# Mechanistic Evidence for Preserved-but-Misaligned Representations in Non-IID FedAvg

arXiv: https://arxiv.org/abs/2512.23043 · HTML: https://mlsanity.com/paper/2512.23043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 28 Dec 2025.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 24 of 24)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [The Non-IID Data Quagmire of Decentralized Machine Learning](https://mlsanity.com/paper/1910.00189/) (2019)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [Stochastic Controlled Averaging for Federated Learning with Communication Compression](https://mlsanity.com/paper/2308.08165/) (2023)
- [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (2025)

## Abstract (arXiv)

Federated Averaging (FedAvg) often degrades under non-IID client data, but it remains unclear whether this degradation reflects the loss of client-learned representations or a failure to use representations that are still present. We study this question mechanistically in sparse client-trained vision models, using dense-model controls to test whether the observed effects depend on sparsity. Our analysis combines class-specific circuit discovery, linear probing of frozen representations, head-only finetuning, and sparse feature dictionaries. Across CNN and ResNet models on CIFAR-10 and Fashion-MNIST, severe label skew can drive some per-class accuracies near zero even when class-specific internal structure remains recoverable. Linear probes substantially outperform the aggregated classifier, head-only finetuning partially restores accuracy, and USAE transfer reveals a largely shared feature basis between IID and non-IID models. Together, these diagnostics suggest that, in our setting, non-IID FedAvg degradation is not fully explained by representational erasure; it also reflects misalignment between preserved internal structure and the final prediction pathway.