Technical Summary: Rethinking Post-Training Recipes for Multimodal Time-Series Forecasting (POSTTIME)

Problem Formulation

Time-Series Foundation Models (TSFMs) have achieved state-of-the-art zero-shot performance on unimodal forecasting benchmarks by leveraging vast corpora of historical numerical data. However, real-world forecasting is rarely unimodal; future trajectories are frequently shaped by exogenous, non-numerical factors such as breaking news, policy changes, and domain-specific textual descriptions. TSFMs are structurally constrained to numerical inputs and cannot directly consume this multimodal context.

Conversely, Large Language Models (LLMs) excel at processing complex multimodal data and executing sophisticated reasoning but have been shown to underperform TSFMs on raw numerical predictive tasks. The central challenge addressed in this work is how to systematically unify the numerical stability of TSFMs with the multimodal reasoning capabilities of LLMs for robust forecasting. Existing approaches often attempt to convert temporal modalities or pretrain models from scratch on multimodal corpora, but this paper proposes a different paradigm: post-training off-the-shelf LLMs to act as context-guided revisers over strong numerical TSFM priors.

Methodology: The POSTTIME Recipe

The authors introduce POSTTIME, a two-stage post-training recipe designed to teach an LLM to generate context-conditioned forecast interventions. The core thesis is that the LLM should not act as a standalone forecaster but rather as a "reviser" that decides whether to preserve, ignore, or revise a base forecast generated by a TSFM (e.g., TimesFM-2.5) based on multimodal context.

1. The Role of the LLM: Reviser over Forecaster

Empirical analysis demonstrates that treating the LLM as a direct forecaster (inputting history and context to generate a forecast) yields suboptimal results compared to using the LLM as a reviser (inputting history, context, and a TSFM prior to generate a revised forecast). The reviser role simplifies the reasoning task, allowing the LLM to focus on incorporating textual information and making calibrated adjustments while anchoring predictions to the strong numerical prior of the TSFM.

2. Stage One: Supervised Fine-Tuning (SFT) with Diverse Traces

The SFT stage aims to teach the LLM effective revision strategies. The authors identify critical design choices that distinguish POSTTIME from standard practices:

• Reasoning Trace Generation: Instead of using the observed horizon (ground truth) as an imitation target—which introduces hindsight bias and is noisy for future prediction—the authors use a frontier LLM (Gemini-3.1-Flash-Lite) to generate forecast-time traces. These traces reason about the context without seeing the future, producing multiple "valid" reasoning paths where validity is defined by whether the revised forecast improves upon the TSFM prior.
• Data Sampling and Hard Cases: Unlike practices that filter for "easy" samples, POSTTIME preserves hard and ambiguous cases. The dataset includes samples where the context is weak or misleading, requiring the LLM to learn when not to revise (i.e., to fall back to the TSFM prior). This is achieved by generating five independent revisions per sample and retaining traces that cover the full spectrum of outcomes: clear improvements, ambiguous interventions, and cases where the prior should be preserved.
• Fallback Mechanism: If no generated revision improves the TSFM prior, a fallback target is inserted where the LLM is trained to explicitly state that the context does not justify a revision and to output the original prior.

3. Stage Two: Reinforcement Learning with Verifiable Rewards (RLVR)

The RL stage refines the policy to maximize revision effectiveness.

• Reward Design: Standard RL approaches often use absolute forecast accuracy (e.g., ExpMAE) as a reward. The authors argue this is insufficient for a reviser, as it does not distinguish between a good revision and a good prior. Instead, POSTTIME uses an Improvement Ratio (ImpRatio) reward, which measures the relative improvement of the revised forecast over the base TSFM prior.
• Benefits: This reward function provides stronger preference signals, reduces reward collapse (where multiple completions receive similar scores), and encourages the model to learn when a revision is actually beneficial versus when it is detrimental.

Key Contributions

1. Paradigm Shift: The paper argues for and validates a "context-guided reviser" paradigm over direct multimodal forecasting, showing that LLMs are best positioned to intervene on strong TSFM priors rather than generating forecasts from scratch.
2. POSTTIME Recipe: A novel post-training framework combining SFT with diverse, forecast-time reasoning traces and RL with improvement-based rewards.
3. Automated Data Construction: A methodology to generate high-quality, automated reasoning traces and fallback examples without human-in-the-loop annotation, effectively handling the spectrum of revision utility (from easy to impossible cases).
4. Reward Innovation: The introduction of the ImpRatio reward function, which aligns the RL objective with the specific goal of improving upon a prior rather than achieving absolute accuracy.

Experimental Results

The authors evaluated POSTTIME on the TimesX multimodal forecasting benchmark using Gemma-3-4B as the LLM and TimesFM-2.5 as the TSFM prior.

• Performance: The POSTTIME model (SFT + RL) significantly outperforms standalone TSFMs, LLM-only baselines, zero-shot LLM+TSFM revision, and existing multimodal forecasting models (including TimeOmni, Aurora, and ChatTS).
  • On the In-Domain (ID) test set, POSTTIME improved the nMAE of TimesFM-2.5 by 6.38% and nMSE by 12.43%.
  • On the Out-of-Domain (OOD) test set, it improved nMAE by 3.93% and nMSE by 11.24%.
• Ablation Studies:
  • Reviser vs. Forecaster: Revising a TSFM prior consistently outperformed direct forecasting across 8 different LLMs.
  • Trace Diversity: Including diverse reasoning traces and hard cases (fallbacks) was critical; filtering for only "easy" cases degraded tail performance (p99 metrics).
  • Reward Design: The ImpRatio reward significantly reduced reward collapse compared to standard ExpMAE rewards, leading to more stable and effective policy optimization.
  • Generalization: The recipe proved robust when applied to different base LLMs (e.g., Qwen3-4B) and different trace generators.

Significance and Claims

The paper claims that POSTTIME provides a scalable, effective recipe for bridging the gap between numerical TSFMs and multimodal LLMs. By redefining the LLM's role as a context-guided reviser and optimizing the post-training process with specific data construction and reward strategies, the approach achieves superior multimodal forecasting accuracy without requiring pretraining from scratch.

The authors emphasize that their method teaches the LLM to be "calibrated"—knowing not only how to revise but also when to preserve the numerical prior when context is insufficient. This capability is crucial for robust real-world deployment where textual context can be noisy or irrelevant. The work suggests that for multimodal time-series tasks, the most effective interaction mechanism may not be fusing modalities at the input or output of a single model, but rather using an LLM to critically evaluate and intervene upon the outputs of specialized numerical models.