Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

The current best bounds on the matrix multiplication exponent $ω$ are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First, we reformulate the optimization problem allowing us to solve it in a larger setting than was previously possible. Second, we leverage recent advances in machine learning to design a new optimization algorithm for this problem. Finally, we refine the resulting optimization algorithm with AlphaEvolve. Our combined approach yields an upper bound of $ω$ < 2.371177, improving the previous best bound of 2.371339.

ArchAgent v2: A Case Study with the Data Prefetching Championship

Agentic artificial intelligence has shown great promise in automating algorithm design, but scaling similar techniques to computer microarchitecture discovery remains challenging due to vast search spaces, strict hardware budgets, and long simulation times. In this work, we present ArchAgent v2, a framework which scales automated microarchitecture search to multi-level data prefetching. While the original ArchAgent successfully discovered single-level cache replacement policies in competition settings, it does not scale to multi-level prefetching where the design space and degrees of freedom are larger. To overcome this, we introduce two new additions to ArchAgent: a cascaded evolutionary search that subdivides the design space by sequentially evolving and freezing prefetchers at individual cache levels, and a hardware-realizability feedback loop that embeds real-time size-estimation directly into the evolution process. Evaluated under identical rules of the 4th Data Prefetching Championship (DPC4), ArchAgent v2 automatically designs a three-level prefetcher that outperforms the winning hand-designed solution, further demonstrating automated agentic discovery as a useful tool for computer architects. Our discovered policy achieves a 3.8\% geometric mean IPC speedup over the baseline overall and a 0.3\% improvement over the prior champion, BertiGO. On low-bandwidth single-core configurations, our policy yields a 4.6\% performance speedup compared to only 2.6\% for BertiGO. However, multi-core evolution still remains a significant challenge due to simulation latency impeding evolution speed. Finally, our profiling of an ArchAgent evolution of over 12,000 candidate designs provides key insights into how automated evolutionary agents explore and synthesize complex microarchitectural logic.

Advancing Mathematics Research with AI-Driven Formal Proof Search

Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the first large-scale evaluation of this method's ability to solve open problems. Our most capable agent autonomously resolved 9 of 353 open Erdős problems at the per-problem cost of a few hundred dollars, proved 44/492 OEIS conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. A basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes but proved costlier on the hardest problems. These findings demonstrate the power of AI-aided formal proof search and shed light on the agent designs that enable it.

ArchAgent: Agentic AI-driven Computer Architecture Discovery

Agile hardware design flows are a critically needed force multiplier to meet the exploding demand for compute. Recently, agentic generative AI systems have demonstrated significant advances in algorithm design, improving code efficiency, and enabling discovery across scientific domains. Bridging these worlds, we present ArchAgent, an automated computer architecture discovery system built on AlphaEvolve. We show ArchAgent's ability to automatically design/implement state-of-the-art (SoTA) cache replacement policies (architecting new mechanisms/logic, not only changing parameters), broadly within the confines of an established cache replacement policy design competition. In two days without human intervention, ArchAgent generated a policy achieving a 5.3% IPC speedup improvement over the prior SoTA on public multi-core Google Workload Traces. On the heavily-explored single-core SPEC06 workloads, it generated a policy in just 18 days showing a 0.9% IPC speedup improvement over the existing SoTA (a similar "winning margin" as reported by the existing SoTA). ArchAgent achieved these gains 3-5x faster than prior human-developed SoTA policies. Agentic flows also enable "post-silicon hyperspecialization" where agents tune runtime-configurable parameters exposed in hardware policies to further align the policies with a specific workload (mix). Exploiting this, we demonstrate a 2.4% IPC speedup improvement over prior SoTA on SPEC06 workloads. Finally, we outline broader implications for computer architecture research in the era of agentic AI. For example, we demonstrate the phenomenon of "simulator escapes", where the agentic AI flow discovered and exploited a loophole in a popular microarchitectural simulator - a consequence of the fact that these research tools were designed for a (now past) world where they were exclusively operated by humans acting in good-faith.

AlphaEvolve: A coding agent for scientific and algorithmic discovery

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.

Amplifying human performance in combinatorial competitive programming

Recent years have seen a significant surge in complex AI systems for competitive programming, capable of performing at admirable levels against human competitors. While steady progress has been made, the highest percentiles still remain out of reach for these methods on standard competition platforms such as Codeforces. Here we instead focus on combinatorial competitive programming, where the target is to find as-good-as-possible solutions to otherwise computationally intractable problems, over specific given inputs. We hypothesise that this scenario offers a unique testbed for human-AI synergy, as human programmers can write a backbone of a heuristic solution, after which AI can be used to optimise the scoring function used by the heuristic. We deploy our approach on previous iterations of Hash Code, a global team programming competition inspired by NP-hard software engineering problems at Google, and we leverage FunSearch to evolve our scoring functions. Our evolved solutions significantly improve the attained scores from their baseline, successfully breaking into the top percentile on all previous Hash Code online qualification rounds, and outperforming the top human teams on several. Our method is also performant on an optimisation problem that featured in a recent held-out AtCoder contest.

Quantum Circuit Optimization with AlphaTensor

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e., minimizing the number of T gates that are needed to implement a given circuit. To achieve this, we develop AlphaTensor-Quantum, a method based on deep reinforcement learning that exploits the relationship between optimizing T-count and tensor decomposition. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets, which significantly reduces the T-count of the optimized circuits. AlphaTensor-Quantum outperforms the existing methods for T-count optimization on a set of arithmetic benchmarks (even when compared without making use of gadgets). Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields. AlphaTensor-Quantum also finds the best human-designed solutions for relevant arithmetic computations used in Shor's algorithm and for quantum chemistry simulation, thus demonstrating it can save hundreds of hours of research by optimizing relevant quantum circuits in a fully automated way.

Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erd\H{o}s, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Neural Program Synthesis with a Differentiable Fixer

We present a new program synthesis approach that combines an encoder-decoder based synthesis architecture with a differentiable program fixer. Our approach is inspired from the fact that human developers seldom get their program correct on the first attempt, and perform iterative testing-based program fixing to get to the desired program functionality. Similarly, our approach first learns a distribution over programs conditioned on an encoding of a set of input-output examples, and then iteratively performs fix operations using the differentiable fixer. The fixer takes as input the original examples and the current program's outputs on example inputs, and generates a new distribution over the programs with the goal of reducing the discrepancies between the current program outputs and the desired example outputs. We train our architecture end-to-end on the RobustFill domain, and show that the addition of the fixer module leads to a significant improvement on synthesis accuracy compared to using beam search.

Fast Training of Sparse Graph Neural Networks on Dense Hardware

Graph neural networks have become increasingly popular in recent years due to their ability to naturally encode relational input data and their ability to scale to large graphs by operating on a sparse representation of graph adjacency matrices. As we look to scale up these models using custom hardware, a natural assumption would be that we need hardware tailored to sparse operations and/or dynamic control flow. In this work, we question this assumption by scaling up sparse graph neural networks using a platform targeted at dense computation on fixed-size data. Drawing inspiration from optimization of numerical algorithms on sparse matrices, we develop techniques that enable training the sparse graph neural network model from Allamanis et al. [2018] in 13 minutes using a 512-core TPUv2 Pod, whereas the original training takes almost a day.