Haocheng Wang

Huajian Xin, Z. Z. Ren, Junxiao Song et al. · pku, stanford

We introduce DeepSeek-Prover-V1.5, an open-source language model designed for theorem proving in Lean 4, which enhances DeepSeek-Prover-V1 by optimizing both training and inference processes. Pre-trained on DeepSeekMath-Base with specialization in formal mathematical languages, the model undergoes supervised fine-tuning using an enhanced formal theorem proving dataset derived from DeepSeek-Prover-V1. Further refinement is achieved through reinforcement learning from proof assistant feedback (RLPAF). Beyond the single-pass whole-proof generation approach of DeepSeek-Prover-V1, we propose RMaxTS, a variant of Monte-Carlo tree search that employs an intrinsic-reward-driven exploration strategy to generate diverse proof paths. DeepSeek-Prover-V1.5 demonstrates significant improvements over DeepSeek-Prover-V1, achieving new state-of-the-art results on the test set of the high school level miniF2F benchmark ($63.5\%$) and the undergraduate level ProofNet benchmark ($25.3\%$).

DeepSeek-AI, Daya Guo, Dejian Yang et al. · stanford, tsinghua

We introduce our first-generation reasoning models, DeepSeek-R1-Zero and DeepSeek-R1. DeepSeek-R1-Zero, a model trained via large-scale reinforcement learning (RL) without supervised fine-tuning (SFT) as a preliminary step, demonstrates remarkable reasoning capabilities. Through RL, DeepSeek-R1-Zero naturally emerges with numerous powerful and intriguing reasoning behaviors. However, it encounters challenges such as poor readability, and language mixing. To address these issues and further enhance reasoning performance, we introduce DeepSeek-R1, which incorporates multi-stage training and cold-start data before RL. DeepSeek-R1 achieves performance comparable to OpenAI-o1-1217 on reasoning tasks. To support the research community, we open-source DeepSeek-R1-Zero, DeepSeek-R1, and six dense models (1.5B, 7B, 8B, 14B, 32B, 70B) distilled from DeepSeek-R1 based on Qwen and Llama.

Z. Z. Ren, Zhihong Shao, Junxiao Song et al. · stanford, tsinghua

We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.

DeepSeek-AI, Aixin Liu, Bei Feng et al. · stanford, tsinghua

We present DeepSeek-V3, a strong Mixture-of-Experts (MoE) language model with 671B total parameters with 37B activated for each token. To achieve efficient inference and cost-effective training, DeepSeek-V3 adopts Multi-head Latent Attention (MLA) and DeepSeekMoE architectures, which were thoroughly validated in DeepSeek-V2. Furthermore, DeepSeek-V3 pioneers an auxiliary-loss-free strategy for load balancing and sets a multi-token prediction training objective for stronger performance. We pre-train DeepSeek-V3 on 14.8 trillion diverse and high-quality tokens, followed by Supervised Fine-Tuning and Reinforcement Learning stages to fully harness its capabilities. Comprehensive evaluations reveal that DeepSeek-V3 outperforms other open-source models and achieves performance comparable to leading closed-source models. Despite its excellent performance, DeepSeek-V3 requires only 2.788M H800 GPU hours for its full training. In addition, its training process is remarkably stable. Throughout the entire training process, we did not experience any irrecoverable loss spikes or perform any rollbacks. The model checkpoints are available at https://github.com/deepseek-ai/DeepSeek-V3.

Yichi Zhou, Jianqiu Zhao, Yongxin Zhang et al.

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in specialized languages like Lean 4 remains a significant challenge for these models, limiting their application in complex theorem proving and automated verification. Current approaches typically require specializing models through fine-tuning on dedicated formal corpora, incurring high costs for data collection and training. In this work, we introduce \textbf{Delta Prover}, an agent-based framework that orchestrates the interaction between a general-purpose LLM and the Lean 4 proof environment. Delta Prover leverages the reflection and reasoning capabilities of general-purpose LLMs to interactively construct formal proofs in Lean 4, circumventing the need for model specialization. At its core, the agent integrates two novel, interdependent components: an algorithmic framework for reflective decomposition and iterative proof repair, and a custom Domain-Specific Language (DSL) built upon Lean 4 for streamlined subproblem management. \textbf{Delta Prover achieves a state-of-the-art 95.9\% success rate on the miniF2F-test benchmark, surpassing all existing approaches, including those requiring model specialization.} Furthermore, Delta Prover exhibits a significantly stronger test-time scaling law compared to standard Best-of-N proof strategies. Crucially, our findings demonstrate that general-purpose LLMs, when guided by an effective agentic structure, possess substantial untapped theorem-proving capabilities. This presents a computationally efficient alternative to specialized models for robust automated reasoning in formal environments.

Priyanka Kargupta, Shuyue Stella Li, Haocheng Wang et al.

Large language models solve complex problems yet fail on simpler variants, suggesting they achieve correct outputs through mechanisms fundamentally different from human reasoning. We synthesize cognitive science research into a taxonomy of 28 cognitive elements spanning computational constraints, meta-cognitive controls, knowledge representations, and transformation operations, then analyze their behavioral manifestations in reasoning traces. We propose a fine-grained cognitive evaluation framework and conduct the first large-scale analysis of 170K traces from 17 models across text, vision, and audio modalities, alongside 54 human think-aloud traces, which we make publicly available. Our analysis reveals systematic structural differences: humans employ hierarchical nesting and meta-cognitive monitoring while models rely on shallow forward chaining, with divergence most pronounced on ill-structured problems. Meta-analysis of 1,598 LLM reasoning papers reveals the research community concentrates on easily quantifiable behaviors (sequential organization: 55%, decomposition: 60%) while neglecting meta-cognitive controls (self-awareness: 16%, evaluation: 8%) that correlate with success. Models possess behavioral repertoires associated with success but fail to deploy them spontaneously. Leveraging these patterns, we develop test-time reasoning guidance that automatically scaffold successful structures, improving performance by up to 60% on complex problems. By bridging cognitive science and LLM research, we establish a foundation for developing models that reason through principled cognitive mechanisms rather than brittle spurious reasoning shortcuts or memorization, opening new directions for both improving model capabilities and testing theories of human cognition at scale.

Qingyuan Liu, Liyan Chen, Yanning Yang et al.

Large Language Models (LLMs) increasingly require processing long text sequences, but GPU memory limitations force difficult trade-offs between memory capacity and bandwidth. While HBM-based acceleration offers high bandwidth, its capacity remains constrained. Offloading data to host-side DIMMs improves capacity but introduces costly data swapping overhead. We identify that the critical memory bottleneck lies in the decoding phase of multi-head attention (MHA) exclusively, which demands substantial capacity for storing KV caches and high bandwidth for attention computation. Our key insight reveals this operation uniquely aligns with modern DIMM-based processing-in-memory (PIM) architectures, which offers scalability of both capacity and bandwidth. Based on this observation and insight, we propose L3, a hardware-software co-designed system integrating DIMM-PIM and GPU devices. L3 introduces three innovations: First, hardware redesigns resolve data layout mismatches and computational element mismatches in DIMM-PIM, enhancing LLM inference utilization. Second, communication optimization enables hiding the data transfer overhead with the computation. Third, an adaptive scheduler coordinates GPU-DIMM-PIM operations to maximize parallelism between devices. Evaluations using real-world traces show L3 achieves up to 6.1$\times$ speedup over state-of-the-art HBM-PIM solutions while significantly improving batch sizes.