Satisfiability Modulo Counting (SMC) is a recently proposed general language to reason about problems integrating statistical and symbolic artificial intelligence. An SMC formula is an extended SAT formula in which the truth values of a few Boolean variables are determined by probabilistic inference. Existing approximate solvers optimize surrogate objectives, which lack formal guarantees. Current exact solvers directly integrate SAT solvers and probabilistic inference solvers resulting in slow performance because of many back-and-forth invocations of both solvers. We propose KOCO-SMC, an integrated exact SMC solver that efficiently tracks lower and upper bounds in the probabilistic inference process. It enhances computational efficiency by enabling early estimation of probabilistic inference using only partial variable assignments, whereas existing methods require full variable assignments. In the experiment, we compare KOCO-SMC with currently available approximate and exact SMC solvers on large-scale datasets and real-world applications. Our approach delivers high-quality solutions with high efficiency.

Vertical Symbolic Regression (VSR) recently has been proposed to expedite the discovery of symbolic equations with many independent variables from experimental data. VSR reduces the search spaces following the vertical discovery path by building from reduced-form equations involving a subset of independent variables to full-fledged ones. Proved successful by many symbolic regressors, deep neural networks are expected to further scale up VSR. Nevertheless, directly combining VSR with deep neural networks will result in difficulty in passing gradients and other engineering issues. We propose Vertical Symbolic Regression using Deep Policy Gradient (VSR-DPG) and demonstrate that VSR-DPG can recover ground-truth equations involving multiple input variables, significantly beyond both deep reinforcement learning-based approaches and previous VSR variants. Our VSR-DPG models symbolic regression as a sequential decision-making process, in which equations are built from repeated applications of grammar rules. The integrated deep model is trained to maximize a policy gradient objective. Experimental results demonstrate that our VSR-DPG significantly outperforms popular baselines in identifying both algebraic equations and ordinary differential equations on a series of benchmarks.

Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical Artificial Intelligence. SMC searches for policy interventions to control probabilistic outcomes. Solving SMC is challenging because of its highly intractable nature($\text{NP}^{\text{PP}}$-complete), incorporating statistical inference and symbolic reasoning. Previous research on SMC solving lacks provable guarantees and/or suffers from sub-optimal empirical performance, especially when combinatorial constraints are present. We propose XOR-SMC, a polynomial algorithm with access to NP-oracles, to solve highly intractable SMC problems with constant approximation guarantees. XOR-SMC transforms the highly intractable SMC into satisfiability problems, by replacing the model counting in SMC with SAT formulae subject to randomized XOR constraints. Experiments on solving important SMC problems in AI for social good demonstrate that XOR-SMC finds solutions close to the true optimum, outperforming several baselines which struggle to find good approximations for the intractable model counting in SMC.

Automating scientific discovery has been a grand goal of Artificial Intelligence (AI) and will bring tremendous societal impact. Learning symbolic expressions from experimental data is a vital step in AI-driven scientific discovery. Despite exciting progress, most endeavors have focused on the horizontal discovery paths, i.e., they directly search for the best expression in the full hypothesis space involving all the independent variables. Horizontal paths are challenging due to the exponentially large hypothesis space involving all the independent variables. We propose Vertical Symbolic Regression (VSR) to expedite symbolic regression. The VSR starts by fitting simple expressions involving a few independent variables under controlled experiments where the remaining variables are held constant. It then extends the expressions learned in previous rounds by adding new independent variables and using new control variable experiments allowing these variables to vary. The first few steps in vertical discovery are significantly cheaper than the horizontal path, as their search is in reduced hypothesis spaces involving a small set of variables. As a consequence, vertical discovery has the potential to supercharge state-of-the-art symbolic regression approaches in handling complex equations with many contributing factors. Theoretically, we show that the search space of VSR can be exponentially smaller than that of horizontal approaches when learning a class of expressions. Experimentally, VSR outperforms several baselines in learning symbolic expressions involving many independent variables.

Meta Reinforcement Learning (Meta RL) trains agents that adapt to fast-changing environments and tasks. Current strategies often lose adaption efficiency due to the passive nature of model exploration, causing delayed understanding of new transition dynamics. This results in particularly fast-evolving tasks being impossible to solve. We propose a novel approach, Hypothesis Network Planned Exploration (HyPE), that integrates an active and planned exploration process via the hypothesis network to optimize adaptation speed. HyPE uses a generative hypothesis network to form potential models of state transition dynamics, then eliminates incorrect models through strategically devised experiments. Evaluated on a symbolic version of the Alchemy game, HyPE outpaces baseline methods in adaptation speed and model accuracy, validating its potential in enhancing reinforcement learning adaptation in rapidly evolving settings.

Design generation requires tight integration of neural and symbolic reasoning, as good design must meet explicit user needs and honor implicit rules for aesthetics, utility, and convenience. Current automated design tools driven by neural networks produce appealing designs, but cannot satisfy user specifications and utility requirements. Symbolic reasoning tools, such as constraint programming, cannot perceive low-level visual information in images or capture subtle aspects such as aesthetics. We introduce the Spatial Reasoning Integrated Generator (SPRING) for design generation. SPRING embeds a neural and symbolic integrated spatial reasoning module inside the deep generative network. The spatial reasoning module decides the locations of objects to be generated in the form of bounding boxes, which are predicted by a recurrent neural network and filtered by symbolic constraint satisfaction. Embedding symbolic reasoning into neural generation guarantees that the output of SPRING satisfies user requirements. Furthermore, SPRING offers interpretability, allowing users to visualize and diagnose the generation process through the bounding boxes. SPRING is also adept at managing novel user specifications not encountered during its training, thanks to its proficiency in zero-shot constraint transfer. Quantitative evaluations and a human study reveal that SPRING outperforms baseline generative models, excelling in delivering high design quality and better meeting user specifications.

Symbolic regression, as one of the most crucial tasks in AI for science, discovers governing equations from experimental data. Popular approaches based on genetic programming, Monte Carlo tree search, or deep reinforcement learning learn symbolic regression from a fixed dataset. They require massive datasets and long training time especially when learning complex equations involving many variables. Recently, Control Variable Genetic Programming (CVGP) has been introduced which accelerates the regression process by discovering equations from designed control variable experiments. However, the set of experiments is fixed a-priori in CVGP and we observe that sub-optimal selection of experiment schedules delay the discovery process significantly. To overcome this limitation, we propose Racing Control Variable Genetic Programming (Racing-CVGP), which carries out multiple experiment schedules simultaneously. A selection scheme similar to that used in selecting good symbolic equations in the genetic programming process is implemented to ensure that promising experiment schedules eventually win over the average ones. The unfavorable schedules are terminated early to save time for the promising ones. We evaluate Racing-CVGP on several synthetic and real-world datasets corresponding to true physics laws. We demonstrate that Racing-CVGP outperforms CVGP and a series of symbolic regressors which discover equations from fixed datasets.

Accelerating the learning of Partial Differential Equations (PDEs) from experimental data will speed up the pace of scientific discovery. Previous randomized algorithms exploit sparsity in PDE updates for acceleration. However such methods are applicable to a limited class of decomposable PDEs, which have sparse features in the value domain. We propose Reel, which accelerates the learning of PDEs via random projection and has much broader applicability. Reel exploits the sparsity by decomposing dense updates into sparse ones in both the value and frequency domains. This decomposition enables efficient learning when the source of the updates consists of gradually changing terms across large areas (sparse in the frequency domain) in addition to a few rapid updates concentrated in a small set of "interfacial" regions (sparse in the value domain). Random projection is then applied to compress the sparse signals for learning. To expand the model applicability, Taylor series expansion is used in Reel to approximate the nonlinear PDE updates with polynomials in the decomposable form. Theoretically, we derive a constant factor approximation between the projected loss function and the original one with poly-logarithmic number of projected dimensions. Experimentally, we provide empirical evidence that our proposed Reel can lead to faster learning of PDE models (70-98% reduction in training time when the data is compressed to 1% of its original size) with comparable quality as the non-compressed models.

The availability of tera-byte scale experiment data calls for AI driven approaches which automatically discover scientific models from data. Nonetheless, significant challenges present in AI-driven scientific discovery: (i) The annotation of large scale datasets requires fundamental re-thinking in developing scalable crowdsourcing tools. (ii) The learning of scientific models from data calls for innovations beyond black-box neural nets. (iii) Novel visualization and diagnosis tools are needed for the collaboration of experimental and theoretical physicists, and computer scientists. We present Phase-Field-Lab platform for end-to-end phase field model discovery, which automatically discovers phase field physics models from experiment data, integrating experimentation, crowdsourcing, simulation and learning. Phase-Field-Lab combines (i) a streamlined annotation tool which reduces the annotation time (by ~50-75%), while increasing annotation accuracy compared to baseline; (ii) an end-to-end neural model which automatically learns phase field models from data by embedding phase field simulation and existing domain knowledge into learning; and (iii) novel interfaces and visualizations to integrate our platform into the scientific discovery cycle of domain scientists. Our platform is deployed in the analysis of nano-structure evolution in materials under extreme conditions (high temperature and irradiation). Our approach reveals new properties of nano-void defects, which otherwise cannot be detected via manual analysis.

This paper proposes an algorithm that aims to improve generalization for reinforcement learning agents by removing overfitting to confounding features. Our approach consists of a max-min game theoretic objective. A generator transfers the style of observation during reinforcement learning. An additional goal of the generator is to perturb the observation, which maximizes the agent's probability of taking a different action. In contrast, a policy network updates its parameters to minimize the effect of such perturbations, thus staying robust while maximizing the expected future reward. Based on this setup, we propose a practical deep reinforcement learning algorithm, Adversarial Robust Policy Optimization (ARPO), to find a robust policy that generalizes to unseen environments. We evaluate our approach on Procgen and Distracting Control Suite for generalization and sample efficiency. Empirically, ARPO shows improved performance compared to a few baseline algorithms, including data augmentation.