More details on each of these datasets are given below. This data is referred to as "in-domain" because the validation data is generated using the same As for cache hits, they are also not counted as visits. Figure 9: MCTS-Guided decoding algorithm for Symbolic Regression with the pre-trained transformer model used for expansion and evaluation steps. MCTS algorithm (Figure 1) which can be used in a similar fashion but without sharing information with the pre-trained transformer. The approach involves fine-tuning an actor-critic-like model to adjust the pre-trained model on a group of symbolic regression instances.

Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's

SHallow REcurrent Decoders (SHRED) are effective for system identification and forecasting from sparse sensor measurements. Such models are light-weight and computationally efficient, allowing them to be trained on consumer laptops. SHRED-based models rely on Recurrent Neural Networks (RNNs) and a simple Multi-Layer Perceptron (MLP) for the temporal encoding and spatial decoding respectively. Despite the relatively simple structure of SHRED, they are able to predict chaotic dynamical systems on different physical, spatial, and temporal scales directly from a sparse set of sensor measurements. In this work, we modify SHRED by leveraging transformers (T-SHRED) embedded with symbolic regression for the temporal encoding, circumventing auto-regressive long-term forecasting for physical data. This is achieved through a new sparse identification of nonlinear dynamics (SINDy) attention mechanism into T-SHRED to impose sparsity regularization on the latent space, which also allows for immediate symbolic interpretation. Symbolic regression improves model interpretability by learning and regularizing the dynamics of the latent space during training. We analyze the performance of T-SHRED on three different dynamical systems ranging from low-data to high-data regimes.

Advances in artificial intelligence (AI) have made AI-driven scientific discovery a highly promising new paradigm [1]. Although AI has achieved remarkable results in tackling domain-specific challenges [2, 3], the ultimate aspiration from a paradigm-shifting perspective still lies in developing reliable AI systems capable of autonomous scientific discovery directly from a large collection of raw data without supervision [4, 5]. Current approaches to automated physics discovery focus on individual experiments, employing either neural network (NN)-based methods [6-25] or symbolic techniques [26-33]. By analyzing data from a single experiment, these methods can construct a specific model capable of predicting future data from the same experiment; if sufficiently simple, such a model may even be expressed in symbolic form [34-36]. Although these methods represent a crucial and successful stage towards automated scientific discovery, they have not yet reached a discovery capacity comparable to that of human physicists.

Medical decision-making makes frequent use of algorithms that combine risk equations with rules, providing clear and standardized treatment pathways. Symbolic regression (SR) traditionally limits its search space to continuous function forms and their parameters, making it difficult to model this decision-making. However, due to its ability to derive data-driven, interpretable models, SR holds promise for developing data-driven clinical risk scores. To that end we introduce Brush, an SR algorithm that combines decision-tree-like splitting algorithms with non-linear constant optimization, allowing for seamless integration of rule-based logic into symbolic regression and classification models. Brush achieves Pareto-optimal performance on SRBench, and was applied to recapitulate two widely used clinical scoring systems, achieving high accuracy and interpretable models. Compared to decision trees, random forests, and other SR methods, Brush achieves comparable or superior predictive performance while producing simpler models.

This paper proposes DeepRule, an integrated framework for automated business rule generation in retail assortment and pricing optimization. Addressing the systematic misalignment between existing theoretical models and real-world economic complexities, we identify three critical gaps: (1) data modality mismatch where unstructured textual sources (e.g. negotiation records, approval documents) impede accurate customer profiling; (2) dynamic feature entanglement challenges in modeling nonlinear price elasticity and time-varying attributes; (3) operational infeasibility caused by multi-tier business constraints. Our framework introduces a tri-level architecture for above challenges. We design a hybrid knowledge fusion engine employing large language models (LLMs) for deep semantic parsing of unstructured text, transforming distributor agreements and sales assessments into structured features while integrating managerial expertise. Then a game-theoretic constrained optimization mechanism is employed to dynamically reconcile supply chain interests through bilateral utility functions, encoding manufacturer-distributor profit redistribution as endogenous objectives under hierarchical constraints. Finally an interpretable decision distillation interface leveraging LLM-guided symbolic regression to find and optimize pricing strategies and auditable business rules embeds economic priors (e.g. non-negative elasticity) as hard constraints during mathematical expression search. We validate the framework in real retail environments achieving higher profits versus systematic B2C baselines while ensuring operational feasibility. This establishes a close-loop pipeline unifying unstructured knowledge injection, multi-agent optimization, and interpretable strategy synthesis for real economic intelligence.

This paper presents a method for uncovering hidden analytic relationships among the fundamental parameters of the Standard Model (SM), a foundational theory in physics that describes the fundamental particles and their interactions, using symbolic regression and genetic programming. Using this approach, we identify the simplest analytic relationships connecting pairs of these constants and report several notable expressions obtained with relative precision better than 1%. These results may serve as valuable inputs for model builders and artificial intelligence methods aimed at uncovering hidden patterns among the SM constants, or potentially used as building blocks for a deeper underlying law that connects all parameters of the SM through a small set of fundamental constants.

Large-scale genomic workflows used in precision medicine can process datasets spanning tens to hundreds of gigabytes per sample, leading to high memory spikes, intensive disk I/O, and task failures due to out-of-memory errors. Simple static resource allocation methods struggle to handle the variability in per-chromosome RAM demands, resulting in poor resource utilization and long runtimes. In this work, we propose multiple mechanisms for adaptive, RAM-efficient par-allelization of chromosome-level bioinformatics workflows. First, we develop a symbolic regression model that estimates per-chromosome memory consumption for a given task and introduces an interpolating bias to conservatively minimize over-allocation. Second, we present a dynamic scheduler that adaptively predicts RAM usage with a polynomial regression model, treating task packing as a Knapsack problem to optimally batch jobs based on predicted memory requirements. Additionally, we present a static scheduler that optimizes chromosome processing order to minimize peak memory while preserving throughput. Our proposed methods, evaluated on simulations and real-world genomic pipelines, provide new mechanisms to reduce memory overruns and balance load across threads. We thereby achieve faster end-to-end execution, showcasing the potential to optimize large-scale genomic workflows.

These explainers, however, only explain an instance (e.g., a graph) and fail to uncover the combinatorial reasoning learned by a G

In the area of explainable artificial intelligence, Symbolic Regression (SR) has emerged as a promising approach by discovering interpretable mathematical expressions that fit data. However, SR faces two main challenges: most methods are evaluated on scientific datasets with well-understood relationships, limiting generalization, and SR primarily targets single-output regression, whereas many real-world problems involve multi-target outputs with interdependent variables. To address these issues, we propose multi-task regression GINN-LP (MTRGINN-LP), an interpretable neural network for multi-target symbolic regression. By integrating GINN-LP with a multi-task deep learning, the model combines a shared backbone including multiple power-term approximator blocks with task-specific output layers, capturing inter-target dependencies while preserving interpretability. We validate multi-task GINN-LP on practical multi-target applications, including energy efficiency prediction and sustainable agriculture. Experimental results demonstrate competitive predictive performance alongside high interpretability, effectively extending symbolic regression to broader real-world multi-output tasks.