Large language models (LLMs) have achieved impressive results in complex reasoning and knowledge tasks, yet they often struggle with factual accuracy and logical consistency. Prior works have improved LLM performance using prompt-based techniques (e.g. chain-of-thought prompting and self-consistency) and post-hoc self-refinement, but these typically operate on a single model instance. Recently, multi-agent debate frameworks have emerged as a complementary approach, wherein multiple LLM agents propose answers and critique each other’s reasoning to reach consensus. Such a “society of minds” approach has been shown to significantly improve mathematical reasoning and reduce factual hallucinations. However, existing debate methods use homogeneous agents with simple majority voting, limiting their effectiveness. In this work, we propose Adaptive Heterogeneous Multi-Agent Debate (A-HMAD), a novel framework that extends multi-agent debate with (i) diverse specialized agents, (ii) dynamic debate routing, and (iii) a learned consensus mechanism. Each agent in A-HMAD is assigned a distinct role or expertise (e.g. logical reasoning, factual verification, strategic planning), enabling more comprehensive error-checking and perspective diversity than identical agents. A coordination policy dynamically selects which agents contribute at each round based on the question’s domain and the evolving debate state. To aggregate viewpoints, we introduce a consensus optimizer that learns to weight each agent’s vote according to its reliability and the confidence of its arguments. On six challenging benchmarks – including arithmetic QA, grade-school math (GSM8K), multifact question answering (MMLU), factual biography generation, and chess strategy – our A-HMAD consistently outperforms prior single-model methods and the original multi-agent debate baseline. Notably, A-HMAD achieves 4–6% absolute accuracy gains over standard debate on these tasks, and reduces factual errors by over 30% in biography facts. We provide extensive ablations demonstrating the benefits of agent heterogeneity, additional debate rounds, and the learned consensus module. Our findings suggest that an adaptive, role-diverse debating ensemble can drive significant advances in LLM-based educational reasoning, paving the way for safer, more interpretable, and pedagogically reliable AI systems.

Online learning platforms face challenges of information overload and biased engagement, which hinder effective course recommendations. Traditional recommender systems struggle to distinguish genuine learner interests from confounding factors such as popularity, often leading to suboptimal suggestions. To address these issues, we propose a novel educational recommendation model that integrates causal contrastive learning. Our approach combines causal inference techniques with contrastive representation learning to disentangle a learner’s intrinsic interests from external biases. We formulate the task as learning user and course representations that remain invariant under causal interventions which remove popularity effects. The proposed model is evaluated on four benchmark datasets using Recall@10/20 and NDCG@10/20. Experimental results show consistent improvements of 2-3 percentage points over state-of-the-art methods on all datasets. In particular, our model outperforms strong baselines (including graph-based and contrastive models) on top-K recommendation accuracy. These gains demonstrate the effectiveness of integrating causal learning to enhance recommendation relevance and robustness. Our contributions include a new causal graph formulation for recommendations, a contrastive learning scheme based on counterfactual augmentations, extensive empirical validation against existing methods, and insightful analysis of how causal contrastive learning improves recommendation quality. The proposed framework offers a fresh perspective for developing next-generation recommender systems that are both accurate and causally aware, with significant implications for educational personalization.