# Coarse-Graining Recursive Expert Computation: Continuation-Relative Interfaces and Failure Modes

arXiv: https://arxiv.org/abs/2610.14413 · HTML: https://mlsanity.com/paper/2610.14413/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 50 references that are in the map.
- First posted on arXiv 10 Oct 2026.

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [Not All Experts are Equal: Efficient Expert Pruning and Skipping for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2402.14800/) (2024)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [BERT-of-Theseus: Compressing BERT by Progressive Module Replacing](https://mlsanity.com/paper/2002.02925/) (2020)
- [Objective Mismatch in Model-based Reinforcement Learning](https://mlsanity.com/paper/2002.04523/) (2020)
- [The Value Equivalence Principle for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2011.03506/) (2020)
- [Similarity and Matching of Neural Network Representations](https://mlsanity.com/paper/2110.14633/) (2021)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [Flow Map Language Models: One-step Language Modeling via Continuous Denoising](https://mlsanity.com/paper/2602.16813/) (2026)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Learning Student-Friendly Teacher Networks for Knowledge Distillation](https://mlsanity.com/paper/2102.07650/) (2021)
- [Streamlining Redundant Layers to Compress Large Language Models](https://mlsanity.com/paper/2403.19135/) (2024)
- [System-1.5 Reasoning: Traversal in Language and Latent Spaces with Dynamic Shortcuts](https://mlsanity.com/paper/2505.18962/) (2025)
- [Self-conditioned Flow Map Language Models via Fixed-point Flows](https://mlsanity.com/paper/2607.00714/) (2026)
- [ReplaceMe: Network Simplification via Depth Pruning and Transformer Block Linearization](https://mlsanity.com/paper/2505.02819/) (2025)
- [MoEcho: Exploiting Side-Channel Attacks to Compromise User Privacy in Mixture-of-Experts LLMs](https://mlsanity.com/paper/2508.15036/) (2025)

## Abstract (arXiv)

Computational coarse-graining aims to replace a sequence of updates with a cheaper module while preserving task performance. We present a continuation-relative evaluation framework that assesses replacements through the computation that follows them, using downstream task quality and total execution cost as joint criteria. The framework distinguishes boundary representations, summaries of skipped computation, executed operations, and downstream loss. It makes interfaces and permitted deployment information explicit, combines fine-path references with directly trained controls using the same shortened architecture, and accounts for selection overhead. An exact loss decomposition separates replacement effects at a fixed downstream action from effects of changing that action. A finite construction shows how retained information can reduce the stipulated cost of zero-error prediction under fixed information and controller restrictions. Experiments in two frozen pretrained language models show that representation fidelity and task loss can favor different fitting objectives. In a prespecified comparison on a 1.7-billion-parameter model, next-token-loss training lowers in-distribution negative log-likelihood by 0.1901 nats per scored token compared with reconstructing the skipped blocks' output, using the same optimizer and update count. This ranking reverses in all nine paired comparisons under distribution shift. In a recursive expert prototype, the jointly adapted candidate lowers task error relative to frozen-bank and router-only baselines, but trails directly trained controls, and the tested input-only selectors fail the joint quality-cost criteria. Together, the protocol and studies provide explicit criteria and diagnostics for distinguishing useful computational replacement from local approximation gains within specified interfaces and evaluation settings.