Recent efforts to accelerate LLM pretraining have focused on computationally-efficient approximations that exploit second-order structure. This raises a key question for large-scale training: how much performance is forfeited by these approximations? To probe this question, we establish a practical upper bound on iteration complexity by applying full Gauss-Newton (GN) preconditioning to transformer models of up to 150M parameters. Our experiments show that full GN updates yield substantial gains over existing optimizers, achieving a 5.4x reduction in training iterations compared to strong baselines like SOAP and Muon. Furthermore, we find that a precise layerwise GN preconditioner, which ignores cross-layer information, nearly matches the performance of the full GN method. Collectively, our results suggest: (1) the GN approximation is highly effective for preconditioning, implying higher-order loss terms may not be critical for convergence speed; (2) the layerwise Hessian structure contains sufficient information to achieve most of these potential gains; and (3) a significant performance gap exists between current approximate methods and an idealized layerwise oracle. With rising compute requirements for training large language models (LLMs), improving optimization methods has become a central strategy for improving training efficiency. Better optimizers can directly reduce the serial runtime to train an LLM, which is crucial for large-scale models that train from days to months. Optimization for LLMs has traditionally leveraged first-order methods such as SGD and Adam (Kingma & Ba, 2017).

Group Relative Policy Optimization (GRPO) has significantly advanced the reasoning ability of large language models (LLMs), particularly by boosting their mathematical performance. However, GRPO and related entropy-regularization methods still face challenges rooted in the sparse token rewards inherent to chain-of-thought (CoT). Current approaches often rely on undifferentiated token-level entropy adjustments, which frequently lead to entropy collapse or model collapse. In this work, we propose TEPO, a novel token-level framework that incorporates Markov Likelihood (sequence likelihood) links group-level rewards with tokens via token-level aggregation. Experiments show that TEPO consistently outperforms existing baselines across key metrics (including @k and accuracy). It not only sets a new state of the art on mathematical reasoning tasks but also significantly enhances training stability.

In the era of exploding survey volumes, traditional methods of spectroscopic analysis are being pushed to their limits. In response, we develop deep-REMAP, a novel deep learning framework that utilizes a regularized, multi-task approach to predict stellar atmospheric parameters from observed spectra. We train a deep convolutional neural network on the PHOENIX synthetic spectral library and use transfer learning to fine-tune the model on a small subset of observed FGK dwarf spectra from the MARVELS survey. We then apply the model to 732 uncharacterized FGK giant candidates from the same survey. When validated on 30 MARVELS calibration stars, deep-REMAP accurately recovers the effective temperature ($T_{\rm{eff}}$), surface gravity ($\log \rm{g}$), and metallicity ([Fe/H]), achieving a precision of, for instance, approximately 75 K in $T_{\rm{eff}}$. By combining an asymmetric loss function with an embedding loss, our regression-as-classification framework is interpretable, robust to parameter imbalances, and capable of capturing non-Gaussian uncertainties. While developed for MARVELS, the deep-REMAP framework is extensible to other surveys and synthetic libraries, demonstrating a powerful and automated pathway for stellar characterization.

Large Language Models (LLMs) fine-tuned for specific domains exhibit strong performance; however, the underlying mechanisms by which this fine-tuning reshapes their parametric space are not well understood. Prior works primarily focus on auto-regressive or general-purpose instruct models, leaving domain-specialised LLMs under-explored. We present the first systematic study of domain-specific fine-tuning in large medical language models. Our analysis reveals that fine-tuning modifies only a small subset of the representational subspace, essentially preserving the pre-trained model's representation. To interpret these changes in subspaces, we propose tuning vectors, a novel framework inspired by task vectors, which explicitly capture the directional parameter shifts induced by fine-tuning. We demonstrate that these vectors are critical for enhancing both instruction-following and generation quality. Furthermore, combining tuning vectors across different domains yields improved generalisation. Upon closer inspection of directional alignment, we find these vectors primarily write new directional information into the MLP layers of the model, while amplifying existing directions in attention heads. Our findings offer new insights into LLM adaptation and provide a general, interpretable framework for analysing specialisation in large language models.

SOAR, a classic symbol-based cognitive architecture, has been fostering the development of general, human-like intelligent agents. Nevertheless, its practical adoption is hindered by the laborious manual rule coding. Emerging Large Language Models (LLMs) present the immense potential for efficient rules generation. However, there is a critical gap that current research predominantly focuses on conceptual frameworks and lacks robust experimental validation. To bridge this gap, we propose \textit{N}atural \textit{L}anguage to \textit{Gen}erative \textit{Sym}bolic Rules (NL2GenSym), a novel framework that integrates LLMs with SOAR to autonomously produce generative symbolic rules from natural language. Specifically, our framework introduces a novel Execution-Grounded Generator-Critic mechanism. The LLM-based Generator, guided by a Retrieval-Augmented Generation-accessed self-evolving domain knowledge base, proposes rules from natural language. Subsequently, these rules are immediately executed within the SOAR environment to rigorously validate their correctness. Based on this execution-grounded feedback, a reflective LLM-based Critic drives the iterative refinement of these rules. Experiments on our specialized Water Jug Problem (WJP) dataset, utilizing both Gemini and Qwen series models, validate the efficacy of our framework. It achieves a success rate over 86\% in generating rules from natural language. Crucially, the framework also generates novel heuristic rules, reducing average decision cycles for solving the WJP to 1.98 times the optimal solution and 1/1000 of baseline methods. Additionally, our initial experiments show that NL2GenSym enables smaller-parameter models to achieve better performance than larger counterparts.

Large reasoning models exhibit long chain-of-thought reasoning with strategies such as backtracking and self-correction, though recent studies suggest that these abilities typically require additional training. We first investigate whether such behaviors can be elicited without any training. To this end, we propose a decoding-time approach, ThinkLogit, which utilizes logit arithmetic to tune a target large non-reasoning model for long reasoning using a substantially smaller reasoning model as the guider. We then show that we can further boost its performance by training the guider model with preference optimization over correct/incorrect reasoning pairs sampled from both the target and guider model, a setup we refer to as ThinkLogit-DPO. Our experiments demonstrate that ThinkLogit and ThinkLogit-DPO achieve a relative improvement in average accuracy by 24.5% and 29.1%, respectively, over five reasoning benchmarks using the Qwen2.5-32B guided by R1-Distill-Qwen-1.5B, a model 21x smaller. Moreover, we find that ThinkLogit remains effective when the guider and target come from different model families. It is also orthogonal to post-training methods for small models, as guiders improved through supervised distillation or reinforcement learning can be directly plugged in to yield stronger large models, offering a practical path to unlock long reasoning in large-scale models without costly post-training.

While Small Language Models (SLMs) have demonstrated promising performance on an increasingly wide array of commonsense reasoning benchmarks, current evaluation practices rely almost exclusively on the accuracy of their final answers, neglecting the validity of the reasoning processes that lead to those answers. To address this issue, we introduce ReTraceQA, a novel benchmark that introduces process-level evaluation for commonsense reasoning tasks. Our expert-annotated dataset reveals that in a substantial portion of instances (14-24%), SLMs provide correct final answers despite flawed reasoning processes, suggesting that the capabilities of SLMs are often overestimated by evaluation metrics that focus only on comparing the final answer with the ground truth. Indeed, we show that when employing strong Large Language Models (LLMs) as automated judges for reasoning-aware evaluation rather than answer-only metrics, SLM performance drops significantly across all models and datasets, with scores decreasing by up to 25%.

The operational efficiency of railway networks, a cornerstone of modern economies, is persistently undermined by the cascading effects of train delays. Accurately forecasting this delay propagation is a critical challenge for real-time traffic management. While recent research has leveraged Graph Neural Networks (GNNs) to model the network structure of railways, a significant gap remains in developing frameworks that provide multi-step autoregressive forecasts at a network-wide scale, while simultaneously offering the live, interpretable explanations needed for decision support. This paper addresses this gap by developing and evaluating a novel XGeoAI framework for live, explainable, multi-step train delay forecasting. The core of this work is a two-stage, autoregressive Graph Attention Network (GAT) model, trained on a real-world dataset covering over 40% of the Dutch railway network. The model represents the system as a spatio-temporal graph of operational events (arrivals and departures) and is enriched with granular features, including platform and station congestion. To test its viability for live deployment, the model is rigorously evaluated using a sequential, k-step-ahead forecasting protocol that simulates real-world conditions where prediction errors can compound. The results demonstrate that while the proposed GATv2 model is challenged on pure error metrics (MAE) by a simpler Persistence baseline, it achieves consistently higher precision in classifying delay events -- a crucial advantage for a reliable decision support tool.

Unlike Business-to-Consumer e-commerce platforms (e.g., Amazon), inexperienced individual sellers on Consumer-to-Consumer platforms (e.g., eBay) often face significant challenges in setting prices for their second-hand products efficiently. Therefore, numerous studies have been proposed for automating price prediction. However, most of them are based on static regression models, which suffer from poor generalization performance and fail to capture market dynamics (e.g., the price of a used iPhone decreases over time). Inspired by recent breakthroughs in Large Language Models (LLMs), we introduce LLP, the first LLM-based generative framework for second-hand product pricing. LLP first retrieves similar products to better align with the dynamic market change. Afterwards, it leverages the LLMs' nuanced understanding of key pricing information in free-form text to generate accurate price suggestions. To strengthen the LLMs' domain reasoning over retrieved products, we apply a two-stage optimization, supervised fine-tuning (SFT) followed by group relative policy optimization (GRPO), on a dataset built via bidirectional reasoning. Moreover, LLP employs a confidence-based filtering mechanism to reject unreliable price suggestions. Extensive experiments demonstrate that LLP substantially surpasses existing methods while generalizing well to unseen categories. We have successfully deployed LLP on Xianyu\footnote\{Xianyu is China's largest second-hand e-commerce platform.\}, significantly outperforming the previous pricing method. Under the same 30\% product coverage, it raises the static adoption rate (SAR) from 40\% to 72\%, and maintains a strong SAR of 47\% even at 90\% recall.

Although large language models (LLM) have achieved remarkable performance, their enormous parameter counts hinder deployment on resource-constrained hardware. Low-rank compression can reduce both memory usage and computational demand, but applying a uniform compression ratio across all layers often leads to significant performance degradation, and previous methods perform poorly during decoding. To address these issues, we propose the Fine-grained Low-Rank Compressor (FLRC), which efficiently determines an optimal rank allocation for each layer, and incorporates progressive low-rank decoding to maintain text generation quality. Comprehensive experiments on diverse benchmarks demonstrate the superiority of FLRC, achieving up to a 17% improvement in ROUGE-L on summarization tasks compared to state-of-the-art low-rank compression methods, establishing a more robust and efficient framework to improve LLM inference.