\(X\)-evolve: Solution space evolution powered by large language models

While combining large language models (LLMs) with evolutionary algorithms (EAs) shows promise for solving complex optimization problems, current approaches typically evolve individual solutions, often incurring high LLM call costs. We introduce \(X\)-evolve, a paradigm-shifting method that instead evolves solution spaces \(X\) (sets of individual solutions) - subsets of the overall search space \(S\). In \(X\)-evolve, LLMs generate tunable programs wherein certain code snippets, designated as parameters, define a tunable solution space. A score-based search algorithm then efficiently explores this parametrically defined space, guided by feedback from objective function scores. This strategy enables broader and more efficient exploration, which can potentially accelerate convergence at a much lower search cost, requiring up to two orders of magnitude fewer LLM calls than prior leading methods. We demonstrate \(X\)-evolve's efficacy across three distinct hard optimization problems. For the cap set problem, we discover a larger partial admissible set, establishing a new tighter asymptotic lower bound for the cap set constant (\(C \ge 2.2203\)). In information theory, we uncover a larger independent set for the 15-vertex cycle graph (\(\mathcal{C}_{15}^{\boxtimes 5}\), size 19,946), thereby raising the known lower bound on its Shannon capacity. Furthermore, for the NP-hard online bin packing problem, we generate heuristics that consistently outperform standard strategies across established benchmarks. By evolving solution spaces, our method considerably improves search effectiveness, making it possible to tackle high-dimensional problems that were previously computationally prohibitive.

TLP: A Deep Learning-based Cost Model for Tensor Program Tuning

Tensor program tuning is a non-convex objective optimization problem, to which search-based approaches have proven to be effective. At the core of the search-based approaches lies the design of the cost model. Though deep learning-based cost models perform significantly better than other methods, they still fall short and suffer from the following problems. First, their feature extraction heavily relies on expert-level domain knowledge in hardware architectures. Even so, the extracted features are often unsatisfactory and require separate considerations for CPUs and GPUs. Second, a cost model trained on one hardware platform usually performs poorly on another, a problem we call cross-hardware unavailability. In order to address these problems, we propose TLP and MTLTLP. TLP is a deep learning-based cost model that facilitates tensor program tuning. Instead of extracting features from the tensor program itself, TLP extracts features from the schedule primitives. We treat schedule primitives as tensor languages. TLP is thus a Tensor Language Processing task. In this way, the task of predicting the tensor program latency through the cost model is transformed into a natural language processing (NLP) regression task. MTL-TLP combines Multi-Task Learning and TLP to cope with the cross-hardware unavailability problem. We incorporate these techniques into the Ansor framework and conduct detailed experiments. Results show that TLP can speed up the average search time by 9.1X and 3.0X on CPU and GPU workloads, respectively, compared to the state-of-the-art implementation. MTL-TLP can achieve a speed-up of 4.7X and 2.9X on CPU and GPU workloads, respectively, using only 7% of the target hardware data.