Paul Biberstein | Search arXiv

arXiv2026

The Output-Space Hypothesis: Enumerative Equivalence Checking for Tensor Programs

Tensor programs, as used in deep learning models, are a prime target for optimization, as small performance improvements can have a large impact across training or inference workloads. However, such optimizations are complicated and can produce subtle bugs. Traditionally, correctness is assumed when differential testing against a reference on random inputs fails to reveal bugs. However, the inputs to these programs are massive tensors, and finding bugs can require generating extremely low likelihood inputs with precise relationships among their values. We propose a novel way to find bugs more consistently by flipping the quantifiers. Rather than generating a single input and checking all output tensor locations for equivalence, what if you could check a single output tensor location's equivalence for all inputs? We implement this idea in a system, \dirigo, by using a novel symbolic execution strategy. We demonstrate that \dirigo can find bugs effectively in a public dataset of 6,988 AI-written CUDA kernels that are all marked correct by differential testing. Of these, \dirigo finds 600 kernels that are actually buggy, and finds 97.3\% of those bugs within two minutes.

cs.PL↗

arXiv2025

Lobster: A GPU-Accelerated Framework for Neurosymbolic Programming

Neurosymbolic programs combine deep learning with symbolic reasoning to achieve better data efficiency, interpretability, and generalizability compared to standalone deep learning approaches. However, existing neurosymbolic learning frameworks implement an uneasy marriage between a highly scalable, GPU-accelerated neural component and a slower symbolic component that runs on CPUs. We propose Lobster, a unified framework for harnessing GPUs in an end-to-end manner for neurosymbolic learning. Lobster maps a general neurosymbolic language based on Datalog to the GPU programming paradigm. This mapping is implemented via compilation to a new intermediate language called APM. The extra abstraction provided by apm allows Lobster to be both flexible, supporting discrete, probabilistic, and differentiable modes of reasoning on GPU hardware with a library of provenance semirings, and performant, implementing new optimization passes. We demonstrate that Lobster programs can solve interesting problems spanning the domains of natural language processing, image processing, program reasoning, bioinformatics, and planning. On a suite of 9 applications, Lobster achieves an average speedup of 3.9x over Scallop, a state-of-the-art neurosymbolic framework, and enables scaling of neurosymbolic solutions to previously infeasible tasks.

cs.PL↗