REATS: LLM Reasoning-based Ensemble Learning for Adaptive Time Series Forecasting

The paper introduces REATS, a framework that leverages Large Language Model (LLM) reasoning capabilities for ensemble learning in time series forecasting (TSF). The authors note that no single model can consistently achieve optimal performance across all datasets and forecasting scenarios and that existing ensemble methods rely on fixed rules or black-box models based solely on numerical inputs, failing to leverage LLM reasoning to improve ensemble effectiveness or explain weighting decisions.

The paper identifies three key advantages of LLMs for time series ensembling: (1) multimodal information fusion—LLMs can integrate textual descriptions of temporal patterns (such as trends, seasonality, and volatility) with numerical data for comprehensive reasoning; (2) flexible scalability—by modifying model descriptions in the prompts, candidate models can be flexibly adjusted without retraining; and (3) inherent interpretability—LLMs can generate natural language explanations clarifying why certain models are more suitable for the given temporal characteristics.

The paper addresses three key challenges in applying LLMs to time series ensemble learning:

1. Token cost: raw time series incur token costs that scale linearly with length, requiring a fixed-budget representation that preserves temporal semantics

2. Supervision construction: relying on LLM API calls to generate CoT for massive samples is prohibitively expensive and demands a scalable alternative, while a single optimal weight vector provides limited supervision diversity

3. GRPO adaptation: typical GRPO applications employ verifiable binary or bounded rewards (e.g., correct/incorrect), which are inadequate for continuous MSE-based optimization

The paper makes four main contributions:

1. REATS framework: an ensemble learning framework that leverages the reasoning capabilities of LLMs for TSF with systematic sample construction and two-stage fine-tuning

2. Hybrid textual–numerical input representation: with fixed token cost that activates semantic reasoning and enables rule-based CoT construction without API dependency

3. Reciprocal reward mapping: that adapts GRPO to continuous regression tasks addressing limitations of naive reward designs

4. Empirical validation: Experiments on eight benchmarks show that REATS consistently surpasses the competitive baselines while demonstrating robust OOD generalization and enhanced transfer learning

Given a univariate historical time series X = [x1, x2,..., x T] and forecast horizon H, with N candidate base forecasting models M = M1, M2,..., M N, the ensemble prediction is obtained by weighting individual predictions: Ŷ = Σ wi·Ŷi, subject to Σ wi = 1 and wi ≥ 0. The goal is to fine-tune an LLM that produces ensemble weights through explicit chain-of-thought reasoning to minimize forecasting error.

The framework extracts eight groups of temporal pattern features Φ(X) = φ sta, φ noise, φ trend, φ sea, φ ac, φ stat, φ out, φ dist, covering stationarity, noise, trend, seasonality, autocorrelation, statistical properties, IQR-based outliers, and distribution. Each feature group uses a two-level structure: an outer group header (e.g., '[trend]') followed by inner key-value pairs (e.g., 'Trend slope: -0.00454', 'Trend strength: Strong'). All values are rounded to three significant figures.

This hybrid representation provides two key benefits: (1) the token count is fixed regardless of input length (1085 tokens for both input length 96 and 512, compared to 1656→7480 for raw text), and (2) the structured format supports rule-based CoT construction, where each feature group serves as an explicit reasoning anchor.

The framework constructs a knowledge pool from training set samples with their optimal ensemble weights. For a query series X, it retrieves the top-K most similar samples using Euclidean distance: R(X) = arg min-K X - Xⱼ2. The retrieved samples provide a reference weight distribution w̄ = (1/K)Σ wⱼ, which is averaged at the raw series level into a single prototype. This grounds the LLM's reasoning in empirical model performance.

The CoT supervision follows a four-step format: (1) identify dominant temporal features; (2) analyze each candidate model's suitability; (3) interpret retrieved similar-sample weights; (4) justify the final weight allocation. The CoT is wrapped in... tags followed by ensemble weights.

Instead of relying on expensive GPT API calls, the authors propose a lightweight rule-based generation approach that achieves comparable quality without API dependency. The process follows: known oracle weights → reverse-engineer plausible explanations via rule-matching between temporal features and tool category strengths → generate natural language through template variants.

The optimal (oracle) weight vector is derived by minimizing ensemble MSE = wTGw (where G ij = (1/T)Σ e i,t·e j,t) subject to Σ wi = 1 and wi ≥ 0. The closed-form solution without non-negativity constraint is w* = G−11/(1TG−11). In practice, the full simplex-constrained quadratic program is solved with regularization G ← G + εI.

To avoid overfitting to a single supervision target, the framework generates 9 diverse weight vectors via Dirichlet sampling and multi-objective greedy selection, combined with the oracle to form K'=10 rows per sample. The selection minimizes: s(w) = (L(w) - L*)/L* - d min(w, S) - H(w), where d min is the minimum l2 distance to already-selected set S and H(w) is entropy encouraging smooth non-sparse distributions.

Weights are represented as integer percentages formatted as a compact comma-separated table, e.g., CARD,SEMixer,TimeXer,LSINet (header) / 35,25,20,20 (row 1) / 30,30,15,25 (row 2). This reduces numerical hallucination and token consumption (103 tokens vs. 292 for dictionary format).

Stage 1: Supervised Fine-Tuning (SFT) — The LLM is fine-tuned using next-token prediction on the constructed dataset, teaching it to follow the reason-then-decide format, produce pattern-aware reasoning, and learn coarse weight allocations by imitating the oracle weight distribution.

Stage 2: Group Relative Policy Optimization (GRPO) — The policy generates G candidate outputs, each parsed into K' weight rows. The composite reward consists of:

• Relative MSE Reward: r mse = (1/K')Σ 1/(1+k·δi), where δi is the MSE gap between predicted and oracle weights

• Oracle Proximity Reward: r oracle = (1/K')Σ 1/(1+k·MSE(wi, w*))

• Format Penalty: negative penalty for format violations

The overall reward is: r = λ1·r mse + λ2·r agg + λ3·r oracle + p format, with default (λ1, λ2, λ3) = (0.8, 0, 0.2).

The paper identifies two problems with the naive reward r = -δ: (1) uniform sensitivity that struggles to discriminate near-optimal candidates, and (2) unbounded range that allows outlier-dominated advantage compression in mixed-quality rollout groups.

The reciprocal mapping r = 1/(1+kδ) addresses both issues: it compresses δ into [0, 1] while concentrating sensitivity near the oracle. The paper proves that the reciprocal mapping maintains adequate sensitivity across a wide δ range with polynomial decay (O(1/δ2)), unlike exponential decay (O(e(-kδ))) or hard cutoff for linear mapping. The paper also proves a positive lower bound on reward dispersion: σ r ≥ k/(2√G·(1+kδ max)2) · maxδi - δⱼ.

The paper evaluates on eight benchmarks: ETTh1/h2, ETTm1/m2, Exchange, Weather, Electricity, and Traffic. All experiments use univariate forecasting with input and prediction length of 96, with train/val/test split ratio of 7:1:2. Metrics are MSE and MAE.

Two groups of candidates are used:

• Small specialized models: TimeXer, LSINet, CARD, TimeMixer, ModernTCN, SEMixer, DLinear, PDF, PatchTST, MLF

• Foundation models: MOMENT, Sundial, Timer, TIME-MOE, TimesFM, MOIRAI, TimerXL, Chronos

Foundation model candidates: REATS-GRPO achieves the lowest average MSE of 0.1384, reducing error by 13.3% over OptW val (0.1597) and winning on all eight datasets. The SFT→GRPO gain (0.1455→0.1384) confirms that MSE-based reward effectively refines weights beyond imitation learning.

Small model candidates: REATS-GRPO achieves 0.1080, reducing error by 20.1% over OptW tr (0.1352). Notably, zero-shot LLM ensembles fall behind traditional baselines in this setting, indicating that without fine-tuning, LLMs struggle to handle highly heterogeneous candidates.

OOD generalization: When trained on small models and evaluated on unseen foundation models, REATS-GRPO achieves 0.1442, outperforming the best traditional baseline (OptW val: 0.1564) by 7.8% and the best zero-shot LLM (DeepSeek-V3.2: 0.1626) by 11.3%.

Scalability: REATS achieves the lowest average MSE across N=2, 4, 6, and 8 candidate models, with the advantage tending to increase as more candidates are available.

Chain-of-Thought: CoT improves ID performance by 8.7% (0.1210 vs. 0.1315) and is critical for OOD generalization: without CoT, MSE degrades from 0.1719 to 0.2675 (+55.6%).

RAG: Removing RAG degrades both ID and OOD performance, with particularly large OOD degradation.

Weight format: The integer percentage table achieves the best ID accuracy (0.1210 vs. 0.1247 for decimal) and is most token-efficient (103 vs. 292 tokens for Dict) and fastest at inference (1.10 vs. 2.05 s/sample).

Diverse weight rows: Reducing K' from 10 to 1 raises average MSE from 0.1080 to 0.1190 (+10.2%), as the K' rows form a neighborhood in weight space providing richer learning signals.

Input representation: The hybrid textual–numerical format generalizes best on OOD data, as textual descriptions activate the LLM's semantic reasoning rather than relying on position-dependent numerical patterns.

The reciprocal mapping consistently achieves the lowest MSE across datasets compared to exponential, linear, and naive unbounded mappings. The paper demonstrates that standard GRPO with our reciprocal mapping consistently outperforms the evaluated optimization-level variants (DAPO, DrGRPO, GSPO, SAPO) that use the naive reward.

REATS-SFT generally achieves the lowest average MSE across source datasets compared to traditional baselines, because the text-based reasoning generalizes across datasets since it operates on semantic-level temporal characteristics rather than dataset-specific numerical distributions.

REATS generates structured chain-of-thought reasoning before producing weights, enabling users to understand why specific tools receive higher allocations. The paper shows that GRPO improves reasoning quality: "on the Weather dataset, SFT defaults to PDF (periodicity-based) for an autocorrelation-dominated series, while GRPO correctly identifies CARD (attention-based) as the primary tool with new reasoning paths, aligning with oracle weights."

The paper concludes with three key findings: (1) "GRPO with reciprocal reward mapping effectively refines weights beyond SFT imitation, and outperforms recent GRPO algorithmic variants in the continuous unbounded reward setting, with multi-row diverse weight supervision providing a denser reward signal; (2) rule-based CoT achieves comparable or better performance than API-generated CoT at zero cost, and is critical for OOD generalization; and (3) LLM-based semantic reasoning enables superior transfer learning across datasets compared to numerical-only baselines."

Based on the paper, here are the specific improvements I can make to AI systems:

Improvement: Integrate LLM-based reasoning into ensemble selection systems that currently rely on fixed rules or black-box numerical optimization. The system will analyze temporal features (trend, seasonality, noise, autocorrelation) as semantic descriptions rather than raw numbers.

Capability: The improved system can dynamically select and weight candidate models based on the meaning of the data patterns, not just statistical correlations. It can explain why certain models are chosen, making the ensemble process transparent and auditable.

Improvement: Adopt the hybrid textual–numerical input format that compresses time series into fixed-token structured features (8 groups, 2-level key-value pairs) with 3-significant-figure rounding.

Improvement: Replace expensive LLM API calls for CoT supervision with the paper's rule-based reverse-engineering approach: oracle weights → feature-tool matching → template-based natural language generation.

Improvement: Implement the Dirichlet sampling + multi-objective greedy selection (balancing error, diversity, entropy) to generate K'=10 weight vectors per sample instead of a single oracle weight.

Improvement: Replace naive rewards (r = -δ) or exponential mappings with the reciprocal function r = 1/(1+kδ) in GRPO, which compresses unbounded MSE differences into [0,1] while maintaining sensitivity near the optimum.

Improvement: Integrate the RAG module that retrieves top-K similar historical samples (by Euclidean distance) and averages their oracle weights as prior knowledge.

Improvement: Use the text-based reasoning format that operates on semantic-level temporal characteristics (e.g., strong upward trend with weekly seasonality) rather than dataset-specific numerical distributions.

Improvement: Generate the four-step CoT format: (1) dominant features, (2) per-model suitability analysis, (3) retrieved-sample interpretation, (4) final weight justification—all wrapped in tags.

Improvement: Use integer-percentage comma-separated tables (e.g., CARD,SEMixer,TimeXer,LSINet / 35,25,20,20) instead of dictionary formats.

Improvement: Implement SFT (imitation learning on rule-based CoT) followed by GRPO (policy optimization with reciprocal rewards), with the composite reward combining relative MSE, oracle proximity, and format penalties.