In Symbolic Regression (SR), Genetic Programming (GP) is a popular search algorithm that delivers state-of-the-art results in term of accuracy. Its success relies on the concept of neutrality, which induces large plateaus that the search can safely navigate to more promising regions. Navigating these plateaus, while necessary, requires the computation of redundant expressions, up to 60% of the total number of evaluation, as noted in a recent study. The equality graph (e-graph) structure can compactly store and group equivalent expressions enabling us to verify if a given expression and their variations were already visited by the search, thus enabling us to avoid unnecessary computation. We propose a new search algorithm for symbolic regression called SymRegg that revolves around the e-graph structure following simple steps: perturb solutions sampled from a selection of expressions stored in the e-graph, if it generates an unvisited expression, insert it into the e-graph and generates its equivalent forms. We show that SymRegg is capable of improving the efficiency of the search, maintaining consistently accurate results across different datasets while requiring a choice of a minimalist set of hyperparameters.

E-graphs have attracted growing interest in many fields, particularly in logic synthesis and formal verification. E-graph extraction is a challenging NP-hard combinatorial optimization problem. It requires identifying optimal terms from exponentially many equivalent expressions, serving as the primary performance bottleneck in e-graph based optimization tasks. However, traditional extraction methods face a critical trade-off: heuristic approaches offer speed but sacrifice optimality, while exact methods provide optimal solutions but face prohibitive computational costs on practical problems. We present e-boost, a novel framework that bridges this gap through three key innovations: (1) parallelized heuristic extraction that leverages weak data dependence to compute DAG costs concurrently, enabling efficient multi-threaded performance without sacrificing extraction quality; (2) adaptive search space pruning that employs a parameterized threshold mechanism to retain only promising candidates, dramatically reducing the solution space while preserving near-optimal solutions; and (3) initialized exact solving that formulates the reduced problem as an Integer Linear Program with warm-start capabilities, guiding solvers toward high-quality solutions faster. Across the diverse benchmarks in formal verification and logic synthesis fields, e-boost demonstrates 558x runtime speedup over traditional exact approaches (ILP) and 19.04% performance improvement over the state-of-the-art extraction framework (SmoothE). In realistic logic synthesis tasks, e-boost produces 7.6% and 8.1% area improvements compared to conventional synthesis tools with two different technology mapping libraries. e-boost is available at https://github.com/Yu-Maryland/e-boost.

--Choice network construction is a critical technique for alleviating structural bias issues in Boolean optimization, equivalence checking, and technology mapping. Previous works on lossless synthesis utilize independent optimization to generate multiple snapshots, and use simulation and SA T solvers to identify functionally equivalent nodes. These nodes are then merged into a subject graph with choice nodes. However, such methods often neglect the quality of these choices--raising the question of whether they truly contribute to effective technology mapping. This paper introduces CRISTAL, a novel methodology and framework to constructing Boolean choice networks. Specifically, CRISTAL introduces a novel flow of choice network-based synthesis and mapping, includes representative logic cone search, structural mutation for generating diverse choice structures via equality saturation, and priority-ranking choice selection along with choice network construction and validation. Our experimental results demonstrate that CRISTAL outperforms the state-of-the-art Boolean choice network construction implemented in ABC in the post-mapping stage, achieving average reductions of 3.85%/8.35% The concept of choice network was pioneered to address optimization limitations in Electronic Design Automation (EDA).

Regression analysis is used for prediction and to understand the effect of independent variables on dependent variables. Symbolic regression (SR) automates the search for non-linear regression models, delivering a set of hypotheses that balances accuracy with the possibility to understand the phenomena. Many SR implementations return a Pareto front allowing the choice of the best trade-off. However, this hides alternatives that are close to non-domination, limiting these choices. Equality graphs (e-graphs) allow to represent large sets of expressions compactly by efficiently handling duplicated parts occurring in multiple expressions. E-graphs allow to store and query all SR solution candidates visited in one or multiple GP runs efficiently and open the possibility to analyse much larger sets of SR solution candidates. We introduce rEGGression, a tool using e-graphs to enable the exploration of a large set of symbolic expressions which provides querying, filtering, and pattern matching features creating an interactive experience to gain insights about SR models. The main highlight is its focus in the exploration of the building blocks found during the search that can help the experts to find insights about the studied phenomena.This is possible by exploiting the pattern matching capability of the e-graph data structure.

The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to sequentially rewrite the input computation graph into an equivalent but faster one by replacing individual subgraphs. This approach gives rise to the so-called phase-ordering problem in which the application of one rewrite rule can eliminate the possibility to apply an even better one later on. Recent work has shown that equality saturation, a technique from compiler optimization, can mitigate this issue by first building an intermediate representation (IR) that efficiently stores multiple optimized versions of the input program before extracting the best solution in a second step. In practice, however, memory constraints prevent the IR from capturing all optimized versions and thus reintroduce the phase-ordering problem in the construction phase. In this paper, we present a tensor graph rewriting approach that uses Monte Carlo tree search to build superior IRs by identifying the most promising rewrite rules. We also introduce a novel extraction algorithm that can provide fast and accurate runtime estimates of tensor programs represented in an IR. Our approach improves the inference speedup of neural networks by up to 11% compared to existing methods.

Query rewrite systems perform graph substitutions using rewrite rules to generate optimal SQL query plans. Rewriting logical and physical relational query plans is proven to be an NP-hard sequential decision-making problem with a search space exponential in the number of rewrite rules. In this paper, we address the query rewrite problem by interleaving Equality Saturation and Graph Reinforcement Learning (RL). The proposed system, Aurora, rewrites relational queries by guiding Equality Saturation, a method from compiler literature to perform non-destructive graph rewriting, with a novel RL agent that embeds both the spatial structure of the query graph as well as the temporal dimension associated with the sequential construction of query plans. Our results show Graph Reinforcement Learning for non-destructive graph rewriting yields SQL plans orders of magnitude faster than existing equality saturation solvers, while also achieving competitive results against mainstream query optimisers.

Rewrite systems [6, 10, 12] have been widely employing equality saturation [9], which is an optimisation methodology that uses a saturated e-graph to represent all possible sequences of rewrite simultaneously, and then extracts the optimal one. As such, optimal results can be achieved by avoiding the phase-ordering problem. However, we observe that when the e-graph is not saturated, it cannot represent all possible rewrite opportunities and therefore the phase-ordering problem is re-introduced during the construction phase of the e-graph. To address this problem, we propose MCTS-GEB, a domain-general rewrite system that applies reinforcement learning (RL) to e-graph construction. At its core, MCTS-GEB uses a Monte Carlo Tree Search (MCTS) [3] to efficiently plan for the optimal e-graph construction, and therefore it can effectively eliminate the phase-ordering problem at the construction phase and achieve better performance within a reasonable time. Evaluation in two different domains shows MCTS-GEB can outperform the state-of-the-art rewrite systems by up to 49x, while the optimisation can generally take less than an hour, indicating MCTS-GEB is a promising building block for the future generation of rewrite systems.

One of the major optimizations employed in deep learning frameworks is graph rewriting. Production frameworks rely on heuristics to decide if rewrite rules should be applied and in which order. Prior research has shown that one can discover more optimal tensor computation graphs if we search for a better sequence of substitutions instead of relying on heuristics. However, we observe that existing approaches for tensor graph superoptimization both in production and research frameworks apply substitutions in a sequential manner. Such sequential search methods are sensitive to the order in which the substitutions are applied and often only explore a small fragment of the exponential space of equivalent graphs. This paper presents a novel technique for tensor graph superoptimization that employs equality saturation to apply all possible substitutions at once. We show that our approach can find optimized graphs with up to 16% speedup over state-of-the-art, while spending on average 48x less time optimizing.