When Does Context Routing Help? A Systematic Study of Multi-Modal Fusion in Time Series Forecasting

Multi-modal time series forecasting methods integrate auxiliary context into temporal predictions through increasingly sophisticated fusion mechanisms. A growing body of work reports substantial gains, yet it is often unclear whether they reflect genuine use of the context or incidental architectural effects. We ask a narrower, checkable question: when can auxiliary context help a forecaster at all? We identify two dataset-level conditions that must both hold: (1) the target is not dominated by a last-value shortcut (low autocorrelation rho_h), and (2) the context carries information about the target beyond history (non-zero conditional mutual information delta; when delta=0 no predictor can benefit---a distribution-free result). Through controlled experiments on MoME (a 14.3B-parameter mixture-of-experts model, 6 datasets, 10 seeds) and four additional fusion mechanisms implemented within a single-backbone testbed (5 datasets), we find that when both conditions hold, text-conditioned expert modulation contributes a sizeable MSE reduction; when either fails, the contribution collapses to the capacity floor of the modulation pathway and carries no context-attributable signal. We establish causality through two interventions: adding a shortcut to MoME suppresses routing contribution by 77-93% across 3 datasets; progressively corrupting context quality drives the context-specific benefit from +44% to negative. We validate the autocorrelation component of our diagnostic on 27 Monash Archive datasets. We provide a calibrated pre-training diagnostic that, on the datasets we test, yields no false positives in well-powered settings. We are explicit about the asymmetry of our evidence: the negative arm is broadly reliable, while the large positive magnitudes come from a single model family (MoME) and are corroborated only in direction by the testbed.

Causal Analysis for Time Series Foundation Models

Transitioning from bespoke time series models towards time series foundation models changes the relationship of model and application from one-to-one to one-to-many. This shift introduces concentration risk as many, potentially high-risk, forecasting applications are exposed to the same biases and failure modes of a single time series foundation model. At the same time, this centralization allows for economies of scale in model development and validation. In this study we investigate how biases and failure modes of time series foundation models can be identified before deployment. We propose a causal analysis framework to investigate the ability of a time series foundation model to preserve time series patterns. To achieve this, we intervene on parameterized synthetic time series generators and measure the corresponding change in model output under ceteris paribus conditions. We apply our causal analysis framework to Chronos-2 and TimesFM-2.5 and test them across six distinct time series patterns. We find safe configurations for trend and harmonic oscillation patterns. The results also indicate a bias in both models towards overestimating persistence, sudden failures for both models against the regime switch pattern and failure for TimesFM-2.5 against the energy-release pattern. Our review of the original works for both models indicates that the findings might be explained by the data used for pretraining. We conclude our study with suggestions for further model development, recommendations for application-specific model selection, and a discussion of limitations and further research directions.

Stored in Optimizer State, Valued by Later Training: A Causal Account of Subliminal Trait Transfer

Subliminal trait transfer allows a student model to acquire behavioral dispositions from teacher-generated data in which the trait is not semantically expressed. Recent work explains how such signals enter gradients, but not how they survive source removal or acquire different signs under later training. We treat parameters and optimizer moments as a single trainer state and derive an exact transport-valuation identity separating observer-independent propagation of the source perturbation from the value assigned by a future continuation and behavioral readout. State surgery identifies the first moment as a causal carrier. Transplanting it alone leaves parameters, hidden states, and outputs unchanged at the cut, yet source-free updates generate growing parameter and hidden-state differences; transplanting parameters with the first moment recovers the terminal behavioral response. Sending the same source-induced difference through matched futures produces negative, near-zero, and positive Qwen effects (-0.658, +0.008, and +0.658 seed means). This ordering recurs in all 12 Llama-3.2-1B seeds after eight updates, while state-difference norms remain nearly equal across routes. Both contrasts grow in every paired seed when the continuation extends to sixteen updates. A full-horizon costate predicts all 42 Qwen route-mean signs and all 21 resolved Llama ordinary-route signs. Observer-independent transport also replicates across Qwen, SmolLM2, and Llama, while the complete-state recurrence predicts physical, hidden, and fixed-head responses in non-LoRA MNIST systems, including CNNs trained with AdamW and momentum SGD. Together, these results identify a two-stage mechanism for subliminal trait transfer: optimizer state transports the source perturbation, and later training determines its behavioral value.

Do Time-Series Forecasters Use the Right History: Recoverability, Recovery, and Functional Use of Temporal Delays

Forecast accuracy does not tell us which past inputs produced a prediction. We separate three questions for time-series models with known delay structure: can the true delay be recovered from the observed data, does the model report it, and does the forecast actually use the same history? We first derive input-conditioned recoverability measures that separate intrinsic ambiguity from model error. We then prove that a delay report can become arbitrarily reliable while forecast risk approaches the oracle even though the predictor still uses the wrong lag. This failure also appears in finite samples on the point-delay task: among forecasts with a correct delay report and normalized excess risk within 10\% of the oracle, the reported history is functionally unused under our matched masking test in 55.4\% of N-HiTS cases and 92.7\% of TCN cases. Finally, we show that routing the prediction through the reported history removes off-report bypass paths; a hard one-hot control achieves exact fixed-report alignment. The main conclusion is simple: a good forecast, even with a correct delay report, does not show that the model used the right history.