Note that these games are two-player games, we select the runner in You-Shall-Not-Pass and kicker in Kick-And-Defend as our target agent. Section 4 mentioned that we download a well-trained policy for each game.

This paper presents a novel approach to many-vs-many missile guidance using virtual targets (VTs) generated by a Normalizing Flows-based trajectory predictor. Rather than assigning n interceptors directly to m physical targets through conventional weapon target assignment algorithms, we propose a centralized strategy that constructs n VT trajectories representing probabilistic predictions of maneuvering target behavior. Each interceptor is guided toward its assigned VT using Zero-Effort-Miss guidance during midcourse flight, transitioning to Proportional Navigation guidance for terminal interception. This approach treats many-vs-many engagements as many-vs-distribution scenarios, exploiting numerical superiority (n > m) by distributing interceptors across diverse trajectory hypotheses rather than pursuing identical deterministic predictions. Monte Carlo simulations across various target-interceptor configurations (1-6 targets, 1-8 interceptors) demonstrate that the VT method matches or exceeds baseline straight-line prediction performance by 0-4.1% when n = m, with improvements increasing to 5.8-14.4% when n > m. The results confirm that probabilistic VTs enable effective exploitation of numerical superiority, significantly increasing interception probability in many-vs-many scenarios.

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers. We evaluate L2C on challenging MPE queries involving high-treewidth PGMs. Experiments show that our learned heuristic significantly reduces the search space while maintaining or improving solution quality over state-of-the-art methods.

Abstract--Large Language Models (LLMs) often struggle with maintaining coherent multi-step reasoning traces, particularly in tasks that require a structured logical flow. This work introduces a quantum-inspired approach to address the challenge by incorporating a fidelity-based reward derived from Projected Entangled Pair States (PEPS) into Proximal Policy Optimization. Unlike prior approaches that use direct supervision or contrastive objectives, the proposed method guides learning through structural consistency, offering a novel approach to enforce global coherence in generated reasoning traces. The proposed framework is evaluated using multiple coherence-determining metrics on diverse datasets such as GSM8K, StrategyQA, and EntailmentBank spanning arithmetic, intuitive, and entailment-based reasoning. Results show that the proposed quantum-inspired approach offers significant improvements over supervised, contrastive, and pretrained baseline approaches, highlighting the effectiveness of quantum-inspired fidelity as a foundation to improve reasoning trace coherence in LLMs. In recent times, large language models (LLMs) have made substantial progress in their ability to perform diverse natural language tasks such as open-domain question answering [1] [2], code generation [3] [4], summarization [5], and dialogue systems [6].

Upper-right indicates better performance w.r.t.