrors principles of thalamo-cortical coordination between cortical-area-like transformer layers. We publicly release the code at https://datexis.github.io/RE-PoLar/