LLM as Forecasting Planner: Training-Free Text Conditioning for Time-Series Foundation Models

Text-conditioned time-series forecasting predicts a series from both its numerical history and natural-language context, allowing forecasts to account for events and constraints that the past alone cannot reveal. This requires both reliable numerical forecasting and the ability to interpret contextual information. Time-series foundation models (TSFMs) provide strong numerical forecasts, while large language models (LLMs) can reason over text, but combining their strengths remains challenging because asking an LLM to generate or revise forecast values directly can distort the temporal structure captured by the TSFM. We instead formulate forecasting as a planning problem over TSFM-generated trajectories. The frozen TSFM acts as a simulator that proposes numerical continuations, while the LLM acts as a policy and value function that guides candidate selection and evaluates completed trajectories against the context. We instantiate this as \rc{} (\textbf{L}LM \textbf{A}s \textbf{F}orecasting \textbf{P}lanner), a training-free framework that bridges the modality gap without retraining either model, using Monte Carlo tree search (MCTS) over the forecast horizon with a \emph{Ranker} LLM as policy and a \emph{Judge} LLM as value function. Experiments on Context-is-Key and Time-MMD across two TSFM backbones (Chronos and TimesFM) and four LLMs show that \rc{} delivers consistent improvements across model choices, supporting sequential search as an effective training-free approach to text-conditioned forecasting.

Expert-Guided Forecast Editing for Time-Series Foundation Models

Time-series foundation models can forecast across heterogeneous domains without task-specific training, but their forecasts are fixed once produced and cannot directly incorporate task-specific expert feedback. We study expert-guided forecast editing: a frozen foundation model generates candidate future trajectories, and an expensive expert evaluator scores them to guide forecast revision. Under a tight query budget, two natural strategies sit at opposite ends: best-of-$N$ purely exploits the foundation model's predictive distribution, while optimization approaches mostly explore the forecast horizon as an unstructured high-dimensional vector. Each extreme is individually sub-optimal. We introduce \textbf{DEFT}, an expert-guided forecast editing framework that balances the two by first exploiting the foundation model's predictive samples in a decomposed trend--seasonal space, then exploring around them via component-wise refinement. DEFT queries the expert only on complete trajectories, then reuses scores for the trend and seasonal components that appeared in the queried recombinations. This lets each expert query provide structured component-level feedback while keeping the foundation model frozen. We compare DEFT against direct search approaches, including best-of-$N$, cross-entropy methods, and Bayesian optimization, under matched expert-query budgets. Across two forecasting benchmarks consisting of 78 datasets, three time-series foundation models, four feedback types, and seven query budgets, DEFT consistently improves the effectiveness of expert guidance. A molecular-dynamics case study further suggests that the same principle extends to more physically grounded feedback, supporting the hypothesis that sparse test-time guidance should be spent balancing prior exploitation with structured exploration.

Beyond Tokenization: Direct Timestep Embedding and Contrastive Alignment for Time-Series Question Answering

Recent advances in large language models (LLMs) have given rise to time-series question answering (TSQA), which formulates time-series analysis as natural-language question answering. However, directly feeding raw numerical series into LLMs suffers from a tokenization bottleneck: Byte Pair Encoding fragments continuous values into unstable tokens whose embeddings lack meaningful metric structure, resulting in the loss of magnitude, scale, and trend information. Prior methods use patch-based encoders that split the series into fixed windows, locking in one granularity that breaks patterns and hides exact timesteps, through a separate module that rarely transfers across datasets with different lengths or sampling rates. To address this challenge, we propose CADE (Contrastive Alignment with Direct Embedding), a novel framework for TSQA built upon two key components: direct timestep embedding and semantic alignment. The proposed framework maps each timestep directly into the LLM embedding space through a point-wise linear encoder and MLP projector, preserving exact index-level access while eliminating the need for patching and padding. To further bridge the semantic gap between time-series and language representations, we introduce a novel one-directional supervised contrastive loss that aligns time-series embeddings with frozen class-name text anchors. Experimental results on the public Time-MQA benchmark demonstrate that our framework consistently improves performance across six TSQA tasks, outperforming both open-source and proprietary LLM baselines.

Does Text Actually Help? Uncovering and Resolving Text Collapse in Multimodal Time Series Forecasting

Multimodal time series forecasting, which pairs numerical sequences with domain-relevant textual reports, promises to inject world knowledge into forecasting pipelines. However, we uncover a critical failure mode in existing frameworks that we term text collapse: the text branch converges to a content-independent transformation, contributing negligible discriminative signal regardless of the input description. We argue that text collapse is a consequence of a fundamental asymmetry in time series forecasting: the numerical input is strongly autocorrelated with the output, making the numerical backbone inherently dominant, while the text branch, despite carrying complementary and often critical information, is insufficiently utilized, leading to its systematic underexploitation. To address this, we propose \textbf{REST-TS} (\textbf{R}esidual-\textbf{E}xclusive \textbf{S}upervision for \textbf{T}ext in \textbf{T}ime \textbf{S}eries), which turns the asymmetry into a design principle: the numerical backbone produces its own independent numerical forecast, and the text branch is exclusively supervised to predict the structured components of the residual, the prediction gap that numbers cannot explain. Because no numerical pathway can reduce these losses, the text branch must extract genuine content from the input description. Evaluated across diverse real-world domains and backbone architectures, REST-TS achieves state-of-the-art performance and consistently demonstrates greater text-branch utilization than existing frameworks, providing strong empirical evidence that supervising the text branch on the residual compels it to extract genuine content from the input.

Spectral Retrieval-Augmented Time-Series Forecasting

Time series forecasting leverages historical patterns to predict future values, but traditional methods face challenges when dealing with complex, non-stationary patterns that are difficult to memorize during training. Retrieval-augmented approaches have emerged as promising solutions by retrieving similar historical patterns to enhance predictions. However, existing retrieval methods suffer from two fundamental limitations: spectral blindness, which overlooks critical frequency-domain characteristics that capture underlying periodic structures, and temporal recency, which treats all historical data equally without emphasizing recent, more relevant patterns. In this paper, we propose SpecReTF, a novel retrieval method that addresses these issues by converting time series into windowed frequency representations, measuring similarity with a combined metric that captures both amplitude and phase information. To balance recency and historical context, we apply an exponential moving average weighting scheme that emphasizes recent windows. Extensive experiments on benchmark datasets demonstrate that SpecReTF outperforms time-domain retrieval methods, achieving superior forecasting accuracy across diverse, non-stationary time series.

Eigenvectors of Experts are Training-free Non-collapsing Routers

Sparse Mixture of Experts (SMoE) architectures improve the training efficiency of Large Language Models (LLMs) by routing input tokens to a selected subset of specialized experts. Despite their remarkable success, both training and inference in SMoE models suffer from the expert collapse issue (Chi et al., 2022), which degrades model performance. Prior studies primarily focus on improving the router; however, such methods rely on training from scratch or fine-tuning, which requires high computational and data-processing costs. Furthermore, we demonstrate that, despite these efforts, the issue persists when advancing well-pretrained SMoE models, as evidenced by both theoretical and empirical results. To fill that gap, we analyze the advanced SMoE models and observe that the eigenvectors of expert weight matrices encode rich semantic information, pointing to an effective alternative to conventional routing strategies. Building on this insight, we propose Singular Value Decomposition SMoE (SSMoE), a novel and training-free framework that leverages spectral properties of the expert weights to address the collapse issue and enhance model performance. Extensive experiments across diverse language and vision tasks, under both clean and corrupt data settings, demonstrate the strong generalization and robustness of SSMoE. Our findings highlight how a deeper understanding of model internals can guide the development of more effective SMoE architectures. Our implementation is publicly available at https://github.com/giangdip2410/SSMoE.

Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoning

Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient: easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB), a concave integer optimization framework that reallocates a fixed sampling budget based on per-question uncertainty estimated at no additional inference cost. In Phase 1, every question receives one generation; its average negative log-likelihood (ANLL), extracted directly from output log-probabilities, serves as a difficulty signal while the generation contributes to the final vote. In Phase 2, the remaining budget is allocated by a marginal-greedy algorithm that solves a concave coverage-maximization surrogate exactly: uncertain questions receive more sampling budget while confident questions receive fewer additional samples. Evaluated on six open-weight and black-box models spanning 1.5B to 27B parameters and five reasoning benchmarks covering math, logic, and preference tasks, UAB outperforms baselines by up to +3% in average accuracy and up to +5% on individual benchmarks, with the largest gains in low-resource settings, requiring no auxiliary model or additional LLM call. Code is publicly available at https://github.com/manhitv/UAB.

Reviving Error Correction in Modern Deep Time-Series Forecasting

Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal-Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models. Code is available at https://github.com/DA2I2-SLM/UEC-STD.

Continual Fine-Tuning of Large Language Models via Program Memory

Parameter-Efficient Fine-Tuning (PEFT), particularly Low-Rank Adaptation (LoRA), has become a standard approach for adapting Large Language Models (LLMs) under limited compute. However, in continual settings where models are updated sequentially with small datasets, conventional LoRA updates struggle to balance rapid adaptation and knowledge retention. Existing methods typically treat the low-rank space as a homogeneous update region, lacking mechanisms to regulate how short-term updates are consolidated over time. We propose a continual LoRA framework with \textbf{Pro}gram memory, inspired by \textbf{C}omplementary \textbf{L}earning Systems in neuroscience. Our approach, dubbed \textbf{ProCL}, organizes LoRA adapters into structured program memory slots that are dynamically retrieved through input-conditioned attention. This enables rapid and localized adaptation, encouraging similar inputs to reuse shared adapter regions while reserving unused capacity for future data. The slots are then combined with the underlying adapter, which maintains a distributed representation that gradually accumulates knowledge across tasks to balance plasticity and stability. Our method operates entirely within the LoRA parameterization and incurs no additional inference cost. Experiments on diverse benchmarks demonstrate improved retention and reduced catastrophic forgetting over other continual LoRA strategies.

Beyond Majority Voting: Efficient Best-Of-N with Radial Consensus Score

Large language models (LLMs) frequently generate multiple candidate responses for a given prompt, yet selecting the most reliable one remains challenging, especially when correctness diverges from surface-level majority agreement. Existing approaches, such as self-consistency, rely on discrete voting, while probability-based methods often fail to capture relationships among candidate answers or tend to underweight high-quality but less frequent responses, and do not fully leverage the geometric structure of answer representations. To address these limitations, we introduce Radial Consensus Score (RCS), a simple, efficient, and training-free method for best-of-N selection. RCS models semantic consensus by computing a weighted Fréchet mean (semantic center) of answer embeddings and ranking candidates by their radial distance to this center. Importantly, RCS provides a general framework that supports multiple weighting schemes, including uniform, frequency-based, and probability-based variants, enabling flexible integration of agreement signals and model confidence while remaining fully applicable in black-box settings. Extensive experiments across seven benchmarks covering short-form QA and long-form reasoning tasks, and five open-weight models, demonstrate that RCS variants consistently outperform strong baselines, with gains becoming more pronounced as the sampling budget increases. RCS also serves as an effective drop-in replacement for majority voting in multi-agent debate and exhibits strong robustness in black-box scenarios. Overall, these results highlight geometric consensus as a scalable and broadly applicable principle for reliable answer selection, extending beyond majority voting to more expressive and robust aggregation in LLM inference.