Language-Like Search Discovers Algorithms Tailored to Each Problem

TL;DR: Researchers reported a system that treats computation itself as language to discover new algorithms tailored to specific problem instances.

On Sept. 9, 2026, a team from the California Institute of Technology and SRI International reported a framework called computational language processing in the journal Science Advances, according to the Science Advances article titled "Discovering algorithms with computational language processing." The paper presents a method that represents operations as tokens, links those tokens with a grammar, and searches combinations with reinforcement-learning-guided tree search to assemble working procedures.

The authors are Théo Bourdais, Abeynaya Gnanasekaran, Houman Owhadi and Tuhin Sahai, according to that same Science Advances article. The author listing identifies Bourdais and Owhadi with the California Institute of Technology and Gnanasekaran and Sahai with SRI International. The funding acknowledgement names the Defense Advanced Research Projects Agency and the Office of Naval Research.

A language made of computation

The central idea is to describe an algorithm the way language models describe text: as a sequence of units joined under rules. In this case the units are not English words or lines of software code. They are computational operations, according to the Science Advances article titled "Discovering algorithms with computational language processing."

The paper calls these units computational tokens. A grammar defines which tokens may follow one another, so random combinations do not produce invalid procedures. Valid chains form increasingly elaborate procedures, from short operation sequences to multi-stage solvers.

New capability enters the vocabulary through byte-pair encoding, according to that Science Advances article. Byte-pair encoding is a compression-inspired procedure that merges frequently co-occurring units into a larger unit. Here it merges frequently useful token chains into new, higher-level tokens. The system can therefore reuse a discovered subroutine as a single building block in later searches.

Search over those chains uses an ensemble version of Monte Carlo tree search guided by reinforcement learning, according to the same Science Advances article. Monte Carlo tree search explores a decision tree by sampling branches, estimating outcomes, and concentrating later samples on branches that look promising. The ensemble variant runs multiple searches in parallel. Reinforcement learning supplies the scoring signal that steers exploration toward chains with stronger measured performance.

Why work below code generation

Much recent work on automated discovery operates by asking a large language model to write program text. The new paper positions itself one level lower, at the computational level rather than the code-generation level, according to the Science Advances article titled "Discovering algorithms with computational language processing."

The distinction matters for reuse. A code generator outputs a specific script in a specific programming language. A computational-level description specifies operations and order, which can later be translated into code for different settings. The authors state that the high-level description simplifies conceptualization and generalization of complex algorithms and interfaces naturally with downstream code-generation methods, according to that Science Advances article.

That design also links the work to older research directions. The introduction cites early theories of program discovery and inductive inference, automatic code generation for numerical solvers, and systematic algebraic searches for faster matrix multiplication beginning with work by Bini and colleagues, according to the same Science Advances article. It then contrasts those problem-specific efforts with the goal of a more general discovery framework.

Instance-specific instead of one-size-fits-all

A second distinction is adaptation to individual inputs. Many solvers are built for an entire problem class and then applied unchanged to every example in that class, according to the Science Advances article titled "Discovering algorithms with computational language processing."

The reported framework instead performs reinforcement learning directly at the computational level of each specific problem instance. That means the search can produce one procedure for a class and different procedures tuned to particular instances within it. The paper argues that procedures exploiting instance-specific structure are likely to outperform uniform procedures that ignore variation between instances, according to that Science Advances article.

This framing responds directly to systems such as AlphaEvolve, which the paper discusses as an example of direct code-generation with ensembles of large language models serving as coding agents, according to the same Science Advances article. Those systems, the paper states, are often combined with evaluation metrics and evolutionary strategies such as genetic algorithms to refine large code segments. The paper characterizes AlphaEvolve and similar methods as yielding a single solution applied uniformly across all instances within a problem class.

Test 1: Hard combinatorial optimization

The team demonstrated the method on the quadratic assignment problem, generally abbreviated QAP, according to the Science Advances article titled "Discovering algorithms with computational language processing." QAP asks for an assignment of facilities to locations that minimizes a cost depending on flows between facilities and distances between locations. It is described in the paper as a generic strongly nondeterministic polynomial-time-hard combinatorial optimization problem to which many other nondeterministic polynomial-time-hard problems can be reduced.

That hardness classification signals practical relevance. Strongly nondeterministic polynomial-time-hard problems lack known efficient exact solvers that scale to large inputs. Researchers therefore compare heuristics by solution quality achieved within a fixed computational budget. The paper reports that its methodology rediscovers, improves and generates new algorithms that substantially outperform existing methods for such problems, according to that Science Advances article.

The reference list places the QAP experiments in a long literature. Cited works include the QAPLIB benchmark library described by Burkard, Karisch and Rendl, surveys of the quadratic assignment problem, studies of simulated annealing for the quadratic assignment problem, and work on generating QAP instances with known optimum solutions, according to the same Science Advances article. Other cited optimization background includes work on the assignment and transportation problems, the Hungarian method, continuous relaxations for the traveling salesman problem, and texts on combinatorial optimization.

The paper does not present the framework as a single fixed heuristic for QAP. Because search runs per instance, the output can include distinct instance-specific procedures tuned to the nuances of individual problems, according to the Science Advances article titled "Discovering algorithms with computational language processing." That allows a deployment to keep a general solver while adding specialized variants for recurring difficult inputs.

Test 2: Quantum search

The second demonstration concerns quantum unstructured search, according to the Science Advances article titled "Discovering algorithms with computational language processing." The canonical reference point is the quantum search procedure introduced by Lov Grover and described in 1996 work on a fast quantum mechanical algorithm for database search. Grover's procedure offers a quadratic speedup over exhaustive classical search for unstructured lookup.

The paper reports that its framework rediscovers, improves and generates new algorithms that substantially outperform existing methods for foundational quantum computing approaches such as Grover's procedure, according to that Science Advances article. The cited background includes work on depth optimization of quantum search algorithms beyond Grover's algorithm by Zhang and Korepin, according to the same Science Advances article.

Operating with computational tokens is a natural fit for quantum circuits. A quantum algorithm can be viewed as an ordered application of gates and diffusion operations. Those operations map directly onto a token vocabulary, while grammar rules enforce physically and logically consistent orderings. Byte-pair encoding can then package a useful gate sequence into a reusable macro-operation. The ensemble tree search explores alternative orderings and macro-operations under a performance score.

Test 3: Quantum approximate optimization

The third demonstration targets the quantum approximate optimization algorithm, usually abbreviated QAOA, according to the Science Advances article titled "Discovering algorithms with computational language processing." QAOA is a hybrid quantum-classical procedure for approximate combinatorial optimization. It alternates parameterized quantum evolutions with classical tuning of the parameters.

The paper reports that the same token-chaining and search machinery generates procedures that substantially outperform existing methods for QAOA, according to that Science Advances article. The result is notable because QAOA itself is already a template whose angles must be chosen well. Discovery here means finding better structural patterns and parameter-setting strategies, not merely running a standard template longer.

Together the three demonstrations span classical discrete optimization and parameterized quantum procedures. The authors state that the high-level framework has potential to extend to other domains such as systems engineering and mathematical discovery, according to the same Science Advances article. They do not report completed results in those additional domains in the Sept. 9 paper.

How this compares with FunSearch

To understand the novelty, it helps to compare with FunSearch, the Google DeepMind system for discovering programs that solve mathematical and algorithmic problems, according to the overview titled "FunSearch." FunSearch combines a large language model with an automated evaluator and an evolutionary search procedure, generating candidate programs, scoring them, and using high-performing programs to produce new candidates.

In FunSearch the user provides a problem specification, an evaluation function, and an initial program or program skeleton, according to that "FunSearch" overview. At each iteration the system samples existing programs from a database, favors higher-scoring programs, builds a prompt for a pretrained large language model, and asks the model to generate modified programs. Generated programs are executed and scored. Valid high performers re-enter the database and seed later prompts.

FunSearch uses an island-based evolutionary method intended to maintain diverse candidate programs and reduce the risk of becoming trapped in local optima, according to the same "FunSearch" overview. One stated advantage is that it outputs programs that can sometimes be inspected, simplified and interpreted by researchers, instead of only producing a final numerical answer or a large list of objects.

Demonstrations reported for FunSearch include the cap set problem in extremal combinatorics and the online bin packing problem, according to that "FunSearch" overview. For cap sets, which concern the largest subset of a vector space over three elements with no three points in a line, FunSearch found a cap set of size 512 in dimension 8, improving on previously known constructions. For online bin packing, where items must be assigned to bins as they arrive, the discovered heuristics outperformed the common first-fit and best-fit baselines on simulated data and OR-Library benchmark instances.

How this compares with AlphaEvolve

AlphaEvolve extends the same broad loop to whole codebases, according to the overview titled "AlphaEvolve." It was developed by Google DeepMind and unveiled in May 2025. It is described as an evolutionary coding agent for designing advanced algorithms based on large language models such as Gemini.

AlphaEvolve needs an evaluation function with metrics to optimize and an initial algorithm, according to that "AlphaEvolve" overview. At each step it uses the language model to produce variants of existing algorithms and then selects the most effective ones. Unlike domain-specific predecessors such as AlphaFold or AlphaTensor, it is designed as a general-purpose system that can operate across scientific and engineering tasks by automatically modifying code and optimizing for multiple objectives. Its architecture allows it to evaluate code programmatically, reducing reliance on human input.

Reported achievements for AlphaEvolve include rediscovery of state-of-the-art solutions about 75% of the time across a selection of 50 open mathematical problems and discovery of improved solutions about 20% of the time, including work advancing the kissing number problem, according to that "AlphaEvolve" overview. Reported production uses include improved data-center scheduling heuristics that enabled recovery of 0.7% of stranded resources, plus work on TPU circuit design and a training matrix-multiplication kernel for Gemini.

A Sept. 8, 2026 commentary titled "When a language model finds new mathematics, the proof is a program" emphasizes a shared design choice across FunSearch and AlphaEvolve: every candidate answer is checked by a machine before a person evaluates it. That commentary notes that in both systems the model proposes short programs, an evaluator runs them against a precisely defined problem and scores them, and the best-scoring programs seed the next round. It adds specific AlphaEvolve examples reported by DeepMind, including an algorithm that multiplies two 4x4 complex-valued matrices using 48 scalar multiplications, improving on Strassen's 1969 algorithm; a configuration of 593 outer spheres setting a new lower bound for the kissing number in 11 dimensions; and a scheduling heuristic reported to recover on average 0.7% of worldwide compute in production.

The new computational-language framework differs by moving search away from program text. According to the Science Advances article titled "Discovering algorithms with computational language processing," operating at the computational rather than code-generation level lets the system tailor algorithms specifically to problem instances, not merely classes. FunSearch and AlphaEvolve search over program fragments or codebases guided by scores; the new system searches over grammatically consistent token chains and creates new tokens during search.

What changes for engineers and labs

For U.S. technology teams, the practical takeaway is specialization at low marginal cost. A logistics, chip-design or scheduling group could maintain a strong general solver while letting the discovery loop craft variants for its hardest recurring instances. The paper explicitly motivates adaptive discovery on the grounds that instance-specific structure, when exploited, can beat uniform treatment, according to the Science Advances article titled "Discovering algorithms with computational language processing."

For quantum-computing efforts, the reported quantum-search and QAOA results suggest that circuit patterns themselves can be discovered rather than hand-derived. Because the token vocabulary can encode gates and classical update steps, the same search machinery applies to both the quantum operations and the surrounding optimization loop. That unified view may shorten the cycle between proposing a new ansatz and testing it on simulators or hardware.

For research evaluation, the FunSearch and AlphaEvolve experience offers a template. The commentary titled "When a language model finds new mathematics, the proof is a program" argues that machine-generated constructions gain trust quickly when evidence is an artifact anyone can run, not a transcript of model reasoning. A cap set either has the claimed size or it does not; a matrix-multiplication scheme either reproduces the product or it does not. The new paper follows that pattern by reporting executable procedures for optimization and quantum tasks rather than unaudited predictions.

Open questions

The Sept. 9 paper establishes a framework and three demonstration areas, not a universal solver. It states substantial outperformance for strongly nondeterministic polynomial-time-hard combinatorial optimization and for Grover-type search and QAOA, according to the Science Advances article titled "Discovering algorithms with computational language processing." It does not claim optimal solutions, nor does it report live deployment on operating power grids, production data centers or commercial quantum processors.

Independent re-execution remains the next step, as emphasized for machine-discovered mathematics in the commentary titled "When a language model finds new mathematics, the proof is a program." That commentary lists three needs for turning celebrated results into routine science: evaluators for messier problems where the objective is not a single verifiable number, provenance records showing which models and how many candidates were tried and discarded, and independent re-execution of results by parties other than the originating system. Those criteria apply directly to the new framework's claims about tailored optimization and quantum procedures.

Provenance and compute cost will also matter. Evolutionary search with language guidance typically evaluates many candidates before finding winners. The paper describes ensemble search and reinforcement-learning guidance as the efficiency mechanism, according to the Science Advances article titled "Discovering algorithms with computational language processing." Detailed budgets, seeds and code releases will determine how easily other labs can reproduce instance-specific gains.