arXiv AI
Aug 5
Deep Divide-and-Reduce in Symbolic Regression
arXiv:2608. 02628v1 Announce Type: cross Abstract: Symbolic regression (SR) is the task of discovering underlying patterns from data and representing them using mathematical expressions.
Learning Randomized Reductions
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.
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arXiv AI
Jul 24
Identifying Good Rules for Efficient SAT Encodings of Single-Constant Multiplication Using Machine Learning
arXiv:2607. 21188v1 Announce Type: new Abstract: The Single Constant Multiplication problem is a fundamental NP-hard optimization task in hardware design, which seeks to decompose a fixed constant using only additions, subtractions, and bit-shifts.
arXiv AI
2d ago
Auto-Formalizing Neuro-Symbolic Predictors
arXiv:2610.01519v1 Announce Type: cross Abstract: Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified...
arXiv Machine Learning
Sep 2
Neural Symbollic Regression Using Deep Learning and Sparse Modelling
Neural Symbolic Regression (NSR) uses neural networks as functional preconditioners to learn smooth, noise‑robust approximations of target functions in an interaction‑aware nonlinear feature space. A subsequent LASSO step extracts sparse, interpretable closed‑form expressions, while distributed hyperparameter optimization with Ray Tune and ASHA scheduling improves predictive accuracy and symbolic fidelity. Experiments on the Nguyen benchmark demonstrate that NSR outperforms SINDy and untuned neural baselines in RMSE, noise robustness, and out‑of‑distribution generalization, with ablation studies highlighting the importance of feature interactions, neural depth, and tuning strategies.
arXiv Machine Learning
Sep 7
SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery
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 AI
Aug 5
Solver-Aware Decompositions for Programming-by-Example: When Dividing Requires Knowing how to Conquer
arXiv:2608. 03461v1 Announce Type: new Abstract: Decomposition-based Programming-by-example (PBE) scales performance by splitting tasks into subtasks that a learned synthesizer solves: a decomposer predicts intermediate subgoals, and a synthesizer generates programs conditioned on them.
arXiv Machine Learning
Jun 9
Decomposable Neuro Symbolic Regression
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 Machine Learning
Aug 6
Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selection
arXiv:2608. 04667v1 Announce Type: cross Abstract: Selective inference (SI) provides statistically valid $p$-values for hypotheses selected by applying an algorithm to the data, correcting for the bias that arises when the same data are used both to select and to test a hypothesis.
arXiv AI
Aug 11
Learning to Coordinate Symbolic Tools: LLM Agents for Verified Sum-of-Squares Certificates
arXiv:2608. 00326v2 Announce Type: replace Abstract: Tool calling allows large language models (LLMs) to invoke external computation during problem solving, a useful capability in various fields including AI for mathematics.
arXiv Machine Learning
Jul 27
Searching the Space of Feed-Forward Neural-Network Weight-Update Rules with Fixed Depth Symbolic Regression
arXiv:2607. 21855v1 Announce Type: new Abstract: We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks.
arXiv Machine Learning
Jul 3
LLM Priors for ERM over Programs
arXiv:2510. 14331v3 Announce Type: replace Abstract: We study program-learning methods that are efficient in both samples and computation.
arXiv Machine Learning
Aug 13
Computational Algebra with Attention: Transformer Oracles for Border Basis Algorithms
arXiv:2505. 23696v2 Announce Type: replace Abstract: Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields.