Micah Goldblum
Publications
Understanding Reasoning from Pretraining to Post-Training
Reinforcement learning (RL) has become central to improving large language models (LLMs) on complex reasoning tasks, yet RL post-training is largely studied in isolation from the pretraining that precedes it. As a result, two basic questions remain open: (1) how do pretraining choices (model size, data) shape the returns to RL compute, and (2) what does RL actually do to the model? These questions are difficult to study in the standard LLM setting: pretraining corpora are vast and uncontrolled, making it hard to attribute behaviors to pretraining versus RL, and systematic compute sweeps across both stages are prohibitively expensive. To address these challenges, we use chess as a controlled testbed for studying reasoning across the full pretraining-to-post-training pipeline. We follow the standard LLM training pipeline by pretraining language models from 5M to 1B parameters on human chess games, supervised fine-tuning on synthetic reasoning traces, and running RL on chess puzzles with verifiable rewards. Using this framework, we find that the post-RL performance at given RL compute level is well-predicted from the pretraining loss, and slope of the RL reward curves improves approximately linearly with the pretraining tokens. Beyond scaling, we find that RL does not simply sharpen the SFT policy: on easy puzzles it amplifies correct moves the SFT policy already preferred, while on hard puzzles it surfaces correct moves that were nearly absent under SFT. We further test whether our findings transfer beyond chess by training a 1B language model on math-domain text, where the same predictive pattern emerges: longer-pretrained checkpoints reach higher post-RL performance and improve faster under RL. In sum, we provide a quantitative account of the pretraining-to-RL interface and a controlled testbed for studying the science of reasoning across the full pretraining-to-post-training pipeline.
End-to-End Context Compression at Scale
Long-context language model inference is bottlenecked by memory, as the KV cache grows with context length. Recent techniques to compress the KV cache fall short: they either degrade model quality substantially or require considerable time and compute to compress a single long prompt. Furthermore, many methods require the input to fit within the target model's context window, and are generally incompatible with modern production inference engines. Encoder-decoder compressors, which map a long token sequence to a shorter sequence of latent embeddings consumed by a decoder, are an appealing alternative in principle. However, existing approaches are not competitive with KV cache compression on the accuracy-efficiency frontier. In this work, we revisit encoder-decoder compression and close this gap. We first perform an architecture search, pre-training many variants from scratch to determine how best to design and train encoder-decoder compressors. Guided by our findings, we continually pre-train a family of 0.6B-encoder, 4B-decoder models on over 350B tokens each, at compression ratios of 1:4, 1:8, and 1:16. We introduce Latent Context Language Models (LCLMs), a family of compressors that improve the Pareto frontier across general-task performance, compression speed, and peak memory usage. We demonstrate that LCLMs serve as efficient backbones for long-horizon agents, letting the agent skim through a compressed long context and adaptively expand relevant segments on demand.
LiveMathematicianBench: A Live Benchmark for Mathematician-Level Reasoning with Proof Sketches
Mathematical reasoning is a hallmark of human intelligence, and whether large language models (LLMs) can meaningfully perform it remains a central question in artificial intelligence and cognitive science. As LLMs are increasingly integrated into scientific workflows, rigorous evaluation of their mathematical capabilities becomes a practical necessity. Existing benchmarks are limited by synthetic settings and data contamination. We present LiveMathematicianBench, a dynamic multiple-choice benchmark for research-level mathematical reasoning built from recent arXiv papers published after model training cutoffs. By grounding evaluation in newly published theorems, it provides a realistic testbed beyond memorized patterns. The benchmark introduces a thirteen-category logical taxonomy of theorem types (e.g., implication, equivalence, existence, uniqueness), enabling fine-grained evaluation across reasoning forms. It employs a proof-sketch-guided distractor pipeline that uses high-level proof strategies to construct plausible but invalid answer choices reflecting misleading proof directions, increasing sensitivity to genuine understanding over surface-level matching. We also introduce a substitution-resistant mechanism to distinguish answer recognition from substantive reasoning. Evaluation shows the benchmark is far from saturated: Gemini-3.1-pro-preview, the best model, achieves only 43.5%. Under substitution-resistant evaluation, accuracy drops sharply: GPT-5.4 scores highest at 30.6%, while Gemini-3.1-pro-preview falls to 17.6%, below the 20% random baseline. A dual-mode protocol reveals that proof-sketch access yields consistent accuracy gains, suggesting models can leverage high-level proof strategies for reasoning. Overall, LiveMathematicianBench offers a scalable, contamination-resistant testbed for studying research-level mathematical reasoning in LLMs.