With the technological advancements of the last couple of decades, machine learning (ML) and artificial intelligence (AI) play an important part in automated decision-making pipelines [1-3]. Even though these tools are generally created by optimising with respect to their accuracy and performance, there are other important aspects that should be considered, such as their fairness, robustness, and privacy [4]. One of these aspects, fairness, becomes even more crucial when AI-based tools are used for decision-making tasks such as checking whether accepting a credit application is profitable and risk-free, if an applicant is worthy of a job position, or if a defendant has a higher risk of committing a crime again.

Instruction subsets (ISs) are heuristics that can shrink the size of the inductive programming (IP) search space by tens of orders of magnitude. Here, we extend the IS approach by introducing instruction and solution probabilities as additional heuristics. Instruction probability reflects the expectation of an instruction occurring in a solution, based on the frequency of instruction occurrence in a large code sample. The solution probability for a partial or complete program is simply the product of all constituent instruction probabilities, including duplicates. We treat the minimum solution probabilities observed in code sample program units of different sizes as solution probability thresholds. These thresholds are used to prune the search space as partial solutions are constructed, thereby eliminating any branches containing unlikely combinations of instructions. The new approach has been evaluated using a large sample of human code. We tested two formulations of instruction probability: one based on instruction occurrence across the entire code sample and another that measured the distribution separately for each IS. Our results show that both variants produce substantial further reductions in the IP search space size of up to tens of orders of magnitude, depending on solution size. In combination with IS, reductions of over 100 orders of magnitude can be achieved. We also carried out cross-validation testing to show that the heuristics should work effectively with unseen code. The approach is described and the results and some ideas for future work are discussed.

We present a suite of scalable algorithms for minimizing feedback arcs in large-scale weighted directed graphs, with the goal of revealing biologically meaningful feedforward structure in neural connectomes. Using the FlyWire Connectome Challenge dataset, we demonstrate the effectiveness of our ranking strategies in maximizing the total weight of forward-pointing edges. Our methods integrate greedy heuristics, gain-aware local refinements, and global structural analysis based on strongly connected components. Experiments show that our best solution improves the forward edge weight over previous top-performing methods. All algorithms are implemented efficiently in Python and validated using cloud-based execution on Google Colab Pro+.

--Typically, research on Explainable Artificial Intelligence (XAI) focuses on black-box models within the context of a general policy in a known, specific domain. This paper advocates for the need for knowledge-agnostic explainability applied to the subfield of XAI called Explainable Search, which focuses on explaining the choices made by intelligent search techniques. It proposes Monte-Carlo Tree Search (MCTS) enhancements as a solution to obtaining additional data and providing higher-quality explanations while remaining knowledge-free, and analyzes the most popular enhancements in terms of the specific types of explainability they introduce. So far, no other research has considered the explainability of MCTS enhancements. We present a proof-of-concept that demonstrates the advantages of utilizing enhancements.

In this white paper, we present AlphaEvolve, an evolutionary coding agent that substantially enhances capabilities of state-of-the-art LLMs on highly challenging tasks such as tackling open scientific problems or optimizing critical pieces of computational infrastructure. AlphaEvolve orchestrates an autonomous pipeline of LLMs, whose task is to improve an algorithm by making direct changes to the code. Using an evolutionary approach, continuously receiving feedback from one or more evaluators, AlphaEvolve iteratively improves the algorithm, potentially leading to new scientific and practical discoveries. We demonstrate the broad applicability of this approach by applying it to a number of important computational problems. When applied to optimizing critical components of large-scale computational stacks at Google, AlphaEvolve developed a more efficient scheduling algorithm for data centers, found a functionally equivalent simplification in the circuit design of hardware accelerators, and accelerated the training of the LLM underpinning AlphaEvolve itself. Furthermore, AlphaEvolve discovered novel, provably correct algorithms that surpass state-of-the-art solutions on a spectrum of problems in mathematics and computer science, significantly expanding the scope of prior automated discovery methods (Romera-Paredes et al., 2023). Notably, AlphaEvolve developed a search algorithm that found a procedure to multiply two $4 \times 4$ complex-valued matrices using $48$ scalar multiplications; offering the first improvement, after 56 years, over Strassen's algorithm in this setting. We believe AlphaEvolve and coding agents like it can have a significant impact in improving solutions of problems across many areas of science and computation.

We introduce MiniMax-M1, the world's first open-weight, large-scale hybrid-attention reasoning model. MiniMax-M1 is powered by a hybrid Mixture-of-Experts (MoE) architecture combined with a lightning attention mechanism. The model is developed based on our previous MiniMax-Text-01 model, which contains a total of 456 billion parameters with 45.9 billion parameters activated per token. The M1 model natively supports a context length of 1 million tokens, 8x the context size of DeepSeek R1. Furthermore, the lightning attention mechanism in MiniMax-M1 enables efficient scaling of test-time compute. These properties make M1 particularly suitable for complex tasks that require processing long inputs and thinking extensively. MiniMax-M1 is trained using large-scale reinforcement learning (RL) on diverse problems including sandbox-based, real-world software engineering environments. In addition to M1's inherent efficiency advantage for RL training, we propose CISPO, a novel RL algorithm to further enhance RL efficiency. CISPO clips importance sampling weights rather than token updates, outperforming other competitive RL variants. Combining hybrid-attention and CISPO enables MiniMax-M1's full RL training on 512 H800 GPUs to complete in only three weeks, with a rental cost of just $534,700. We release two versions of MiniMax-M1 models with 40K and 80K thinking budgets respectively, where the 40K model represents an intermediate phase of the 80K training. Experiments on standard benchmarks show that our models are comparable or superior to strong open-weight models such as the original DeepSeek-R1 and Qwen3-235B, with particular strengths in complex software engineering, tool utilization, and long-context tasks. We publicly release MiniMax-M1 at https://github.com/MiniMax-AI/MiniMax-M1.

This paper presents Generalized Proof-Number Monte-Carlo Tree Search: a generalization of recently proposed combinations of Proof-Number Search (PNS) with Monte-Carlo Tree Search (MCTS), which use (dis)proof numbers to bias UCB1-based Selection strategies towards parts of the search that are expected to be easily (dis)proven. We propose three core modifications of prior combinations of PNS with MCTS. First, we track proof numbers per player. This reduces code complexity in the sense that we no longer need disproof numbers, and generalizes the technique to be applicable to games with more than two players. Second, we propose and extensively evaluate different methods of using proof numbers to bias the selection strategy, achieving strong performance with strategies that are simpler to implement and compute. Third, we merge our technique with Score Bounded MCTS, enabling the algorithm to prove and leverage upper and lower bounds on scores - as opposed to only proving wins or not-wins. Experiments demonstrate substantial performance increases, reaching the range of 80% for 8 out of the 11 tested board games.

Kinodynamic planning of articulated vehicles in cluttered environments faces additional challenges arising from high-dimensional state space and complex system dynamics. Built upon [1],[2], this work proposes the DE-AGT algorithm that grows a tree using pre-computed motion primitives (MPs) and A* heuristics. The first feature of DE-AGT is a delayed expansion of MPs. In particular, the MPs are divided into different modes, which are ranked online. With the MP classification and prioritization, DE-AGT expands the most promising mode of MPs first, which eliminates unnecessary computation and finds solutions faster. To obtain the cost-to-go heuristic for nonholonomic articulated vehicles, we rely on supervised learning and train neural networks for fast and accurate cost-to-go prediction. The learned heuristic is used for online mode ranking and node selection. Another feature of DE-AGT is the improved goal-reaching. Exactly reaching a goal state usually requires a constant connection checking with the goal by solving steering problems -- non-trivial and time-consuming for articulated vehicles. The proposed termination scheme overcomes this challenge by tightly integrating a light-weight trajectory tracking controller with the search process. DE-AGT is implemented for autonomous parking of a general car-like tractor with 3-trailer. Simulation results show an average of 10x acceleration compared to a previous method.

Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover that even without any training, careful neuro-symbolic coordination of existing off-the-shelf reasoning models and tactic step provers can achieve comparable performance. This paper introduces \textbf{DSP+}, an improved version of the Draft, Sketch, and Prove framework, featuring a \emph{fine-grained and integrated} neuro-symbolic enhancement for each phase: (1) In the draft phase, we prompt reasoning models to generate concise natural-language subgoals to benefit the sketch phase, removing thinking tokens and references to human-written proofs; (2) In the sketch phase, subgoals are autoformalized with hypotheses to benefit the proving phase, and sketch lines containing syntactic errors are masked according to predefined rules; (3) In the proving phase, we tightly integrate symbolic search methods like Aesop with step provers to establish proofs for the sketch subgoals. Experimental results show that, without any additional model training or fine-tuning, DSP+ solves 80.7\%, 32.8\%, and 24 out of 644 problems from miniF2F, ProofNet, and PutnamBench, respectively, while requiring fewer budgets compared to state-of-the-arts. DSP+ proves \texttt{imo\_2019\_p1}, an IMO problem in miniF2F that is not solved by any prior work. Additionally, DSP+ generates proof patterns comprehensible by human experts, facilitating the identification of formalization errors; For example, eight wrongly formalized statements in miniF2F are discovered. Our results highlight the potential of classical reasoning patterns besides the RL-based training. All components will be open-sourced.

Reinforcement learning (RL) with tree search has demonstrated superior performance in traditional reasoning tasks. Compared to conventional independent chain sampling strategies with outcome supervision, tree search enables better exploration of the reasoning space and provides dense, on-policy process rewards during RL training but remains under-explored in On-Policy LLM RL. We propose TreeRL, a reinforcement learning framework that directly incorporates on-policy tree search for RL training. Our approach includes intermediate supervision and eliminates the need for a separate reward model training. Existing approaches typically train a separate process reward model, which can suffer from distribution mismatch and reward hacking. We also introduce a cost-effective tree search approach that achieves higher search efficiency under the same generation token budget by strategically branching from high-uncertainty intermediate steps rather than using random branching. Experiments on challenging math and code reasoning benchmarks demonstrate that TreeRL achieves superior performance compared to traditional ChainRL, highlighting the potential of tree search for LLM. TreeRL is open-sourced at https://github.com/THUDM/TreeRL.