# Dynamical Parameters: An Interpretability Framework for Time-Series Foundation Models

arXiv: https://arxiv.org/abs/2609.34316 · HTML: https://mlsanity.com/paper/2609.34316/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Chronos-2: From Univariate to Universal Forecasting](https://mlsanity.com/paper/2510.15821/) (2025)
- [TimeGPT-1](https://mlsanity.com/paper/2310.03589/) (2023)
- [Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2310.08278/) (2023)
- [On the Internal Semantics of Time-Series Foundation Models](https://mlsanity.com/paper/2511.15324/) (2025)
- [Universal Redundancies in Time Series Foundation Models](https://mlsanity.com/paper/2602.01605/) (2026)
- [time2time: Causal Intervention in Hidden States to Simulate Rare Events in Time Series Foundation Models](https://mlsanity.com/paper/2509.05801/) (2025)
- [Dissecting Chronos: Sparse Autoencoders Reveal Causal Feature Hierarchies in Time Series Foundation Models](https://mlsanity.com/paper/2603.10071/) (2026)
- [Aionoscope: Debugging Latent-State Accessibility in Time-Series Representations](https://mlsanity.com/paper/2607.00956/) (2026)
- [Causal Analysis for Time Series Foundation Models](https://mlsanity.com/paper/2608.24303/) (2026)
- [Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control](https://mlsanity.com/paper/2602.02592/) (2026)
- [EIDOS: Latent-Space Predictive Learning for Time Series Foundation Models](https://mlsanity.com/paper/2602.14024/) (2026)

## Abstract (arXiv)

This work studies a central gap in interpreting time-series foundation models (TSFMs): a dynamical property may be accessible in a hidden state even when the forecast fails to respond correctly as that property changes. We formalize these properties as Dynamical Parameters, including trend slope, oscillation frequency, and autoregressive dependence. We compare their representation accessibility, measured by recovery from hidden states, with their forecast response, measured by agreement with the expected forecast change. Across nine frozen TSFMs and thirteen laws, 42 of 63 model-parameter cells achieve accessibility above 0.95, whereas their median reference-aligned response relative to the conditional reference is only 0.46. To explain this gap, causal geometry compares the hidden-state change required to produce the reference response with the change induced by the parameter intervention. Directly modifying the hidden state recovers the reference response, but the parameter intervention often moves the state in a different direction. These results show that accessible parameter information need not be expressed in forecasts when input changes miss the required hidden-state direction.