Technical Summary: Reasoning-Aware Training for Time Series Forecasting (STRIDE)

1. Problem Statement

Time Series Foundation Models (TSFMs) have established new baselines in numerical forecasting by leveraging large-scale pretraining. However, they operate as "black boxes," functioning purely as mathematical extrapolators that lack qualitative reasoning. They approximate the conditional distribution $P(Y|X)$ using only continuous numerical representations, rendering them blind to semantic context, external variables (e.g., holidays, economic shifts), and the ability to articulate predictive logic.

Conversely, directly applying Large Language Models (LLMs) to time series forecasting introduces a significant "modality gap." Forcing continuous temporal signals through discrete text tokenizers fragments numerical values, degrading mathematical precision and exploding sequence lengths, which leads to computational bottlenecks and information loss. Recent studies suggest that using LLMs alone for forecasting often fails to meaningfully outperform TSFMs due to these structural limitations.

The core challenge addressed by this work is how to integrate the semantic reasoning capabilities of LLMs with the numerical precision of TSFMs without incurring the information loss associated with discrete tokenization or the computational overhead of autoregressive numerical generation.

2. Methodology: STRIDE Framework

The authors propose STRIDE (Strategic Time-series Reasoning Injected via Distilled Embeddings), a framework that natively integrates LLM reasoning into the continuous embedding space of TSFMs. The approach avoids discrete tokenization entirely, instead using a cross-modal latent projection mechanism.

Core Architecture

The framework consists of two primary branches fused via a generalized latent projection:

1. Textual Reasoning Branch: A lightweight "Student" LLM generates analytical strategies.
2. Numerical Forecasting Branch: A target TSFM (e.g., Chronos-2, Timer-S1) performs the actual numerical prediction.

Training Pipeline

The training process is divided into two phases:

Phase 1: Oracle Reasoning Generation (Offline)

• A powerful "Teacher" LLM (e.g., Gemini-3.1-Pro) generates high-quality, step-by-step "oracle" reasoning ($R_{ref}$).
• This generation utilizes historical context ($X$), pseudo-future ground truth ($Y$), and retrieved external events ($E$) to create a concrete, structured reasoning trace that details expected trends, seasonality, and residual impacts.

Phase 2: Joint Optimization (Online)

• Reasoning Distillation: A lightweight Student LLM is trained to generate equivalent analytical insights ($\hat{R}$) using only the historical context ($X$) and a baseline reasoning draft. It does not have access to future ground truth.
• Cross-Modal Latent Projection: Instead of passing text tokens to the forecaster, the framework extracts the continuous mean-pooled hidden states ($h_R$) from the Student LLM. These states are projected via a trainable linear matrix ($W_{proj}$) into the exact dimensionality of the target TSFM's embedding space, creating a continuous reasoning prior ($e_R$).
• Latent Fusion: The reasoning prior ($e_R$) is fused with the native time series embeddings ($E_{TS}$) using a generalized operator (either sequence prefixing or initial state substitution).
• Joint Loss Function: The entire pipeline is optimized end-to-end using a combined objective:
  $$L_{total} = \alpha L_{CE} + \beta L_{Quantile}$$
  Where $L_{CE}$ is the cross-entropy loss for the textual reasoning generation, and $L_{Quantile}$ is the quantile loss for the numerical forecasting.

Inference

During evaluation, the Student LLM generates explicit semantic reasoning ($\hat{R}$) and its hidden states are simultaneously projected into the TSFM. The TSFM, conditioned on this injected strategic guide, outputs future quantiles. This allows the system to produce both human-interpretable reasoning and continuous numerical forecasts in a single forward pass.

3. Key Contributions

The paper outlines three primary contributions:

1. A Novel Cross-Modal Framework: STRIDE utilizes a generalized latent projection mechanism to inject LLM reasoning directly into TSFM embedding spaces. This bypasses the discrete token bottleneck, preserving mathematical precision while enabling semantic guidance.
2. A Reasoning Distillation Pipeline: The framework enables a lightweight student LLM to generate high-quality, statistically grounded analytical strategies using strictly historical context, distilled from a teacher model that has access to future ground truth.
3. Superior Numerical and Reasoning Performance: The framework demonstrates state-of-the-art performance on both numerical accuracy and reasoning quality benchmarks, acting as a model-agnostic, plug-and-play enhancement.

4. Experimental Results

The framework was evaluated on two large-scale benchmarks: GIFT-Eval (for numerical precision) and TFRBench (for generalizability and reasoning quality).

Numerical Forecasting Performance

• GIFT-Eval: STRIDE achieved state-of-the-art results with a Mean Absolute Scaled Error (MASE) of 0.674 and a Continuous Ranked Probability Score (CRPS) of 0.454, outperforming leading TSFMs like Chronos-2 and Timer-S1. Integrating STRIDE with Timer-S1 reduced its MASE from 0.693 to 0.674.
• TFRBench:
  • In-Domain: Achieved an average MASE of 0.615, outperforming the best baseline (Chronos-2.0 at 0.765).
  • Out-of-Domain: Achieved an average MASE of 0.724, outperforming the best baseline (Chronos-2.0 at 0.778).
  • The framework consistently improved diverse TSFMs (e.g., Chronos-2, Timer-S1) across various configurations.

Reasoning Performance

Evaluated via an "LLM-as-a-Judge" protocol on TFRBench across four metrics (Domain Relevance, Forecasting Correctness, Event Relevance, Logic-to-Number Consistency):

• STRIDE consistently achieved the highest average scores across both in-domain and out-of-domain settings.
• It demonstrated superior "Logic-to-Number Consistency," ensuring that the generated narrative strictly aligned with the numerical forecast, avoiding the hallucinations common in zero-shot LLM forecasters.
• Ablation studies confirmed that the performance gains are robust across different student LLMs (e.g., Gemma-3-4B-it, Qwen3-4B-Instruct) and teacher LLMs (e.g., Gemini-3.1-Pro, Claude-Sonnet-4.5).

5. Significance and Claims

The authors claim that STRIDE fundamentally bridges the gap between qualitative reasoning and continuous numerical forecasting. By treating the LLM's reasoning as a control signal injected into the latent space, the framework:

• Reduces Predictive Variance: Theoretical analysis suggests that injecting reasoning priors helps isolate the true future mode among multiple plausible trajectories, thereby reducing forecast variance.
• Provides Inherent Interpretability: Unlike post-hoc explainability methods (e.g., SHAP), STRIDE generates "inherent interpretability" by producing natural language reasoning traces that explain why a prediction is made, grounded in cross-channel dependencies and events.
• Resolves the Modality Gap: By decoupling the modalities—using continuous hidden states for the forecaster and text generation for the reasoning—the framework avoids the mathematical degradation caused by tokenizing numerical time series.

The paper concludes that STRIDE serves as a robust, plug-and-play enhancement for foundational architectures, equipping black-box numerical extrapolators with strategic planning capabilities and human-interpretable reasoning, which is critical for responsible deployment in high-stakes domains.