# TSAE: Structured Sparse Autoencoders for Interpreting Time-Series Forecasting Models

arXiv: https://arxiv.org/abs/2610.04925 · HTML: https://mlsanity.com/paper/2610.04925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Interpreting time-series and weather models, one of 13 directions in Mechanistic interpretability.
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Placed in

- Mechanistic interpretability / [Interpreting time-series and weather models](https://mlsanity.com/mechinterp/interpreting-time-series-and-weather-models/)

## Builds on (most cited first, 14 of 14)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Does Circuit Analysis Interpretability Scale? Evidence from Multiple Choice Capabilities in Chinchilla](https://mlsanity.com/paper/2307.09458/) (2023)
- [TimeSHAP: Explaining Recurrent Models through Sequence Perturbations](https://mlsanity.com/paper/2012.00073/) (2020)
- [Explaining Time Series Predictions with Dynamic Masks](https://mlsanity.com/paper/2106.05303/) (2021)

## Abstract (arXiv)

Time-series forecasting informs critical decisions in energy dispatch, industrial operations, and environmental monitoring; understanding the patterns models rely on is essential for assessing reliability and identifying failures. Input attribution identifies important variables and time segments but offers limited insight into internal features, while standard sparse autoencoder (SAE) objectives do not directly constrain cross-variable structure or temporal continuity. We introduce TSAE, a structured sparse autoencoder for forecasting representations that decomposes hidden states into individually inspectable features. TSAE organizes cross-variable structure through shared and variable-routed private dictionaries, separates feature detection from magnitude estimation with gated encoding, and constrains neighboring sparse-code changes according to raw-segment similarity. These mechanisms support analysis of variable context, activation strength, and temporal evolution. Forecast-consistency fine-tuning further improves preservation of the frozen forecaster's outputs. The accompanying TSEVAL protocol separately audits fidelity, feature coherence, and physical calibration to ground feature interpretation. In three-seed experiments with frozen PatchTST on ETTh1, ETTh2, and ETTm1, TSAE achieves the lowest hidden-state reconstruction error, normalized forecast-reconstruction error (NFRE), and feature transition rate among five SAEs at comparable per-token activity. NFRE decreases by 4.3-26.4% relative to the next-best mean. Dataset-dependent tradeoffs in selectivity, physical correlation, and calibration show that fidelity and temporal-stability gains require independent semantic validation to support feature interpretation.