Md Sajid Ahmed | Searcharxiv

arXiv2026

Discrete MeanFlow: One-Step Generation via Conditional Transition Kernels

MeanFlow enables one-step generation in continuous spaces by learning an average velocity over a time interval rather than the instantaneous velocity field of flow matching. However, discrete state spaces lack smooth trajectories or spatial derivatives, so the continuous formulation does not directly apply. We introduce Discrete MeanFlow, a theoretical finite-state formulation that replaces point motion with probability-mass transport. Our key object is the conditional transition kernel of a continuous-time Markov chain (CTMC), from which we define a mean discrete rate that measures average transition-probability change over a finite interval. We prove a Discrete MeanFlow identity that relates this finite-interval rate to the instantaneous CTMC generator at the endpoint, using the Kolmogorov forward equation in place of the spatial chain rule in continuous MeanFlow. We parameterize the transition kernel directly using a boundary-by-construction design that guarantees valid probability outputs and exact boundary conditions without auxiliary losses. Because the learned kernel defines a probability distribution, generation requires only a single forward pass followed by direct sampling, eliminating the need for iterative denoising, ODE integration, or multi-step refinement. We validate the identity on exact finite-state Markov chains, demonstrating that the learned kernel recovers the analytical ground truth with high precision. We also investigate the training objective and the limits of factorization on synthetic sequence tasks across varying alphabet sizes and sequence lengths.

cs.LG↗

arXiv2025

Improving Multi-turn Task Completion in Task-Oriented Dialog Systems via Prompt Chaining and Fine-Grained Feedback

Task-oriented dialog (TOD) systems facilitate users in accomplishing complex, multi-turn tasks through natural language. While instruction-tuned large language models (LLMs) have demonstrated strong performance on a range of single-turn NLP tasks, they often struggle with reliable multi-turn task completion in TOD settings, particularly when generating API calls required to interact with external systems. To address this, we introduce RealTOD, a novel framework that improves LLM-based TOD systems through (1) prompt chaining and (2) fine-grained feedback. Prompt chaining enables zero-shot generalization to new domains by automatically synthesizing a schema-aligned in-context example for the target task. Fine-grained feedback verifies each generated API call against the domain schema, identifies specific errors, and provides targeted correction prompts. To evaluate task completion reliability, we introduce full API Call Accuracy as a robust metric, along with detailed sub-metrics to capture common failure modes. We conduct extensive experiments on the SGD and BiTOD benchmarks using four LLMs. RealTOD improves Full API accuracy, surpassing state-of-the-art AutoTOD by 37.10% on SGD and supervised learning-based baseline SimpleTOD by 10.32% on BiTOD. Human evaluations further confirm that LLMs integrated with RealTOD achieve superior task completion, fluency, and informativeness compared to existing methods.

cs.CL↗