arXiv:2312. 08472v2 Announce Type: replace-cross Abstract: Transcendental functions, such as the exponential, are central to scientific computing, yet they cannot be natively calculated by digital hardware.
arXiv:2505. 23851v2 Announce Type: replace-cross Abstract: Large language models (LLMs) are increasingly applied to symbolic mathematics, yet existing evaluations often conflate pattern memorization with genuine reasoning.
arXiv:2606. 09930v1 Announce Type: cross Abstract: The boundary between program execution and gradient-based optimization has long limited the use of code itself as a learnable scientific model.
The paper introduces a GPU-resident, batched Levenberg–Marquardt solver that efficiently optimizes constants in tree-based genetic programming for symbolic regression. By using reverse-mode automatic differentiation to assemble per-tree Jacobians in a single backward sweep, the solver’s per-iteration cost becomes independent of the number of constants per tree, achieving up to 510,000 trees per second on an NVIDIA A100. Integrated into EvoGP, the solver enables end-to-end search that recovers governing equations on 10 of 18 constructed problems, a significant improvement over stock EvoGP.
arXiv:2511. 04124v3 Announce Type: replace Abstract: Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data.
arXiv:2604. 17402v2 Announce Type: replace Abstract: Symbolic regression (SR) with genetic programming (GP) aims to discover interpretable mathematical expressions directly from data.
arXiv:2512. 03476v3 Announce Type: replace-cross Abstract: Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a major bottleneck.
SMILE (Sine, Multiplication, Identity, Logarithm, Exponential) is a hybrid framework that merges continuous gradient-based optimization with discrete symbolic recovery for symbolic regression. It operates in three stages: structural analysis to uncover the compositional hierarchy of the target expression, continuous optimization to learn parameters of a network using interpretable activations, and symbolic recovery via structured pruning, coefficient optimization, and rounding to produce a compact expression with exact symbolic constants. Evaluated on SRBench, SMILE achieves the highest symbolic solution rate under high noise, remains on the Pareto front of accuracy versus complexity, and recovers simpler expressions much faster than competing methods.
arXiv:2608. 16876v1 Announce Type: cross Abstract: We introduce Automatic Symbolic Regression (AutoSR), a fully automated system that instantiates Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations.
arXiv:2412. 18134v5 Announce Type: replace Abstract: Randomized self-reductions (RSRs) express $f(x)$ using $f$ evaluated at random correlated points, enabling self-correcting programs, instance-hiding protocols, and applications in complexity theory and cryptography.
arXiv:2606. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.
arXiv:2609.37849v1 Announce Type: cross Abstract: Scientific software is increasingly required to process larger datasets while maintaining acceptable execution times. Software optimization tradition...
arXiv:2606. 17289v1 Announce Type: new Abstract: AI systems based on artificial neural networks are being developed with aspirations of pushing the boundary of human mathematical knowledge.