Expected Value Alignment for Generative Reward Modeling in Formal Mathematics Verification

Large Language Models (LLMs) are increasingly used with formal interactive theorem provers such as Lean 4. Scaling these systems with reinforcement learning or search methods requires process reward models (PRMs) that can evaluate intermediate reasoning steps. Existing reward-model designs expose a practical trade-off. Value-head models provide continuous scores but modify the generative model interface, while generative reward models preserve textual rationales but are poorly matched to continuous floating-point regression because numeric values are split across tokens. We introduce Expected Value Alignment (EVA), a reward-modeling procedure that keeps the surface output discrete while extracting continuous scores from the model's token distribution. The model emits integer scores in a structured JSON format, and EVA computes a continuous score as the expectation over the logits of the corresponding anchor tokens. Training combines the causal language modeling objective with an auxiliary mean squared error loss on these expected values. We instantiate EVA in \textit{Leibniz}, a reward model for Lean 4 formal verification, and evaluate it against zero-shot and reward-modeling baselines. The evaluation demonstrates that continuous logit-based scoring significantly reduces discretization artifacts while retaining the interpretability of generative critiques.

Soft-NBCE: Entropy-Weighted Chunk Fusion for Long-Context

The quadratic complexity of self-attention remains a bottleneck for Large Language Models (LLMs) processing ultra-long contexts. The Naive Bayes Cognitive Engine (NBCE) parallelizes long-context inference by chunking documents and routing to the lowest-entropy chunk at each decoding step. This hard-selection strategy causes semantic fragmentation during cross-chunk reasoning, as abrupt routing changes between adjacent tokens disrupt the model's contextual grounding. We present Soft-NBCE, a lightweight extension that replaces discrete chunk selection with soft entropy-weighted chunk fusion. A temperature-scaled Softmax over predictive entropies assigns continuous weights to all chunks, enabling log-space aggregation across chunk-conditioned distributions. To partially compensate for the conditional independence assumption introduced by chunking, we propose Consistency Distillation, a LoRA-based self-distillation that constrains the chunked logit distribution toward a full-context teacher via KL-divergence. On LongBench multi-hop benchmarks, Soft-NBCE with Consistency Distillation improves consistently over NBCE-style baselines (MuSiQue F1: 0.310 vs.\ 0.275 for Vanilla NBCE; HotpotQA F1: 0.479 vs.\ 0.427) while maintaining retrieval accuracy (NIAH-32K: 0.909) at O(L^2/n) peak memory.

Bayesian Model Merging

Model merging aims to combine multiple task-specific expert models into a single model without joint retraining, offering a practical alternative to multi-task learning when data access or computational budget is limited. Existing methods, however, face two key limitations: (1) they overlook the valuable inductive bias of strong anchor models and estimate the merged weights from scratch, and (2) they rely on a shared hyperparameter setting across different modules of the network, lacking a global optimization strategy. This paper introduces Bayesian Model Merging (BMM), a plug-and-play bi-level optimization framework, where the inner level formulates the model merging as an activation-based Bayesian regression under a strong prior induced by an anchor model, yielding an efficient closed-form solution; and the outer level leverages a Bayesian optimization procedure to search module-specific hyperparameters globally based on a small validation set. Furthermore, we reveal a key alignment between activation statistics and task vectors, enabling us to derive a data-free variant of BMM that estimates the Gram matrix for regression without any auxiliary data. Across extensive benchmarks, including up to 20-task merging in vision and 5-task merging in language, BMM consistently outperforms all plug-and-play anchor baselines (e.g., TA, WUDI-Merging, and TSV). In particular, on the ViT-L/14 benchmark for 8-task merging, a single merged model reaches 95.1, closely matching the average performance of eight task-specific experts (95.8).

Low-Rank Adaptation for Critic Learning in Off-Policy Reinforcement Learning

Scaling critic capacity is a promising direction for enhancing off-policy reinforcement learning (RL). However, larger critics are prone to overfitting and unstable in replay-buffer-based bootstrap training. This paper leverages Low-Rank Adaptation (LoRA) as a structural-sparsity regularizer for off-policy critics. Our approach freezes randomly initialized base matrices and solely optimizes low-rank adapters, thereby constraining critic updates to a low-dimensional subspace. Built on top of SimbaV2, we further develop a LoRA formulation, compatible with SimbaV2, that preserves its hyperspherical normalization geometry under frozen-backbone training. We evaluate our method with SAC and FastTD3 on DeepMind Control locomotion and IsaacLab robotics benchmarks. LoRA consistently achieves lower critic loss during training and stronger policy performance. Extensive experiments demonstrate that adaptive low-rank updates provide a simple, scalable, and effective structural regularization for critic learning in off-policy RL.

Approximate Subgraph Matching with Neural Graph Representations and Reinforcement Learning

Approximate subgraph matching (ASM) is a task that determines the approximate presence of a given query graph in a large target graph. Being an NP-hard problem, ASM is critical in graph analysis with a myriad of applications ranging from database systems and network science to biochemistry and privacy. Existing techniques often employ heuristic search strategies, which cannot fully utilize the graph information, leading to sub-optimal solutions. This paper proposes a Reinforcement Learning based Approximate Subgraph Matching (RL-ASM) algorithm that exploits graph transformers to effectively extract graph representations and RL-based policies for ASM. Our model is built upon the branch-and-bound algorithm that selects one pair of nodes from the two input graphs at a time for potential matches. Instead of using heuristics, we exploit a Graph Transformer architecture to extract feature representations that encode the full graph information. To enhance the training of the RL policy, we use supervised signals to guide our agent in an imitation learning stage. Subsequently, the policy is fine-tuned with the Proximal Policy Optimization (PPO) that optimizes the accumulative long-term rewards over episodes. Extensive experiments on both synthetic and real-world datasets demonstrate that our RL-ASM outperforms existing methods in terms of effectiveness and efficiency. Our source code is available at https://github.com/KaiyangLi1992/RL-ASM.

OpenGrok: Enhancing SNS Data Processing with Distilled Knowledge and Mask-like Mechanisms

This report details Lumen Labs' novel approach to processing Social Networking Service (SNS) data. We leverage knowledge distillation, specifically a simple distillation method inspired by DeepSeek-R1's CoT acquisition, combined with prompt hacking, to extract valuable training data from the Grok model. This data is then used to fine-tune a Phi-3-mini model, augmented with a mask-like mechanism specifically designed for handling the nuances of SNS data. Our method demonstrates state-of-the-art (SOTA) performance on several SNS data processing tasks, outperforming existing models like Grok, Phi-3, and GPT-4. We provide a comprehensive analysis of our approach, including mathematical formulations, engineering details, ablation studies, and comparative evaluations.

Enhancing Large Language Model Efficiencyvia Symbolic Compression: A Formal Approach Towards Interpretability

Large language models (LLMs) face significant token efficiency bottlenecks in code generation and logical reasoning tasks, a challenge that directly impacts inference cost and model interpretability. This paper proposes a formal framework based on symbolic compression,integrating combinatory logic, information-theoretic optimal encoding, and context-aware inference techniques to achieve a step-change improvement in token efficiency while preserving semantic integrity. We establish a mathematical framework within a functional programming paradigm, derive the quantitative relationship between symbolic density and model interpretability, and propose a differentiable compression factor metric to evaluate encoding efficiency. Furthermore, we leverage parameter-efficient fine-tuning (PEFT) techniques to achieve a low-cost application of the GAEL language. Experimental results show that this method achieves a 78.3% token compression rate in code generation tasks while improving logical traceability by 62% through structural explicitness. This research provides new theoretical tools for efficient inference in LLMs and opens a symbolic path for modelinterpretability research.

Chinese Stock Prediction Based on a Multi-Modal Transformer Framework: Macro-Micro Information Fusion

This paper proposes an innovative Multi-Modal Transformer framework (MMF-Trans) designed to significantly improve the prediction accuracy of the Chinese stock market by integrating multi-source heterogeneous information including macroeconomy, micro-market, financial text, and event knowledge. The framework consists of four core modules: (1) A four-channel parallel encoder that processes technical indicators, financial text, macro data, and event knowledge graph respectively for independent feature extraction of multi-modal data; (2) A dynamic gated cross-modal fusion mechanism that adaptively learns the importance of different modalities through differentiable weight allocation for effective information integration; (3) A time-aligned mixed-frequency processing layer that uses an innovative position encoding method to effectively fuse data of different time frequencies and solves the time alignment problem of heterogeneous data; (4) A graph attention-based event impact quantification module that captures the dynamic impact of events on the market through event knowledge graph and quantifies the event impact coefficient. We introduce a hybrid-frequency Transformer and Event2Vec algorithm to effectively fuse data of different frequencies and quantify the event impact. Experimental results show that in the prediction task of CSI 300 constituent stocks, the root mean square error (RMSE) of the MMF-Trans framework is reduced by 23.7% compared to the baseline model, the event response prediction accuracy is improved by 41.2%, and the Sharpe ratio is improved by 32.6%.

UAV3D: A Large-scale 3D Perception Benchmark for Unmanned Aerial Vehicles

Unmanned Aerial Vehicles (UAVs), equipped with cameras, are employed in numerous applications, including aerial photography, surveillance, and agriculture. In these applications, robust object detection and tracking are essential for the effective deployment of UAVs. However, existing benchmarks for UAV applications are mainly designed for traditional 2D perception tasks, restricting the development of real-world applications that require a 3D understanding of the environment. Furthermore, despite recent advancements in single-UAV perception, limited views of a single UAV platform significantly constrain its perception capabilities over long distances or in occluded areas. To address these challenges, we introduce UAV3D, a benchmark designed to advance research in both 3D and collaborative 3D perception tasks with UAVs. UAV3D comprises 1,000 scenes, each of which has 20 frames with fully annotated 3D bounding boxes on vehicles. We provide the benchmark for four 3D perception tasks: single-UAV 3D object detection, single-UAV object tracking, collaborative-UAV 3D object detection, and collaborative-UAV object tracking. Our dataset and code are available at https://huiyegit.github.io/UAV3D_Benchmark/.

Unsqueeze [CLS] Bottleneck to Learn Rich Representations

Distillation-based self-supervised learning typically leads to more compressed representations due to its radical clustering process and the implementation of a sharper target distribution. To overcome this limitation and preserve more information from input, we introduce UDI, conceptualized as Unsqueezed Distillation-based self-supervised learning (SSL). UDI enriches the learned representation by encouraging multimodal prediction distilled from a consolidated profile of local predictions that are derived via stratified sampling. Our evaluations show that UDI not only promotes semantically meaningful representations at instance level, delivering superior or competitive results to state-of-the-art SSL methods in image classification, but also effectively preserves the nuisance of input, which yields significant improvement in dense prediction tasks, including object detection and segmentation. Additionally, UDI performs competitively in low-shot image classification, improving the scalability of joint-embedding pipelines. Various visualizations and ablation studies are presented to further elucidate the mechanisms behind UDI. Our source code is available at https://github.com/ISL-CV/udi.