ThetaEvolve enables small open-source LLMs to achieve new best-known bounds on open problems such as circle packing by combining test-time RL with a large program database and lazy penalties.
Orrick, Bruce Solomon, Roland Dowdeswell, and Warren D
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abstract
We report new world records for the maximal determinant of an n-by-n matrix with entries +/-1. Using various techniques, we beat existing records for n=22, 23, 27, 29, 31, 33, 34, 35, 39, 45, 47, 53, 63, 69, 73, 77, 79, 93, and 95, and we present the record-breaking matrices here. We conjecture that our n=22 value attains the globally maximizing determinant in its dimension. We also tabulate new records for n=67, 75, 83, 87, 91 and 99, dimensions for which no previous claims have been made. The relevant matrices in all these dimensions, along with other pertinent information, are posted at http://www.indiana.edu/~maxdet \.
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SimpleTES scales test-time evaluation in LLMs to discover state-of-the-art solutions on 21 scientific problems across six domains, outperforming frontier models and optimization pipelines with examples like 2x faster LASSO and new Erdos constructions.
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ThetaEvolve: Test-time Learning on Open Problems
ThetaEvolve enables small open-source LLMs to achieve new best-known bounds on open problems such as circle packing by combining test-time RL with a large program database and lazy penalties.
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Evaluation-driven Scaling for Scientific Discovery
SimpleTES scales test-time evaluation in LLMs to discover state-of-the-art solutions on 21 scientific problems across six domains, outperforming frontier models and optimization pipelines with examples like 2x faster LASSO and new Erdos constructions.