Vishvesh Bhat | Search arXiv

arXiv2026

Program Learning with Verifiable Rewards: Symbolic Backpropagation for Post-Training LLMs

Post training a language model to reason means updating its weights. Supervised finetuning and reinforcement learning both place the acquired capability inside the model where it cannot be inspected cannot be checked step by step and cannot be moved to another model. We argue that for tasks whose intermediate steps admit verification, reasoning is better placed outside the base models weights as an explicit program composed from deterministic and neural primitives. We introduce PLVR (Program Learning with Verifiable Rewards): a post training method that learns such programs directly from input-output examples. Its mechanism is symbolic backpropagation: each program layer carries a typed ontology a loss is computed at the output against ground truth and required input ontologies are propagated backward by type inference over primitive signatures: an analogue of the chain rule in which credit assignment is a derivation rather than an estimate. Where RLVR verifies a terminal outcome, PLVRs reward is a per step contract verdict dense over program structure. On LiveCodeBench v6 and Tau2Bench, 30B base models with PLVR outperform RL at matched budget by 27.8 points on average and frontier models an order of magnitude larger by 13.6 points. A single primitive library serves two benchmarks, so the marginal cost of a new task is 100 examples of program search and no new finetuning data. Replacing the loss guided search with uniform sampling over the same type admissible space at equal budget collapses the median program from 65.6 to 17.5, identifying the backward pass rather than the type system as the source of the advantage. We release the symbolic backpropagation library and a conformance checker so the method can be applied to primitive libraries other than our own.

cs.AI↗

arXiv2026

Neurosymbolics for Data Engineering: Achieving Long Context Token Reduction Without Finetuning

Large Language Models are increasingly deployed for sophisticated data engineering tasks such as generating structured queries from natural language, Text-to-SQL, and automating complex spreadsheet operations. However, maximizing their utility demands both higher finetuning-free accuracy and solutions to the computational bottleneck imposed by the Transformer architectures inherent quadratic (On2) time complexity. This paper introduces a novel drop-in neurosymbolic layer designed to seamlessly integrate into existing LLM backbones enhancing logical reasoning and mitigating long-context resource consumption. On the reasoning front, the layer immediately and significantly improves performance yielding an average accuracy increase of 85% across rigorous benchmarks including BIRD-CRITIC and LiveSQLBench, critically achieving these gains without any task specific finetuning or RLHF. Concurrently, we repurpose this approach to address the severe computational strain of long context inference. By leveraging symbolic processing to prioritize and compress relevant contextual information the layer reduces the effective token usage by over 50% and brings the effective time complexity down from O(n2) to approximately O(n) on certain long context tasks. This dual impact approach not only makes LLMs substantially more reliable for data engineering but also drastically reduces the computational pressure on inference chips, making long context tasks more manageable and cost effective.

cs.CL↗