An Overview of Low-Rank Structures in the Training and Adaptation of Large Models

The rise of deep learning has revolutionized data processing and prediction in signal processing and machine learning, yet the substantial computational demands of training and deploying modern large-scale deep models present significant challenges, including high computational costs and energy consumption. Recent research has uncovered a widespread phenomenon in deep networks: the emergence of low-rank structures in weight matrices and learned representations during training. These implicit low-dimensional patterns provide valuable insights for improving the efficiency of training and fine-tuning large-scale models. Practical techniques inspired by this phenomenon, such as low-rank adaptation (LoRA) and training, enable significant reductions in computational cost while preserving model performance. In this paper, we present a comprehensive review of recent advances in exploiting low-rank structures for deep learning and shed light on their mathematical foundations. Mathematically, we present two complementary perspectives on understanding the low-rankness in deep networks: (i) the emergence of low-rank structures throughout the whole optimization dynamics of gradient and (ii) the implicit regularization effects that induce such low-rank structures at convergence. From a practical standpoint, studying the low-rank learning dynamics of gradient descent offers a mathematical foundation for understanding the effectiveness of LoRA in fine-tuning large-scale models and inspires parameter-efficient low-rank training strategies. Furthermore, the implicit low-rank regularization effect helps explain the success of various masked training approaches in deep neural networks, ranging from dropout to masked self-supervised learning.

SPIN-Bench: How Well Do LLMs Plan Strategically and Reason Socially?

Reasoning and strategic behavior in \emph{social interactions} is a hallmark of intelligence. This form of reasoning is significantly more sophisticated than isolated planning or reasoning tasks in static settings (e.g., math problem solving). In this paper, we present \textit{Strategic Planning, Interaction, and Negotiation} (\textbf{SPIN-Bench}), a new multi-domain evaluation designed to measure the intelligence of \emph{strategic planning} and \emph{social reasoning}. While many existing benchmarks focus on narrow planning or single-agent reasoning, SPIN-Bench combines classical PDDL tasks, competitive board games, cooperative card games, and multi-agent negotiation scenarios in one unified framework. The framework includes both a benchmark as well as an arena to simulate and evaluate the variety of social settings to test reasoning and strategic behavior of AI agents. We formulate the benchmark SPIN-Bench by systematically varying action spaces, state complexity, and the number of interacting agents to simulate a variety of social settings where success depends on not only methodical and step-wise decision making, but also \emph{conceptual inference} of other (adversarial or cooperative) participants. Our experiments reveal that while contemporary LLMs handle \emph{basic fact retrieval} and \emph{short-range planning} reasonably well, they encounter significant performance bottlenecks in tasks requiring \emph{deep multi-hop reasoning} over large state spaces and \emph{socially adept} coordination under uncertainty. We envision SPIN-Bench as a catalyst for future research on robust multi-agent planning, social reasoning, and human--AI teaming.

Make Optimization Once and for All with Fine-grained Guidance

Learning to Optimize (L2O) enhances optimization efficiency with integrated neural networks. L2O paradigms achieve great outcomes, e.g., refitting optimizer, generating unseen solutions iteratively or directly. However, conventional L2O methods require intricate design and rely on specific optimization processes, limiting scalability and generalization. Our analyses explore general framework for learning optimization, called Diff-L2O, focusing on augmenting sampled solutions from a wider view rather than local updates in real optimization process only. Meanwhile, we give the related generalization bound, showing that the sample diversity of Diff-L2O brings better performance. This bound can be simply applied to other fields, discussing diversity, mean-variance, and different tasks. Diff-L2O's strong compatibility is empirically verified with only minute-level training, comparing with other hour-levels.

You Only Debias Once: Towards Flexible Accuracy-Fairness Trade-offs at Inference Time

Deep neural networks are prone to various bias issues, jeopardizing their applications for high-stake decision-making. Existing fairness methods typically offer a fixed accuracy-fairness trade-off, since the weight of the well-trained model is a fixed point (fairness-optimum) in the weight space. Nevertheless, more flexible accuracy-fairness trade-offs at inference time are practically desired since: 1) stakes of the same downstream task can vary for different individuals, and 2) different regions have diverse laws or regularization for fairness. If using the previous fairness methods, we have to train multiple models, each offering a specific level of accuracy-fairness trade-off. This is often computationally expensive, time-consuming, and difficult to deploy, making it less practical for real-world applications. To address this problem, we propose You Only Debias Once (YODO) to achieve in-situ flexible accuracy-fairness trade-offs at inference time, using a single model that trained only once. Instead of pursuing one individual fixed point (fairness-optimum) in the weight space, we aim to find a "line" in the weight space that connects the accuracy-optimum and fairness-optimum points using a single model. Points (models) on this line implement varying levels of accuracy-fairness trade-offs. At inference time, by manually selecting the specific position of the learned "line", our proposed method can achieve arbitrary accuracy-fairness trade-offs for different end-users and scenarios. Experimental results on tabular and image datasets show that YODO achieves flexible trade-offs between model accuracy and fairness, at ultra-low overheads. For example, if we need $100$ levels of trade-off on the \acse dataset, YODO takes $3.53$ seconds while training $100$ fixed models consumes $425$ seconds. The code is available at https://github.com/ahxt/yodo.

Stable-SPAM: How to Train in 4-Bit More Stably than 16-Bit Adam

This paper comprehensively evaluates several recently proposed optimizers for 4-bit training, revealing that low-bit precision amplifies sensitivity to learning rates and often causes unstable gradient norms, leading to divergence at higher learning rates. Among these, SPAM, a recent optimizer featuring momentum reset and spike-aware gradient clipping, achieves the best performance across various bit levels, but struggles to stabilize gradient norms, requiring careful learning rate tuning. To address these limitations, we propose Stable-SPAM, which incorporates enhanced gradient normalization and clipping techniques. In particular, Stable-SPAM (1) adaptively updates the clipping threshold for spiked gradients by tracking their historical maxima; (2) normalizes the entire gradient matrix based on its historical $l_2$-norm statistics; and $(3)$ inherits momentum reset from SPAM to periodically reset the first and second moments of Adam, mitigating the accumulation of spiked gradients. Extensive experiments show that Stable-SPAM effectively stabilizes gradient norms in 4-bit LLM training, delivering superior performance compared to Adam and SPAM. Notably, our 4-bit LLaMA-1B model trained with Stable-SPAM outperforms the BF16 LLaMA-1B trained with Adam by up to $2$ perplexity. Furthermore, when both models are trained in 4-bit, Stable-SPAM achieves the same loss as Adam while requiring only about half the training steps. Code is available at https://github.com/TianjinYellow/StableSPAM.git.

MedHallu: A Comprehensive Benchmark for Detecting Medical Hallucinations in Large Language Models

Advancements in Large Language Models (LLMs) and their increasing use in medical question-answering necessitate rigorous evaluation of their reliability. A critical challenge lies in hallucination, where models generate plausible yet factually incorrect outputs. In the medical domain, this poses serious risks to patient safety and clinical decision-making. To address this, we introduce MedHallu, the first benchmark specifically designed for medical hallucination detection. MedHallu comprises 10,000 high-quality question-answer pairs derived from PubMedQA, with hallucinated answers systematically generated through a controlled pipeline. Our experiments show that state-of-the-art LLMs, including GPT-4o, Llama-3.1, and the medically fine-tuned UltraMedical, struggle with this binary hallucination detection task, with the best model achieving an F1 score as low as 0.625 for detecting "hard" category hallucinations. Using bidirectional entailment clustering, we show that harder-to-detect hallucinations are semantically closer to ground truth. Through experiments, we also show incorporating domain-specific knowledge and introducing a "not sure" category as one of the answer categories improves the precision and F1 scores by up to 38% relative to baselines.

Enhance-A-Video: Better Generated Video for Free

DiT-based video generation has achieved remarkable results, but research into enhancing existing models remains relatively unexplored. In this work, we introduce a training-free approach to enhance the coherence and quality of DiT-based generated videos, named Enhance-A-Video. The core idea is enhancing the cross-frame correlations based on non-diagonal temporal attention distributions. Thanks to its simple design, our approach can be easily applied to most DiT-based video generation frameworks without any retraining or fine-tuning. Across various DiT-based video generation models, our approach demonstrates promising improvements in both temporal consistency and visual quality. We hope this research can inspire future explorations in video generation enhancement.

PIPA: Preference Alignment as Prior-Informed Statistical Estimation

Offline preference alignment for language models such as Direct Preference Optimization (DPO) is favored for its effectiveness and simplicity, eliminating the need for costly reinforcement learning. Various offline algorithms have been developed for different data settings, yet they lack a unified understanding. In this study, we introduce Pior-Informed Preference Alignment (PIPA), a unified, RL-free probabilistic framework that formulates language model preference alignment as a Maximum Likelihood Estimation (MLE) problem with prior constraints. This method effectively accommodates both paired and unpaired data, as well as answer and step-level annotations. We illustrate that DPO and KTO are special cases with different prior constraints within our framework. By integrating different types of prior information, we developed two variations of PIPA: PIPA-M and PIPA-N. Both algorithms demonstrate a $3\sim10\%$ performance enhancement on the GSM8K and MATH benchmarks across all configurations, achieving these gains without additional training or computational costs compared to existing algorithms.

LLM-AutoDiff: Auto-Differentiate Any LLM Workflow

Large Language Models (LLMs) have reshaped natural language processing, powering applications from multi-hop retrieval and question answering to autonomous agent workflows. Yet, prompt engineering -- the task of crafting textual inputs to effectively direct LLMs -- remains difficult and labor-intensive, particularly for complex pipelines that combine multiple LLM calls with functional operations like retrieval and data formatting. We introduce LLM-AutoDiff: a novel framework for Automatic Prompt Engineering (APE) that extends textual gradient-based methods (such as Text-Grad) to multi-component, potentially cyclic LLM architectures. Implemented within the AdalFlow library, LLM-AutoDiff treats each textual input as a trainable parameter and uses a frozen backward engine LLM to generate feedback-akin to textual gradients -- that guide iterative prompt updates. Unlike prior single-node approaches, LLM-AutoDiff inherently accommodates functional nodes, preserves time-sequential behavior in repeated calls (e.g., multi-hop loops), and combats the "lost-in-the-middle" problem by isolating distinct sub-prompts (instructions, formats, or few-shot examples). It further boosts training efficiency by focusing on error-prone samples through selective gradient computation. Across diverse tasks, including single-step classification, multi-hop retrieval-based QA, and agent-driven pipelines, LLM-AutoDiff consistently outperforms existing textual gradient baselines in both accuracy and training cost. By unifying prompt optimization through a graph-centric lens, LLM-AutoDiff offers a powerful new paradigm for scaling and automating LLM workflows - mirroring the transformative role that automatic differentiation libraries have long played in neural network research.

SPAM: Spike-Aware Adam with Momentum Reset for Stable LLM Training

Large Language Models (LLMs) have demonstrated exceptional performance across diverse tasks, yet their training remains highly resource-intensive and susceptible to critical challenges such as training instability. A predominant source of this instability stems from gradient and loss spikes, which disrupt the learning process, often leading to costly interventions like checkpoint recovery and experiment restarts, further amplifying inefficiencies. This paper presents a comprehensive investigation into gradient spikes observed during LLM training, revealing their prevalence across multiple architectures and datasets. Our analysis shows that these spikes can be up to $1000\times$ larger than typical gradients, substantially deteriorating model performance. To address this issue, we propose Spike-Aware Adam with Momentum Reset SPAM, a novel optimizer designed to counteract gradient spikes through momentum reset and spike-aware gradient clipping. Extensive experiments, including both pre-training and fine-tuning, demonstrate that SPAM consistently surpasses Adam and its variants across various tasks, including (1) LLM pre-training from 60M to 1B, (2) 4-bit LLM pre-training,(3) reinforcement learning, and (4) Time Series Forecasting. Additionally, SPAM facilitates memory-efficient training by enabling sparse momentum, where only a subset of momentum terms are maintained and updated. When operating under memory constraints, SPAM outperforms state-of-the-art memory-efficient optimizers such as GaLore and Adam-Mini. Our work underscores the importance of mitigating gradient spikes in LLM training and introduces an effective optimization strategy that enhances both training stability and resource efficiency at scale. Code is available at https://github.com/TianjinYellow/SPAM-Optimizer.git