Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical interpretability. This paper systematically studies matrix product states (MPS) for generative modeling and shows that unitary MPS, which is a tensor-network architecture that is both simple and expressive, offers clear benefits for unsupervised learning by reducing ambiguity in parameter updates and improving efficiency. To overcome the inefficiency of standard gradient-based MPS training, we develop a Riemannian optimization approach that casts probabilistic modeling as an optimization problem with manifold constraints, and further derive an efficient space-decoupling algorithm. Experiments on Bars-and-Stripes and EMNIST datasets demonstrate fast adaptation to data structure, stable updates, and strong performance while maintaining the efficiency and expressive power of MPS.

Gradually Excavating External Knowledge for Implicit Complex Question Answering

Recently, large language models (LLMs) have gained much attention for the emergence of human-comparable capabilities and huge potential. However, for open-domain implicit question-answering problems, LLMs may not be the ultimate solution due to the reasons of: 1) uncovered or out-of-date domain knowledge, 2) one-shot generation and hence restricted comprehensiveness. To this end, this work proposes a gradual knowledge excavation framework for open-domain complex question answering, where LLMs iteratively and actively acquire external information, and then reason based on acquired historical knowledge. Specifically, during each step of the solving process, the model selects an action to execute, such as querying external knowledge or performing a single logical reasoning step, to gradually progress toward a final answer. Our method can effectively leverage plug-and-play external knowledge and dynamically adjust the strategy for solving complex questions. Evaluated on the StrategyQA dataset, our method achieves 78.17% accuracy with less than 6% parameters of its competitors, setting new SOTA for ~10B-scale LLMs.

The Art of Efficient Reasoning: Data, Reward, and Optimization

Large Language Models (LLMs) consistently benefit from scaled Chain-of-Thought (CoT) reasoning, but also suffer from heavy computational overhead. To address this issue, efficient reasoning aims to incentivize short yet accurate thinking trajectories, typically through reward shaping with Reinforcement Learning (RL). In this paper, we systematically investigate the mechanics of efficient reasoning for LLMs. For comprehensive evaluation, we advocate for more fine-grained metrics, including length distribution conditioned on correctness and performance across a wide spectrum of token budgets ranging from 2k to 32k. First, we reveal that the training process follows a two-stage paradigm: length adaptation and reasoning refinement. After that, we conduct extensive experiments (about 0.2 million GPU hours) in a unified protocol, deconstructing training prompts and rollouts, reward shaping, and optimization strategies. In particular, a key finding is to train on relatively easier prompts, ensuring the density of positive reward signals and thus avoiding the length collapse. Meanwhile, the learned length bias can be generalized across domains. We distill all findings into valuable insights and practical guidelines, and further validate them across the Qwen3 series, ranging from 0.6B to 30B, demonstrating the robustness and generalization.

Nonparametric Teaching of Attention Learners

Attention learners, neural networks built on the attention mechanism, e.g., transformers, excel at learning the implicit relationships that relate sequences to their corresponding properties, e.g., mapping a given sequence of tokens to the probability of the next token. However, the learning process tends to be costly. To address this, we present a novel paradigm named Attention Neural Teaching (AtteNT) that reinterprets the learning process through a nonparametric teaching perspective. Specifically, the latter provides a theoretical framework for teaching mappings that are implicitly defined (i.e., nonparametric) via example selection. Such an implicit mapping is embodied through a dense set of sequence-property pairs, with the AtteNT teacher selecting a subset to accelerate convergence in attention learner training. By analytically investigating the role of attention on parameter-based gradient descent during training, and recasting the evolution of attention learners, shaped by parameter updates, through functional gradient descent in nonparametric teaching, we show for the first time that teaching attention learners is consistent with teaching importance-adaptive nonparametric learners. These new findings readily commit AtteNT to enhancing learning efficiency of attention learners. Specifically, we observe training time reductions of 13.01% for LLMs and 20.58% for ViTs, spanning both fine-tuning and training-from-scratch regimes. Crucially, these gains are achieved without compromising accuracy; in fact, performance is consistently preserved and often enhanced across a diverse set of downstream tasks.

InjectRBP: Steering Large Language Model Reasoning Behavior via Pattern Injection

Reasoning can significantly enhance the performance of Large Language Models. While recent studies have exploited behavior-related prompts adjustment to enhance reasoning, these designs remain largely intuitive and lack a systematic analysis of the underlying behavioral patterns. Motivated by this, we investigate how models' reasoning behaviors shape reasoning from the perspective of behavioral patterns. We observe that models exhibit adaptive distributions of reasoning behaviors when responding to specific types of questions, and that structurally injecting these patterns can substantially influence the quality of the models' reasoning processes and outcomes. Building on these findings, we propose two optimization methods that require no parameter updates: InjectCorrect and InjectRLOpt. InjectCorrect guides the model by imitating behavioral patterns derived from its own past correct answers. InjectRLOpt learns a value function from historical behavior-pattern data and, via our proposed Reliability-Aware Softmax Policy, generates behavioral injectant during inference to steer the reasoning process. Our experiments demonstrate that both methods can improve model performance across various reasoning tasks without requiring any modifications to model parameters, achieving gains of up to 5.34% and 8.67%, respectively.

BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models

Large language model (LLM) inference is often bounded by memory footprint and memory bandwidth in resource-constrained deployments, making quantization a fundamental technique for efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. Fundamentally, existing methods enforce a shape-invariant quantization grid (e.g., the fixed uniform intervals of UINT2) for each group, severely restricting the feasible set for error minimization. To address this, we propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients, and iteratively refines them using approximate second-order information while progressively compensating quantization errors to minimize output discrepancy. In the 2-bit regime, BPDQ enables serving Qwen2.5-72B on a single RTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit). Moreover, we provide theoretical analysis showing that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. Code: github.com/KingdalfGoodman/BPDQ.

Residual Decoding: Mitigating Hallucinations in Large Vision-Language Models via History-Aware Residual Guidance

Large Vision-Language Models (LVLMs) can reason effectively from image-text inputs and perform well in various multimodal tasks. Despite this success, they are affected by language priors and often produce hallucinations. Hallucinations denote generated content that is grammatically and syntactically coherent, yet bears no match or direct relevance to actual visual input. To address this problem, we propose Residual Decoding (ResDec). It is a novel training-free method that uses historical information to aid decoding. The method relies on the internal implicit reasoning mechanism and token logits evolution mechanism of LVLMs to correct biases. Extensive experiments demonstrate that ResDec effectively suppresses hallucinations induced by language priors, significantly improves visual grounding, and reduces object hallucinations. In addition to mitigating hallucinations, ResDec also performs exceptionally well on comprehensive LVLM benchmarks, highlighting its broad applicability.

OVD: On-policy Verbal Distillation

Knowledge distillation offers a promising path to transfer reasoning capabilities from large teacher models to efficient student models; however, existing token-level on-policy distillation methods require token-level alignment between the student and teacher models, which restricts the student model's exploration ability, prevent effective use of interactive environment feedback, and suffer from severe memory bottlenecks in reinforcement learning. We introduce On-policy Verbal Distillation (OVD), a memory-efficient framework that replaces token-level probability matching with trajectory matching using discrete verbal scores (0--9) from teacher models. OVD dramatically reduces memory consumption while enabling on-policy distillation from teacher models with verbal feedback, and avoids token-level alignment, allowing the student model to freely explore the output space. Extensive experiments on Web question answering and mathematical reasoning tasks show that OVD substantially outperforms existing methods, delivering up to +12.9% absolute improvement in average EM on Web Q&A tasks and a up to +25.7% gain on math benchmarks (when trained with only one random samples), while also exhibiting superior training efficiency. Our project page is available at https://OVD.github.io

Locate, Steer, and Improve: A Practical Survey of Actionable Mechanistic Interpretability in Large Language Models

Mechanistic Interpretability (MI) has emerged as a vital approach to demystify the opaque decision-making of Large Language Models (LLMs). However, existing reviews primarily treat MI as an observational science, summarizing analytical insights while lacking a systematic framework for actionable intervention. To bridge this gap, we present a practical survey structured around the pipeline: "Locate, Steer, and Improve." We formally categorize Localizing (diagnosis) and Steering (intervention) methods based on specific Interpretable Objects to establish a rigorous intervention protocol. Furthermore, we demonstrate how this framework enables tangible improvements in Alignment, Capability, and Efficiency, effectively operationalizing MI as an actionable methodology for model optimization. The curated paper list of this work is available at https://github.com/rattlesnakey/Awesome-Actionable-MI-Survey.

MMFormalizer: Multimodal Autoformalization in the Wild

Autoformalization, which translates natural language mathematics into formal statements to enable machine reasoning, faces fundamental challenges in the wild due to the multimodal nature of the physical world, where physics requires inferring hidden constraints (e.g., mass or energy) from visual elements. To address this, we propose MMFormalizer, which extends autoformalization beyond text by integrating adaptive grounding with entities from real-world mathematical and physical domains. MMFormalizer recursively constructs formal propositions from perceptually grounded primitives through recursive grounding and axiom composition, with adaptive recursive termination ensuring that every abstraction is supported by visual evidence and anchored in dimensional or axiomatic grounding. We evaluate MMFormalizer on a new benchmark, PhyX-AF, comprising 115 curated samples from MathVerse, PhyX, Synthetic Geometry, and Analytic Geometry, covering diverse multimodal autoformalization tasks. Results show that frontier models such as GPT-5 and Gemini-3-Pro achieve the highest compile and semantic accuracy, with GPT-5 excelling in physical reasoning, while geometry remains the most challenging domain. Overall, MMFormalizer provides a scalable framework for unified multimodal autoformalization, bridging perception and formal reasoning. To the best of our knowledge, this is the first multimodal autoformalization method capable of handling classical mechanics (derived from the Hamiltonian), as well as relativity, quantum mechanics, and thermodynamics. More details are available on our project page: MMFormalizer.github.io