Reinforcement Learning for Code Optimization

RL for code correctness is now established: have the model generate a program, run it against hidden test cases, and reward solutions that pass. Extending this to code optimization seems straightforward: just add execution time to the reward. But in practice, once timing drives the reward, small problems in measurement noise, reward sparsity, or GRPO instability overwhelm the signal and make RL fail: generated solutions are barely faster, and more of them can fail. We make execution time learnable through three stages: (1) how code is tested, by building DMC-Optim with large optimization tests and a calibrated sandbox; (2) how speed is turned into reward, by composing correctness and speed in the RL environment and using an offline simulator to predict the most promising configurations; and (3) how the model learns from that reward, by adapting GRPO and evaluation to the sparser, noisier timed-execution setting. On DMC-Optim, the strongest optimization-aware configurations improve strict top-50% pass@1 from 18.0% to 31.3% on Qwen 2.5 7B and from 30.7% to 50.4% on CWM 32B. These gains further increase at stricter percentiles such as top-30%, with 125% relative improvement for CWM 32B, while preserving pure-correctness scores. When the timing sandbox is degraded, robust optimization RL reaches 100% to 200% improvement over standard RLVR, depending on the evaluation criterion. On LCB, CWM 32B wins up to 83% of median-sample speed comparisons against standard RLVR. Relative to the fastest correct human submissions per problem, it reaches about half the human rate of complexity-class improvements (14% vs. 28%).

Sparse Delta Memory: Scaling the State of Linear RNNs through Sparsity

Linear attention models allow a fixed state size and a fixed amount of compute per token. However, due to their limited state size, linear attention models fall behind in long-context recall compared to softmax-attention-based transformer architectures. Increasing the state size of linear attention improves recall performance but at the cost of higher FLOPs. In this work, we introduce Sparse Delta Memory (SDM), an architecture that scales the hidden state of gated linear RNNs to orders of magnitude higher capacity using a sparse addressing scheme. SDM extends the Gated DeltaNet architecture by replacing the dense key-value outer product with sparse reads and writes to a large explicit memory. We show that, under an isoFLOP constraint and with an identical number of parameters, a higher state memory capacity significantly improves performance on in-context learning and long-context retrieval tasks. Moreover, by learning the initial state of the SDM memory and therefore using it as a parametric memory, we show that the model further improves on a wide range of common-knowledge and reasoning tasks.

DecompRL: Solving Harder Problems by Learning Modular Code Generation

How can Large Language Models (LLMs) solve problems they currently cannot? Repeated sampling scales test-time compute but GPU cost grows linearly with attempts, while reinforcement learning (RL) with verifiable rewards improves single-attempt accuracy at the expense of sample diversity. Both strategies ultimately fail when the base policy has near-zero probability of producing a correct solution: no amount of sampling or gradient signal can overcome a search space that is simply too large. We take a different approach: rather than sampling harder, we make the task easier by decomposing problems into smaller, independently solvable sub-functions whose implementations can be recombined. Since off-the-shelf models are not trained for this modular generation, we introduce DecompRL, an RL algorithm that explicitly learns to decompose and implement hierarchical code structures. Recombining $k$ implementations of $n$ modules yields up to $k^{n}$ candidate solutions, shifting the bottleneck from GPU inference to cheap CPU evaluation and cutting GPU token cost by $\sim$50$\times$. On LiveCodeBench and CodeContests (Qwen~2.5~7B, Code World Model~32B), DecompRL outperforms standard and diversity-optimized RL baselines beyond $10^5$ tokens per problem, solving problems that standard generation cannot reach.

Don't Let Gains FADE: Breaking Down Policy Gradient Weights in RL

Reinforcement learning post-training dramatically improves LLM reasoning, but suffers from training instability and diversity collapse. Advantage functions offer an appealing fix: they reshape the training objective, reweight which rollouts drive learning, and are trivial to implement. Yet a proliferation of methods makes it unclear which advantage to use and when. We cut through the confusion with a unifying framework that decomposes any advantage into its positive and negative gradient mass along two orthogonal axes. On the sign axis, imbalanced updates collapse either entropy or weight geometry. On the difficulty axis, hard-problem focus sharpens signal but costs sample size. Both trade-offs shift during training: exploration favors balance and hard focus; exploitation favors suppression and medium focus. This motivates FADE (Focal Advantage with Dynamic Entropy), a self-adapting advantage that reads training dynamics to schedule the gradient weight automatically. FADE reaches peak pass@1 20k steps earlier than the best static baseline at the 7B scale and 2k steps earlier at the 32B , while achieving the best accuracy-diversity trade-off across all pass@k on LiveCodeBench and AIME.

Extrapolative Weight Averaging Reveals Correctness-Efficiency Frontiers in Code RL

Linear interpolation between fine-tuned checkpoints has been shown to trace the Pareto front between competing objectives, but whether extrapolative weight averaging can extend such frontiers to new checkpoints useful at inference time, without additional RL training, remains unclear. We study this question in RL for competitive programming, where hidden unit tests under time and memory limits enforce both functional correctness and computational efficiency. Starting from a shared initialization, we train checkpoints under nested unit-test coverage: low-coverage rewards require passing smaller-input tests, while high-coverage rewards require passing progressively larger tests up to the full suite. This sweep reveals the emergence of a correctness-efficiency frontier: on hard problems, higher-coverage reward reduces optimization failures but increases correctness failures, leaving solve rate nearly unchanged. Interpolation between low- and high-coverage checkpoints recovers this frontier, while extrapolation extends it beyond the trained endpoints. Both the frontier and its extrapolative continuation appear across three inference settings, pure reasoning, tool use, and agentic coding, and across two model scales, 32B and 7B. At the problem level, moving along the frontier changes which problems are solved, making extrapolated checkpoints complementary policies in inference-time scaling. Ensembles with extrapolative weight averaging broaden coverage and improve pass@250 on LCB/hard by 3.3% over the best single checkpoint at matched sample budget. These results show that nested unit-test coverage in code RL induces a frontier that extrapolative weight averaging can navigate, extend, and exploit.

ProgramBench: Can Language Models Rebuild Programs From Scratch?

Turning ideas into full software projects from scratch has become a popular use case for language models. Agents are being deployed to seed, maintain, and grow codebases over extended periods with minimal human oversight. Such settings require models to make high-level software architecture decisions. However, existing benchmarks measure focused, limited tasks such as fixing a single bug or developing a single, specified feature. We therefore introduce ProgramBench to measure the ability of software engineering agents to develop software holisitically. In ProgramBench, given only a program and its documentation, agents must architect and implement a codebase that matches the reference executable's behavior. End-to-end behavioral tests are generated via agent-driven fuzzing, enabling evaluation without prescribing implementation structure. Our 200 tasks range from compact CLI tools to widely used software such as FFmpeg, SQLite, and the PHP interpreter. We evaluate 9 LMs and find that none fully resolve any task, with the best model passing 95\% of tests on only 3\% of tasks. Models favor monolithic, single-file implementations that diverge sharply from human-written code.

Automatic Textbook Formalization

We present a case study where an automatic AI system formalizes a textbook with more than 500 pages of graduate-level algebraic combinatorics to Lean. The resulting formalization represents a new milestone in textbook formalization scale and proficiency, moving from early results in undergraduate topology and restructuring of existing library content to a full standalone formalization of a graduate textbook. The formalization comprises 130K lines of code and 5900 Lean declarations and was conducted within one week by a total of 30K Claude 4.5 Opus agents collaborating in parallel on a shared code base via version control, simultaneously setting a record in multi-agent software engineering with usable results. The inference cost matches or undercuts what we estimate as the salaries required for a team of human experts, and we expect there is still the potential for large efficiencies to be made without the need for better models. We make our code, the resulting Lean code base and a side-by-side blueprint website available open-source.

WybeCoder: Verified Imperative Code Generation

Recent progress in large language models (LLMs) has advanced automatic code generation and formal theorem proving, yet software verification has not seen the same improvement. To address this gap, we propose WybeCoder, an agentic code verification framework that enables prove-as-you-generate development where code, invariants, and proofs co-evolve. It builds on a recent framework that combines automatic verification condition generation and SMT solvers with interactive proofs in Lean. To enable systematic evaluation, we translate two benchmarks for functional verification in Lean, Verina and Clever, to equivalent imperative code specifications. On complex algorithms such as Heapsort, we observe consistent performance improvements by scaling our approach, synthesizing dozens of valid invariants and dispatching of dozens of subgoals, resulting in hundreds of lines of verified code, overcoming plateaus reported in previous works. Our best system solves 74% of Verina tasks and 62% of Clever tasks at moderate compute budgets, significantly surpassing previous evaluations and paving a path to automated construction of large-scale datasets of verified imperative code.

A Deep Dive into Scaling RL for Code Generation with Synthetic Data and Curricula

Reinforcement learning (RL) has emerged as a powerful paradigm for improving large language models beyond supervised fine-tuning, yet sustaining performance gains at scale remains an open challenge, as data diversity and structure, rather than volume alone, become the limiting factor. We address this by introducing a scalable multi-turn synthetic data generation pipeline in which a teacher model iteratively refines problems based on in-context student performance summaries, producing structured difficulty progressions without any teacher fine-tuning. Compared to single-turn generation, this multi-turn approach substantially improves the yield of valid synthetic problems and naturally produces stepping stones, i.e. easier and harder variants of the same core task, that support curriculum-based training. We systematically study how task difficulty, curriculum scheduling, and environment diversity interact during RL training across the Llama3.1-8B Instruct and Qwen3-8B Base model families, with additional scaling experiments on Qwen2.5-32B. Our results show that synthetic augmentation consistently improves in-domain code and in most cases out-of-domain math performance, and we provide empirical insights into how curriculum design and data diversity jointly shape RL training dynamics.

Towards a Neural Debugger for Python

Training large language models (LLMs) on Python execution traces grounds them in code execution and enables the line-by-line execution prediction of whole Python programs, effectively turning them into neural interpreters (FAIR CodeGen Team et al., 2025). However, developers rarely execute programs step by step; instead, they use debuggers to stop execution at certain breakpoints and step through relevant portions only while inspecting or modifying program variables. Existing neural interpreter approaches lack such interactive control. To address this limitation, we introduce neural debuggers: language models that emulate traditional debuggers, supporting operations such as stepping into, over, or out of functions, as well as setting breakpoints at specific source lines. We show that neural debuggers -- obtained via fine-tuning large LLMs or pre-training smaller models from scratch -- can reliably model both forward execution (predicting future states and outputs) and inverse execution (inferring prior states or inputs) conditioned on debugger actions. Evaluated on CruxEval, our models achieve strong performance on both output and input prediction tasks, demonstrating robust conditional execution modeling. Our work takes first steps towards future agentic coding systems in which neural debuggers serve as a world model for simulated debugging environments, providing execution feedback or enabling agents to interact with real debugging tools. This capability lays the foundation for more powerful code generation, program understanding, and automated debugging.