Heaviside Continuity of Rolling Coefficients for Eliminating Epistemic Entropy in Large Language Models
2026-07-06 • Artificial Intelligence
Artificial IntelligenceNeural and Evolutionary Computing
AI summaryⓘ
The authors present HCRC, a new method to make large language models (LLMs) more reliable by checking each step of their reasoning before moving forward. Instead of trusting the model's output blindly, HCRC uses a 'gate' that only allows progress if certain correctness checks pass, helping to avoid mistakes from piling up. They tested HCRC on coding and reasoning tasks, finding it reduces errors to zero for strong models and safely stops weaker ones from producing wrong answers. This approach works without changing the original model and has been used successfully in real coding tools for months.
large language modelsautoregressive decodingverificationHeaviside Gatepredicate-gated transitionsfalse-completion rateepistemic entropyparallel worker architectureagentic coding environmentexecution control
Authors
MY Pitsane, Hope Mogale
Abstract
Large language models (LLMs) generate fluent outputs that can be wrong. Unlike humans, who often exhibit cues when providing false information, LLMs produce errors that are difficult to detect because autoregressive decoding provides no mechanism for verifying intermediate reasoning before state progression. We introduce Heaviside Continuity of Rolling Coefficients (HCRC), a verification-first execution framework that reformulates inference as predicate-gated state transitions governed by a Heaviside Gate. HCRC combines model confidence with independent verification signals from a parallel worker architecture, allowing execution to advance only when predefined correctness predicates are satisfied. This prevents invalid intermediate states from propagating, reducing epistemic entropy without modifying the underlying model. We evaluate HCRC on software-engineering and reasoning tasks across thirteen proposers from four providers. On capable proposers, the gate reduces the false-completion rate (FCR) from 4--7% to 0% while remaining latency-competitive and, in some settings, faster than the unwrapped model. On weaker proposers, it converts false completions into honest halts instead of corrupting downstream state. Beyond benchmarking, HCRC has operated for months as the production control plane of an agentic coding environment, authorizing file mutations, verification-driven progress reporting, and memory compaction. These results establish HCRC as a general framework for verification-driven LLM execution, showing that reliable reasoning can be achieved through principled execution control rather than model scale alone.