Pitfalls of Rule- and Model-based Verifiers -- A Case Study on Mathematical Reasoning

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical reasoning, rule-based verifiers have been widely adopted in previous works to train strong reasoning models. However, the reliability of these verifiers and their impact on the RL training process remain poorly understood. In this work, we take mathematical reasoning as a case study and conduct a comprehensive analysis of various verifiers in both static evaluation and RL training scenarios. First, we find that current open-source rule-based verifiers often fail to recognize equivalent answers presented in different formats across multiple commonly used mathematical datasets, resulting in non-negligible false negative rates. This limitation adversely affects RL training performance and becomes more pronounced as the policy model gets stronger. Subsequently, we investigate model-based verifiers as a potential solution to address these limitations. While the static evaluation shows that model-based verifiers achieve significantly higher verification accuracy, further analysis and RL training results imply that they are highly susceptible to hacking, where they misclassify certain patterns in responses as correct (i.e., false positives). This vulnerability is exploited during policy model optimization, leading to artificially inflated rewards. Our findings underscore the unique risks inherent to both rule-based and model-based verifiers, aiming to offer valuable insights to develop more robust reward systems in reinforcement learning.

Learn to Reason Efficiently with Adaptive Length-based Reward Shaping

Large Reasoning Models (LRMs) have shown remarkable capabilities in solving complex problems through reinforcement learning (RL), particularly by generating long reasoning traces. However, these extended outputs often exhibit substantial redundancy, which limits the efficiency of LRMs. In this paper, we investigate RL-based approaches to promote reasoning efficiency. Specifically, we first present a unified framework that formulates various efficient reasoning methods through the lens of length-based reward shaping. Building on this perspective, we propose a novel Length-bAsed StEp Reward shaping method (LASER), which employs a step function as the reward, controlled by a target length. LASER surpasses previous methods, achieving a superior Pareto-optimal balance between performance and efficiency. Next, we further extend LASER based on two key intuitions: (1) The reasoning behavior of the model evolves during training, necessitating reward specifications that are also adaptive and dynamic; (2) Rather than uniformly encouraging shorter or longer chains of thought (CoT), we posit that length-based reward shaping should be difficulty-aware i.e., it should penalize lengthy CoTs more for easy queries. This approach is expected to facilitate a combination of fast and slow thinking, leading to a better overall tradeoff. The resulting method is termed LASER-D (Dynamic and Difficulty-aware). Experiments on DeepSeek-R1-Distill-Qwen-1.5B, DeepSeek-R1-Distill-Qwen-7B, and DeepSeek-R1-Distill-Qwen-32B show that our approach significantly enhances both reasoning performance and response length efficiency. For instance, LASER-D and its variant achieve a +6.1 improvement on AIME2024 while reducing token usage by 63%. Further analysis reveals our RL-based compression produces more concise reasoning patterns with less redundant "self-reflections". Resources are at https://github.com/hkust-nlp/Laser.

SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild

DeepSeek-R1 has shown that long chain-of-thought (CoT) reasoning can naturally emerge through a simple reinforcement learning (RL) framework with rule-based rewards, where the training may directly start from the base models-a paradigm referred to as zero RL training. Most recent efforts to reproduce zero RL training have primarily focused on the Qwen2.5 model series, which may not be representative as we find the base models already exhibit strong instruction-following and self-reflection abilities. In this work, we investigate zero RL training across 10 diverse base models, spanning different families and sizes including LLama3-8B, Mistral-7B/24B, DeepSeek-Math-7B, Qwen2.5-math-7B, and all Qwen2.5 models from 0.5B to 32B. Leveraging several key design strategies-such as adjusting format reward and controlling query difficulty-we achieve substantial improvements in both reasoning accuracy and response length across most settings. However, by carefully monitoring the training dynamics, we observe that different base models exhibit distinct patterns during training. For instance, the increased response length does not always correlate with the emergence of certain cognitive behaviors such as verification (i.e., the "aha moment"). Notably, we observe the "aha moment" for the first time in small models not from the Qwen family. We share the key designs that enable successful zero RL training, along with our findings and practices. To facilitate further research, we open-source the code, models, and analysis tools.

External Large Foundation Model: How to Efficiently Serve Trillions of Parameters for Online Ads Recommendation

Ads recommendation is a prominent service of online advertising systems and has been actively studied. Recent studies indicate that scaling-up and advanced design of the recommendation model can bring significant performance improvement. However, with a larger model scale, such prior studies have a significantly increasing gap from industry as they often neglect two fundamental challenges in industrial-scale applications. First, training and inference budgets are restricted for the model to be served, exceeding which may incur latency and impair user experience. Second, large-volume data arrive in a streaming mode with data distributions dynamically shifting, as new users/ads join and existing users/ads leave the system. We propose the External Large Foundation Model (ExFM) framework to address the overlooked challenges. Specifically, we develop external distillation and a data augmentation system (DAS) to control the computational cost of training/inference while maintaining high performance. We design the teacher in a way like a foundation model (FM) that can serve multiple students as vertical models (VMs) to amortize its building cost. We propose Auxiliary Head and Student Adapter to mitigate the data distribution gap between FM and VMs caused by the streaming data issue. Comprehensive experiments on internal industrial-scale applications and public datasets demonstrate significant performance gain by ExFM.

Movable Antenna Array Aided Ultra Reliable Covert Communications

In this paper, we construct a framework of the movable antenna (MA) aided covert communication shielded by the general noise uncertainty for the first time. According to the analysis performance on the derived closed-form expressions of the sum of the probabilities of the detection errors and the communication outage probability, the perfect covertness and the ultra reliability can be achieved by adjusting the antenna position in the MA array. Then, we formulate the communication covertness maximization problem with the constraints of the ultra reliability and the independent discrete movable position to optimize the transmitter's parameter. With the maximal ratio transmitting (MRT) design for the beamforming, we solve the closed-form optimal information transmit power and design a lightweight discrete projected gradient descent (DPGD) algorithm to determine the optimal antenna position. The numerical results show that the optimal achievable covertness and the feasible region of the steering angle with the MA array is significant larger than the one with the fixed-position antenna (FPA) array.

B-STaR: Monitoring and Balancing Exploration and Exploitation in Self-Taught Reasoners

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. However, the critical factors underlying the mechanism of these iterative self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to generate sufficiently diverse responses (exploration); and (2) the effectiveness of external rewards in distinguishing high-quality candidates from lower-quality ones (exploitation). Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-improving effectiveness based on the current policy model and available rewards. Our experiments on mathematical reasoning, coding, and commonsense reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance.

Compression Represents Intelligence Linearly

There is a belief that learning to compress well will lead to intelligence. Recently, language modeling has been shown to be equivalent to compression, which offers a compelling rationale for the success of large language models (LLMs): the development of more advanced language models is essentially enhancing compression which facilitates intelligence. Despite such appealing discussions, little empirical evidence is present for the interplay between compression and intelligence. In this work, we examine their relationship in the context of LLMs, treating LLMs as data compressors. Given the abstract concept of "intelligence", we adopt the average downstream benchmark scores as a surrogate, specifically targeting intelligence related to knowledge and commonsense, coding, and mathematical reasoning. Across 12 benchmarks, our study brings together 30 public LLMs that originate from diverse organizations. Remarkably, we find that LLMs' intelligence -- reflected by average benchmark scores -- almost linearly correlates with their ability to compress external text corpora. These results provide concrete evidence supporting the belief that superior compression indicates greater intelligence. Furthermore, our findings suggest that compression efficiency, as an unsupervised metric derived from raw text corpora, serves as a reliable evaluation measure that is linearly associated with the model capabilities. We open-source our compression datasets as well as our data collection pipelines to facilitate future researchers to assess compression properly.

C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models

New NLP benchmarks are urgently needed to align with the rapid development of large language models (LLMs). We present C-Eval, the first comprehensive Chinese evaluation suite designed to assess advanced knowledge and reasoning abilities of foundation models in a Chinese context. C-Eval comprises multiple-choice questions across four difficulty levels: middle school, high school, college, and professional. The questions span 52 diverse disciplines, ranging from humanities to science and engineering. C-Eval is accompanied by C-Eval Hard, a subset of very challenging subjects in C-Eval that requires advanced reasoning abilities to solve. We conduct a comprehensive evaluation of the most advanced LLMs on C-Eval, including both English- and Chinese-oriented models. Results indicate that only GPT-4 could achieve an average accuracy of over 60%, suggesting that there is still significant room for improvement for current LLMs. We anticipate C-Eval will help analyze important strengths and shortcomings of foundation models, and foster their development and growth for Chinese users.

Pre-train and Search: Efficient Embedding Table Sharding with Pre-trained Neural Cost Models

Sharding a large machine learning model across multiple devices to balance the costs is important in distributed training. This is challenging because partitioning is NP-hard, and estimating the costs accurately and efficiently is difficult. In this work, we explore a "pre-train, and search" paradigm for efficient sharding. The idea is to pre-train a universal and once-for-all neural network to predict the costs of all the possible shards, which serves as an efficient sharding simulator. Built upon this pre-trained cost model, we then perform an online search to identify the best sharding plans given any specific sharding task. We instantiate this idea in deep learning recommendation models (DLRMs) and propose NeuroShard for embedding table sharding. NeuroShard pre-trains neural cost models on augmented tables to cover various sharding scenarios. Then it identifies the best column-wise and table-wise sharding plans with beam search and greedy grid search, respectively. Experiments show that NeuroShard significantly and consistently outperforms the state-of-the-art on the benchmark sharding dataset, achieving up to 23.8% improvement. When deployed in an ultra-large production DLRM with multi-terabyte embedding tables, NeuroShard achieves 11.6% improvement in embedding costs over the state-of-the-art, which translates to 6.6% end-to-end training throughput improvement. To facilitate future research of the "pre-train, and search" paradigm in ML for Systems, we open-source our code at https://github.com/daochenzha/neuroshard

Fast Distributed Training of Deep Neural Networks: Dynamic Communication Thresholding for Model and Data Parallelism

Data Parallelism (DP) and Model Parallelism (MP) are two common paradigms to enable large-scale distributed training of neural networks. Recent trends, such as the improved model performance of deeper and wider neural networks when trained with billions of data points, have prompted the use of hybrid parallelism---a paradigm that employs both DP and MP to scale further parallelization for machine learning. Hybrid training allows compute power to increase, but it runs up against the key bottleneck of communication overhead that hinders scalability. In this paper, we propose a compression framework called Dynamic Communication Thresholding (DCT) for communication-efficient hybrid training. DCT filters the entities to be communicated across the network through a simple hard-thresholding function, allowing only the most relevant information to pass through. For communication efficient DP, DCT compresses the parameter gradients sent to the parameter server during model synchronization, while compensating for the introduced errors with known techniques. For communication efficient MP, DCT incorporates a novel technique to compress the activations and gradients sent across the network during the forward and backward propagation, respectively. This is done by identifying and updating only the most relevant neurons of the neural network for each training sample in the data. Under modest assumptions, we show that the convergence of training is maintained with DCT. We evaluate DCT on natural language processing and recommender system models. DCT reduces overall communication by 20x, improving end-to-end training time on industry scale models by 37%. Moreover, we observe an improvement in the trained model performance, as the induced sparsity is possibly acting as an implicit sparsity based regularization.