On the Learnability of Test-Time Adaptation: A Recovery Complexity Perspective

Test-time adaptation (TTA) aims to adapt models to maintain reliable performance on non-stationary test streams without requiring labeled data. Despite its empirical success, the learnability of TTA under non-stationary streams remains unexplored. A key challenge is the lack of a principled theoretical framework that simultaneously aligns with the TTA objective and captures both continuously evolving distribution shifts and intrinsic information constraints. To address this gap, we propose the first theoretical framework for studying the learnability of TTA and introduce $(ε,δ)$-Recovery Complexity and $(ε,ρ)$-TTA Learnability. Recovery complexity measures the post-shift time needed to maintain excess risk below a target level with high probability, and is further extended to TTA learnability, which measures the long-term reliability of TTA. Within this framework, we introduce a novel discrete surrogate for non-stationary test streams, enabling a unified and tractable analysis of both gradual and abrupt shifts. We derive order-wise matching lower and upper bounds on recovery complexity, revealing fundamental limits of TTA and an intrinsic adaptivity-information trade-off. These results provide unified learnability guarantees for TTA that complement regret-based analyses.

Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence. Through latent dynamics analysis, we find an inherent trade-off between stability and effectiveness in existing architectures and strategies. By conceptualizing reasoning as uncertainty reduction, we propose that convergence toward stable fixed points while preserving effectiveness represents a promising way. To this end, we propose STARS (STAbility-driven Recurrent Scaling), a training framework that constrains latent states to approach asymptotically stable fixed points. This is realized via efficient Jacobian Spectral Radius Regularization with random loop sampling, enabling STARS to maximize effectiveness while ensuring rigorous stability. Experiments on arithmetic tasks show that STARS achieves reliable test-time scaling, and on complex mathematical reasoning it substantially mitigates performance degradation as recurrence depth increases while also improving peak performance.

Revisiting the Travel Planning Capabilities of Large Language Models

Travel planning serves as a critical task for long-horizon reasoning, exposing significant deficits in LLMs. However, existing benchmarks and evaluations primarily assess final plans in an end-to-end manner, which lacks interpretability and makes it difficult to analyze the root causes of failures. To bridge this gap, we decompose travel planning into five constituent atomic sub-capabilities, including \emph{Constraint Extraction}, \emph{Tool Use}, \emph{Plan Generation}, \emph{Error Identification}, and \emph{Error Correction}. We implement a decoupled evaluation protocol leveraging oracle intermediate contexts to rigorously isolate these components, thereby measuring the atomic performance boundary without the noise of cascading errors. Our results highlight a clear contrast in performance: while LLMs are proficient in extracting explicit constraints, they struggle to infer implicit, open-world requirements. Furthermore, they exhibit structural biases in plan generation and suffer from ineffective self-correction, characterized by excessive sensitivity and erroneous persistence. These findings offer precise directions for improving LLM reasoning and planning abilities.

Programmatic Context Augmentation for LLM-based Symbolic Regression

Symbolic regression (SR), the task of discovering mathematical expressions that best describe a given dataset, remains a fundamental challenge in scientific discovery. Traditional approaches, primarily based on genetic algorithms and related evolutionary methods, have proven useful but suffer from scalability and expressivity limitations. Recently, large language model (LLM)-based evolutionary search methods have been introduced into SR and show promise. However, existing LLM-based approaches typically rely on scalar evaluation metrics, such as mean squared error, as the sole source of feedback during the search process, thereby overlooking the rich information embedded in the dataset. To address this limitation, we propose a novel LLM-based evolutionary search framework that incorporates programmatic context augmentation. By enabling code-based interactions with the dataset, our method can actively perform data analysis and extract informative signals, beyond aggregated evaluation scores. We evaluate our framework on advanced benchmarks, such as LLM-SRBench, and demonstrate superior efficiency and accuracy compared to strong baselines.

LAST: Leveraging Tools as Hints to Enhance Spatial Reasoning for Multimodal Large Language Models

Spatial reasoning is a cornerstone capability for intelligent systems to perceive and interact with the physical world. However, multimodal large language models (MLLMs) frequently suffer from hallucinations and imprecision when parsing complex geometric layouts. As data-driven scaling struggles to internalize structured geometric priors and spatial constraints, integrating mature, specialized vision models presents a compelling alternative. Despite its promise, applying this paradigm to spatial reasoning is hindered by two key challenges: The difficulty of invoking heterogeneous, parameter-rich tools, as well as the challenge of understanding and effectively leveraging their diverse low-level outputs (e.g., segmentation masks, depth maps) in high-level reasoning. To address these challenges, we propose LAST, a unified framework for tool-augmented spatial reasoning. LAST features an extensible interactive sandbox, termed LAST-Box, which abstracts heterogeneous tool invocations into atomic instructions and reusable spatial skills, returning multimodal hints (e.g., annotated images and textual descriptions) that can be directly consumed by LLMs. We further design a three-stage progressive training strategy that guides models from understanding tool outputs to proficient and adaptive tool invocation. Experiments on four datasets show that LAST-7B achieves around 20\% performance gains over its backbone and outperforms strong proprietary closed-source LLMs, substantially enhancing reasoning on complex spatial tasks.

Thinking with Tables: Enhancing Multi-Modal Tabular Understanding via Neuro-Symbolic Reasoning

Multimodal Large Language Models (MLLMs) have demonstrated remarkable reasoning capabilities across modalities such as images and text. However, tabular data, despite being a critical real-world modality, remains relatively underexplored in multimodal learning. In this paper, we focus on the task of Tabular-Vision Multi-Modal Understanding (TVMU) and identify three core challenges: (1) high structural variability and data incompleteness in tables, (2) implicit and complex feature dependencies, and (3) significant heterogeneity in problem-solving pipelines across downstream tasks. To address these issues, we propose Thinking with Tables (TWT). TWT employs a program-aided code-based neuro-symbolic reasoning mechanism that facilitates key operations, such as information extraction and element modeling, by interacting with external environments. We evaluate TWT on eight representative datasets. Experimental results demonstrate that TWT consistently outperforms existing baselines by an average of 10\% in accuracy, achieving performance comparable to, or even surpassing, proprietary commercial SOTA LLMs on TVMU tasks. Models and codes are available at https://github.com/kunyang-YU/Thinking-with-Tables

NeSy-Route: A Neuro-Symbolic Benchmark for Constrained Route Planning in Remote Sensing

Remote sensing underpins crucial applications such as disaster relief and ecological field surveys, where systems must understand complex scenes and constraints and make reliable decisions. Current remote-sensing benchmarks mainly focus on evaluating perception and reasoning capabilities of multimodal large language models (MLLMs). They fail to assess planning capability, stemming either from the difficulty of curating and validating planning tasks at scale or from evaluation protocols that are inaccurate and inadequate. To address these limitations, we introduce NeSy-Route, a large-scale neuro-symbolic benchmark for constrained route planning in remote sensing. Within this benchmark, we introduce an automated data-generation framework that integrates high-fidelity semantic masks with heuristic search to produce diverse route-planning tasks with provably optimal solutions. This allows NeSy-Route to comprehensively evaluate planning across 10,821 route-planning samples, nearly 10 times larger than the largest prior benchmark. Furthermore, a three-level hierarchical neuro-symbolic evaluation protocol is developed to enable accurate assessment and support fine-grained analysis on perception, reasoning, and planning simultaneously. Our comprehensive evaluation of various state-of-the-art MLLMs demonstrates that existing MLLMs show significant deficiencies in perception and planning capabilities. We hope NeSy-Route can support further research and development of more powerful MLLMs for remote sensing.

Beyond Single: A Data Selection Principle for LLM Alignment via Fine-Grained Preference Signals

Aligning Large Language Models (LLMs) with diverse human values requires moving beyond a single holistic "better-than" preference criterion. While collecting fine-grained, aspect-specific preference data is more reliable and scalable, existing methods like Direct Preference Optimization (DPO) struggle with the severe noise and conflicts inherent in such aggregated datasets. In this paper, we tackle this challenge from a data-centric perspective. We first derive the Direct Multi-Preference Optimization (DMPO) objective, and uncover a key Preference Divergence (PD) term that quantifies inter-aspect preference conflicts. Instead of using this term for direct optimization, we leverage it to formulate a novel, theoretically-grounded data selection principle. Our principle advocates for selecting a subset of high-consensus data-identified by the most negative PD values-for efficient DPO training. We prove the optimality of this strategy by analyzing the loss bounds of the DMPO objective in the selection problem. To operationalize our approach, we introduce practical methods of PD term estimation and length bias mitigation, thereby proposing our PD selection method. Evaluation on the UltraFeedback dataset with three varying conflict levels shows that our simple yet effective strategy achieves over 10% relative improvement against both the standard holistic preference and a stronger oracle using aggregated preference signals, all while boosting training efficiency and obviating the need for intractable holistic preference annotating, unlocking the potential of robust LLM alignment via fine-grained preference signals.

When Is Prior Knowledge Helpful? Exploring the Evaluation and Selection of Unsupervised Pretext Tasks from a Neuro-Symbolic Perspective

Neuro-symbolic (Nesy) learning improves the target task performance of models by enabling them to satisfy knowledge, while semi/self-supervised learning (SSL) improves the target task performance by designing unsupervised pretext tasks for unlabeled data to make models satisfy corresponding assumptions. We extend the Nesy theory based on reliable knowledge to the scenario of unreliable knowledge (i.e., assumptions), thereby unifying the theoretical frameworks of SSL and Nesy. Through rigorous theoretical analysis, we demonstrate that, in theory, the impact of pretext tasks on target performance hinges on three factors: knowledge learnability with respect to the model, knowledge reliability with respect to the data, and knowledge completeness with respect to the target. We further propose schemes to operationalize these theoretical metrics, and thereby develop a method that can predict the effectiveness of pretext tasks in advance. This will change the current status quo in practical applications, where the selections of unsupervised tasks are heuristic-based rather than theory-based, and it is difficult to evaluate the rationality of unsupervised pretext task selection before testing the model on the target task. In experiments, we verify a high correlation between the predicted performance-estimated using minimal data-and the actual performance achieved after large-scale semi-supervised or self-supervised learning, thus confirming the validity of the theory and the effectiveness of the evaluation method.

Automated Text-to-Table for Reasoning-Intensive Table QA: Pipeline Design and Benchmarking Insights

Reasoning with tabular data holds increasing importance in modern applications, yet comprehensive evaluation methodologies for reasoning-intensive Table Question Answering (QA) tasks remain nascent. Existing research is constrained by two primary bottlenecks: 1) Reliance on costly manually annotated real-world data, which is difficult to cover complex reasoning scenarios; 2) The heterogeneity of table structures hinders systematic analysis of the intrinsic mechanisms behind the underperformance of LLMs, especially in reasoning-intensive tasks. To address these issues, we propose an automated generation pipeline AutoT2T that transforms mathematical word problems into table-based reasoning tasks, eliminating the need for manual annotation. The pipeline can generate multiple variants of a table for the same reasoning problem, including noisy versions to support robustness evaluation. Based on this, we construct a new benchmark TabularGSM, which systematically spans a range of table complexities and trap problems. Experimental analyses through AutoT2T and TabularGSM reveal that the tight coupling between reasoning and retrieval or identification processes is a key factor underlying the failure of LLMs in complex Table QA tasks. This highlights the necessity for models to develop synergistic reasoning capabilities in order to perform effectively in complex Table QA tasks.