Daily Papers

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.

We present a systematic, empirical evaluation of five local large language model (LLM) runtimes on Apple Silicon: MLX, MLC-LLM, llama.cpp, Ollama, and PyTorch MPS. Experiments were conducted on a Mac Studio equipped with an M2 Ultra processor and 192 GB of unified memory. Using the Qwen-2.5 model family across prompts ranging from a few hundred to 100,000 tokens, we measure time-to-first-token (TTFT), steady-state throughput, latency percentiles, long-context behavior (key-value and prompt caching), quantization support, streaming performance, batching and concurrency behavior, and deployment complexity. Under our settings, MLX achieves the highest sustained generation throughput, while MLC-LLM delivers consistently lower TTFT for moderate prompt sizes and offers stronger out-of-the-box inference features. llama.cpp is highly efficient for lightweight single-stream use, Ollama emphasizes developer ergonomics but lags in throughput and TTFT, and PyTorch MPS remains limited by memory constraints on large models and long contexts. All frameworks execute fully on-device with no telemetry, ensuring strong privacy guarantees. We release scripts, logs, and plots to reproduce all results. Our analysis clarifies the design trade-offs in Apple-centric LLM deployments and provides evidence-based recommendations for interactive and long-context processing. Although Apple Silicon inference frameworks still trail NVIDIA GPU-based systems such as vLLM in absolute performance, they are rapidly maturing into viable, production-grade solutions for private, on-device LLM inference.