arXiv subjects

Zijian Zhao

Publications and source records attributed to Zijian Zhao.

At least 19 recordsLinked to original sources

arXiv2026

RideSkill: A Hierarchical Algorithm for Generalized Ride Sharing with LLM-Driven Automatic Evolution

Ride-sharing, which allows multiple passengers with different origin-destination (OD) pairs to share a single vehicle, is a challenging operational problem, as it requires orders with different OD pairs to be efficiently bundled and assigned to vehicles under uncertain and varying scenarios. Although multi-agent reinforcement learning (MARL) solutions have achieved promising performance, they suffer from limited generalization (adapting to different environmental scenarios), low transferability (adapting to different platform objectives), and training difficulties in large-scale systems, such as the curse of dimensionality. Recently, motivated by the scaling of large language models (LLMs), several works have incorporated LLMs into ride-hailing systems, either by employing LLMs directly as decision-making agents or using them for automatic algorithm design. However, none of these approaches support vehicle sharing, which complicates the problem by expanding both the state and action spaces exponentially. Moreover, most of them require frequent LLM calls at inference time, making them infeasible for real-time deployment. To address these issues, we propose RideSkill, a hierarchical method for ride-sharing that leverages LLM-assisted automatic algorithmic design. RideSkill consists of a combiner that assigns appropriate skills to each vehicle from a learned skill repository, enabling adaptive dispatch under varying scenarios and objectives, and a repositioner that sequentially relocates idle vehicles to emerging regions, avoiding conflicts among vehicles. Crucially, the skill repository, combiner, and repositioner are all trained by an LLM-based automatic evolutionary method, eliminating the need for LLM calls during deployment and thus ensuring high real-time performance.

cs.MA↗

arXiv2026

Is Per-Agent Policy Composition Safe? Rethinking Successor-Feature Transfer in Cooperative Multi-Agent Reinforcement Learning

Many reinforcement learning systems, from fleet management to traffic signal control, must serve an objective that changes dynamically after deployment, and retraining a policy for each new objective is prohibitively expensive. For a single agent, this problem is well understood: successor features with generalized policy improvement, together with their universal extension, recombine a library of learned policies into a policy for any new objective, with a guarantee that the result is never worse than any policy in the library. However, multi-agent transfer has received far less attention, and the common practice of letting each agent recombine its own library independently inherits the recipe but not the guarantee. We prove that this independent composition can produce joint behavior strictly worse than every policy in the library, because recombining teammates changes the environment each agent faces and invalidates the values it relies on, a failure with no single-agent counterpart. We further show that the only unconditionally safe fixed rule is synchronized composition, which moves the whole team to one jointly trained policy but cannot serve objectives that assign different goals to different agents. To attain safety and flexibility at once, we propose MA-USFA, a hierarchical method with two layers: a lower layer of universal successor feature approximators that predicts each agent's successor features while conditioned on its teammates' objectives, and an upper composer that selects, across agents, which library entry each agent should follow and supplies the cross-agent correction a per-agent value cannot represent. Trained once over the distribution of objectives, it is applied at deployment with no per-task adaptation.

cs.LG↗

arXiv2026

Low-Interaction-Rank Learning: Unifying Multiplicative Dual-Encoder Heads

A multiplicative dual-encoder network computes a real-valued output for a pair of inputs as the inner product of their separate encodings. This architecture has been developed independently in operator learning, bipartite matching, contrastive vision-language models, retrieval, and other areas, yet no unified theory guides the basic design decisions: how many interaction modes to represent, how to normalize the encoders, and when the architecture should be avoided. We provide such a foundation by introducing the class of functions of low interaction rank, a class whose intrinsic complexity is measured by its interaction spectrum. Within this framework, approximation error decomposes into a spectral truncation term and an encoder-realization term; sample complexity is governed by the sum of the two encoder complexities rather than their product; and a usability criterion based on spectral decay determines when the architecture can succeed. The same framework exposes a central identifiability problem: the encoders are defined only up to a linear gauge symmetry that leaves the learned coordinates arbitrary. We show that normalization is gauge fixing and that whitening pins the interaction modes up to permutation and sign, thereby explaining the uninterpretability of contrastive dimensions and providing a constructive remedy. Experiments on synthetic kernels, operator learning, and CLIP models validate the theoretical predictions: spectral decay rates match the predicted scaling, whitening recovers the true modes, and independently trained CLIP models are related by a single rotation which, after removal by whitening, exposes interpretable concept axes. The code of this paper is provided at https://github.com/RS2002/Mul-Net .

cs.LG↗

arXiv2026

AutoFed: Personalized Federated Traffic Prediction via Adaptive Prompt

Accurate traffic prediction is essential for Intelligent Transportation Systems, including ride-hailing, urban road planning, and vehicle fleet management. However, due to significant privacy concerns surrounding traffic data, most existing methods rely on local training, resulting in data silos and limited knowledge sharing. Federated Learning (FL) offers an efficient solution through privacy-preserving collaborative training; however, standard FL struggles with the non-independent and identically distributed (non-IID) problem among clients. This challenge has led to the emergence of Personalized Federated Learning (PFL) as a promising paradigm. Nevertheless, current PFL frameworks require further adaptation for traffic prediction tasks, such as specialized graph feature engineering, data processing, and network architecture design. A notable limitation of many prior studies is their reliance on hyper-parameter optimization across datasets-information that is often unavailable in real-world scenarios-thus impeding practical deployment. To address this challenge, we propose AutoFed, a novel PFL framework for traffic prediction that eliminates the need for manual hyper-parameter tuning. Inspired by prompt learning, AutoFed introduces a federated representor that employs a client-aligned adapter to distill local data into a compact, globally shared prompt matrix. This prompt then conditions a personalized predictor, allowing each client to benefit from cross-client knowledge while maintaining local specificity. Extensive experiments on real-world datasets demonstrate that AutoFed consistently achieves superior performance across diverse scenarios. The code of this paper is provided at https://github.com/RS2002/AutoFed .

cs.LG↗

arXiv2026

Bridging MARL to SARL: An Order-Independent Multi-Agent Transformer via Latent Consensus

Cooperative multi-agent reinforcement learning (MARL) is widely used to address large joint observation and action spaces by decomposing a centralized control problem into multiple interacting agents. However, such decomposition often introduces additional challenges, including non-stationarity, unstable training, weak coordination, and limited theoretical guarantees. In this paper, we propose the Consensus Multi-Agent Transformer (CMAT), a centralized framework that bridges cooperative MARL to a hierarchical single-agent reinforcement learning (SARL) formulation. CMAT treats all agents as a unified entity and employs a Transformer encoder to process the large joint observation space. To handle the extensive joint action space, we introduce a hierarchical decision-making mechanism in which a Transformer decoder autoregressively generates a high-level consensus vector, simulating the process by which agents reach agreement on their strategies in latent space. Conditioned on this consensus, all agents generate their actions simultaneously, enabling order-independent joint decision making and avoiding the sensitivity to action-generation order in conventional Multi-Agent Transformers (MAT). This factorization allows the joint policy to be optimized using single-agent PPO while preserving expressive coordination through the latent consensus. To evaluate the proposed method, we conduct experiments on benchmark tasks from StarCraft II, Multi-Agent MuJoCo, and Google Research Football. The results show that CMAT achieves superior performance over recent centralized solutions, sequential MARL methods, and conventional MARL baselines. The code for this paper is available at:https://github.com/RS2002/CMAT .

cs.LG↗

arXiv2026

Aggregate in the Advantage, Not the Ratio: A Canonical-Form Analysis of Cooperative Multi-Agent Policy Optimization

Multi-agent policy optimization, exemplified by PPO-based methods, is a key branch of cooperative Multi-Agent Reinforcement Learning (MARL). A central design question is how many neighboring agents\footnote{In this paper, "neighbors" refer not only to physical proximity but also to agents whose actions influence one another.} to aggregate in order to effectively utilize global information for cooperation. This decision must be made along two dimensions: in the advantage (which agents' rewards contribute to the credit signal) and in the ratio (which agents' likelihood ratios form the clipped importance weight). Existing methods occupy scattered, underexplored points on these two axes: IPPO treats both separately; MAPPO pairs a team-level advantage with per-agent ratios; HAPPO employs sequential ratios with per-agent advantages; and single-agent reductions operating on factorized joint policies aggregate both into fully joint products. We formalize these two design choices as support matrices $\SA$ and $\SR$, and prove a canonical structure: the expected multi-agent policy optimization objective depends on the pair $(\SA,\SR)$ only through their matrix product $\tS=\SR\SA$. This yields two key consequences: (i) Redundancy: the two support matrices are interchangeable with respect to the signal, meaning neither aggregation pattern is inherently superior.(ii) Variance Ordering: the advantage aggregates rewards as a sum (additive variance with an interior bias-variance optimum at the coupling neighborhood), whereas the ratio aggregates likelihood ratios as a product (multiplicative variance that grows exponentially with support size, with no accompanying bias reduction). The resulting design principle is unambiguous: aggregate neighbors in the advantage, sized to the coupling neighborhood, and keep the ratio per-agent.

cs.MA↗

arXiv2026

Optimizing Denoising Trajectories in dLLMs: A Lightweight Evolutionary Heuristic Approach

Diffusion Large Language Models (dLLMs) have recently emerged as a promising alternative to conventional Auto-Regressive (AR) Large Language Models (LLMs). By leveraging bidirectional attention and parallel decoding, dLLMs enable more efficient generation. However, they require a carefully designed denoising scheduler at inference time (absent during training) whose choice significantly impacts generation quality. While confidence-based heuristic schedulers have shown strong empirical performance, they suffer from two critical failure modes: EOS Overflow and Proximal Bias. Through in-depth analysis of the Transformer's attention patterns, we reveal that these failures stem from certain positions assigning disproportionately high attention weights to invalid tokens (e.g., [MASK] and [EOS]), which produce misleading confidence signals. Building on this insight, empirical evidence shows that valid attention scores can provide complementary guidance to conventional confidence-based heuristics, yet no single metric consistently excels across all scenarios, implying that the optimal denoising trajectory is highly context-dependent. To address this problem, we propose a lightweight evolutionary heuristic scheduler optimized using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Our scheduler dynamically integrates multiple heuristic features with a contextual mean-field embedding, while requiring only 393 trainable parameters. Evaluated on LLaDA and Dream across four reasoning and planning benchmarks, our method consistently outperforms strong baselines, including conventional heuristics, block auto-regressive methods, and recent State-Of-The-Art (SOTA) approaches. To the best of our knowledge, it represents the most parameter-efficient neural scheduler to date. Our code is available at https://github.com/RS2002/Evo-Denoise .

cs.CL↗

arXiv2026

RideGym: A Standardized Interface for Real-World Large-Scale Ride-Sharing System

Ride-sharing has become an essential component of modern urban transportation and has attracted significant attention across computer science, transportation, and management science. While the field spans a broad range of problems, such as driver relocation, dynamic pricing, and vehicle charging or fueling dispatch, the core challenge remains order assignment and trip bundling, which directly affect urban traffic efficiency and carbon emissions. Despite its importance, existing simulation platforms are typically tailored to specific operational studies or tightly coupled to a particular dispatch algorithm, and rarely expose a standardized, learning-friendly interface. As a result, most researchers still build customized environments from scratch, raising serious concerns about reproducibility and fair comparison, and incurring substantial redundant effort. To address this gap, we present RideGym, the first open-source, standardized Gym-style interface tailored to MARL-based order dispatch in real-world ride-sharing systems. By fully decoupling the environment from the dispatch algorithm, RideGym enables diverse learning-based and model-based methods to be developed and compared under identical, fully specified conditions. It supports efficient, large-scale city-level simulations on real road networks, and offers flexible configurations for vehicle attributes, order specifications, and automatic shortest-path routing. We validate RideGym by reproducing several baselines, and demonstrate its high efficiency, with a one-hour simulation involving thousands of vehicles and tens of thousands of orders completed within one minute across all methods. Moreover, we reveal that the choice of exploration noise can significantly affect both the performance and the relative ranking of MARL solutions, an aspect often overlooked in prior work.

cs.MA↗

arXiv2026

Towards Advanced Mathematical Reasoning for LLMs via First-Order Logic Theorem Proving

Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B's low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs' generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs' mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.

cs.AI↗

arXiv2026

Pushing the Boundaries of Natural Reasoning: Interleaved Bonus from Formal-Logic Verification

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4% and 14.2%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.

cs.LG↗

arXiv2026

Stage Light is Sequence$^2$: Multi-Light Control via Imitation Learning

Music-inspired Automatic Stage Lighting Control (ASLC) has gained increasing attention in recent years due to the substantial time and financial costs associated with hiring and training professional lighting engineers. However, existing methods suffer from several notable limitations: the low interpretability of rule-based approaches, the restriction to single-primary-light control in music-to-color-space methods, and the limited transferability of music-to-controlling-parameter frameworks. To address these gaps, we propose SeqLight, a hierarchical deep learning framework that maps music to multi-light Hue-Saturation-Value (HSV) space. Our approach first customizes SkipBART, an end-to-end single primary light generation model, to predict the full light color distribution for each frame, followed by hybrid Imitation Learning (IL) techniques to derive an effective decomposition strategy that distributes the global color distribution among individual lights. Notably, the light decomposition module can be trained under varying venue-specific lighting configurations using only mixed light data and no professional demonstrations, thereby flexibly adapting across diverse venues. In this stage, we formulate the light decomposition task as a Goal-Conditioned Markov Decision Process (GCMDP), construct an expert demonstration set inspired by Hindsight Experience Replay (HER), and introduce a three-phase IL training pipeline, achieving strong generalization capability. To validate our IL solution for the proposed GCMDP, we conduct a series of quantitative analysis and human study. The code and trained models are provided at https://github.com/RS2002/SeqLight .

cs.MM↗

arXiv2026

One Step is Enough: Multi-Agent Reinforcement Learning based on One-Step Policy Optimization for Order Dispatch on Ride-Sharing Platforms

Order dispatch is a critical task in ride-sharing systems with Autonomous Vehicles (AVs), directly influencing efficiency and profits. Recently, Multi-Agent Reinforcement Learning (MARL) has emerged as a promising solution to this problem by decomposing the large state and action spaces among individual agents, effectively addressing the Curse of Dimensionality (CoD) in transportation market, which is caused by the substantial number of vehicles, passengers, and orders. However, conventional MARL-based approaches heavily rely on accurate estimation of the value function, which becomes problematic in large-scale, highly uncertain environments. To address this issue, we propose two novel methods that bypass value function estimation, leveraging the homogeneous property of AV fleets. First, we draw an analogy between AV fleets and groups in Group Relative Policy Optimization (GRPO), adapting it to the order dispatch task. By replacing the Proximal Policy Optimization (PPO) baseline with the group average reward-to-go, GRPO eliminates critic estimation errors and reduces training bias. Inspired by this baseline replacement, we further propose One-Step Policy Optimization (OSPO), demonstrating that the optimal policy can be trained using only one-step group rewards under a homogeneous fleet. Experiments on a real-world ride-hailing dataset show that both GRPO and OSPO achieve promising performance across all scenarios, efficiently optimizing pickup times and the number of served orders using simple Multilayer Perceptron (MLP) networks. Furthermore, OSPO outperforms GRPO in all scenarios, attributed to its elimination of bias caused by the bounded time horizon of GRPO. Our code, trained models, and processed data are provided at https://github.com/RS2002/OSPO .

cs.AI↗

arXiv2026

Zero-Effort Image-to-Music Generation: An Interpretable RAG-based VLM Approach

Recently, Image-to-Music (I2M) generation has garnered significant attention, with potential applications in fields such as gaming, advertising, and multi-modal art creation. However, due to the ambiguous and subjective nature of I2M tasks, most end-to-end methods lack interpretability, leaving users puzzled about the generation results. Even methods based on emotion mapping face controversy, as emotion represents only a singular aspect of art. Additionally, most learning-based methods require substantial computational resources and large datasets for training, hindering accessibility for common users. To address these challenges, we propose the first Vision Language Model (VLM)-based I2M framework that offers high interpretability and low computational cost. Specifically, we utilize ABC notation to bridge the text and music modalities, enabling the VLM to generate music using natural language. We then apply multi-modal Retrieval-Augmented Generation (RAG) and self-refinement techniques to allow the VLM to produce high-quality music without external training. Furthermore, we leverage the generated motivations in text and the attention maps from the VLM to provide explanations for the generated results in both text and image modalities. To validate our method, we conduct both human studies and machine evaluations, where our method outperforms others in terms of music quality and music-image consistency, indicating promising results. Our code is available at https://github.com/RS2002/Image2Music .

cs.SD↗

arXiv2025

Automatic Stage Lighting Control: Is it a Rule-Driven Process or Generative Task?

Stage lighting is a vital component in live music performances, shaping an engaging experience for both musicians and audiences. In recent years, Automatic Stage Lighting Control (ASLC) has attracted growing interest due to the high costs of hiring or training professional lighting engineers. However, most existing ASLC solutions only classify music into limited categories and map them to predefined light patterns, resulting in formulaic and monotonous outcomes that lack rationality. To address this gap, this paper presents Skip-BART, an end-to-end model that directly learns from experienced lighting engineers and predict vivid, human-like stage lighting. To the best of our knowledge, this is the first work to conceptualize ASLC as a generative task rather than merely a classification problem. Our method adapts the BART model to take audio music as input and produce light hue and value (intensity) as output, incorporating a novel skip connection mechanism to enhance the relationship between music and light within the frame grid. To address the lack of available datasets, we create the first stage lighting dataset, along with several pre-training and transfer learning techniques to improve model training with limited data. We validate our method through both quantitative analysis and an human evaluation, demonstrating that Skip-BART outperforms conventional rule-based methods across all evaluation metrics and shows only a limited gap compared to real lighting engineers. To support further research, we have made our self-collected dataset, code, and trained model parameters available at https://github.com/RS2002/Skip-BART .

cs.LG↗

arXiv2025

Triple-BERT: Do We Really Need MARL for Order Dispatch on Ride-Sharing Platforms?

On-demand ride-sharing platforms, such as Uber and Lyft, face the intricate real-time challenge of bundling and matching passengers-each with distinct origins and destinations-to available vehicles, all while navigating significant system uncertainties. Due to the extensive observation space arising from the large number of drivers and orders, order dispatching, though fundamentally a centralized task, is often addressed using Multi-Agent Reinforcement Learning (MARL). However, independent MARL methods fail to capture global information and exhibit poor cooperation among workers, while Centralized Training Decentralized Execution (CTDE) MARL methods suffer from the curse of dimensionality. To overcome these challenges, we propose Triple-BERT, a centralized Single Agent Reinforcement Learning (MARL) method designed specifically for large-scale order dispatching on ride-sharing platforms. Built on a variant TD3, our approach addresses the vast action space through an action decomposition strategy that breaks down the joint action probability into individual driver action probabilities. To handle the extensive observation space, we introduce a novel BERT-based network, where parameter reuse mitigates parameter growth as the number of drivers and orders increases, and the attention mechanism effectively captures the complex relationships among the large pool of driver and orders. We validate our method using a real-world ride-hailing dataset from Manhattan. Triple-BERT achieves approximately an 11.95% improvement over current state-of-the-art methods, with a 4.26% increase in served orders and a 22.25% reduction in pickup times. Our code, trained model parameters, and processed data are publicly available at the repository https://github.com/RS2002/Triple-BERT .

cs.LG↗

arXiv2025

KNN-MMD: Cross Domain Wireless Sensing via Local Distribution Alignment

Wireless sensing has recently found widespread applications in diverse environments, including homes, offices, and public spaces. By analyzing patterns in channel state information (CSI), it is possible to infer human actions for tasks such as person identification, gesture recognition, and fall detection. However, CSI is highly sensitive to environmental changes, where even minor alterations can significantly distort the CSI patterns. This sensitivity often leads to performance degradation or outright failure when applying wireless sensing models trained in one environment to another. To address this challenge, Domain Alignment (DAL) has been widely adopted for cross-domain classification tasks, as it focuses on aligning the global distributions of the source and target domains in feature space. Despite its popularity, DAL often neglects inter-category relationships, which can lead to misalignment between categories across domains, even when global alignment is achieved. To overcome these limitations, we propose K-Nearest Neighbors Maximum Mean Discrepancy (KNN-MMD), a novel few-shot method for cross-domain wireless sensing. Our approach begins by constructing a help set using KNN from the target domain, enabling local alignment between the source and target domains within each category using MMD. Additionally, we address a key instability issue commonly observed in cross-domain methods, where model performance fluctuates sharply between epochs. Further, most existing methods struggle to determine an optimal stopping point during training due to the absence of labeled data from the target domain. Our method resolves this by excluding the support set from the target domain during training and employing it as a validation set to determine the stopping criterion. The dataset and code are publicly available at https://github.com/RS2002/KNN-MMD .

cs.CV↗

arXiv2025

CSI-BERT2: A BERT-inspired Framework for Efficient CSI Prediction and Classification in Wireless Communication and Sensing

Channel state information (CSI) is a fundamental component in both wireless communication and sensing systems, enabling critical functions such as radio resource optimization and environmental perception. In wireless sensing, data scarcity and packet loss hinder efficient model training, while in wireless communication, high-dimensional CSI matrices and short coherent times caused by high mobility present challenges in CSI estimation. To address these issues, we propose a unified framework named CSI-BERT2 for CSI prediction and classification tasks, built on CSI-BERT, which adapts BERT to capture the complex relationships among CSI sequences through a bidirectional self-attention mechanism. We introduce a two-stage training method that first uses a mask language model (MLM) to enable the model to learn general feature extraction from scarce datasets in an unsupervised manner, followed by fine-tuning for specific downstream tasks. Specifically, we extend MLM into a mask prediction model (MPM), which efficiently addresses the CSI prediction task. To further enhance the representation capacity of CSI data, we modify the structure of the original CSI-BERT. We introduce an adaptive re-weighting layer (ARL) to enhance subcarrier representation and a multi-layer perceptron (MLP)-based temporal embedding module to mitigate temporal information loss problem inherent in the original Transformer. Extensive experiments on both real-world collected and simulated datasets demonstrate that CSI-BERT2 achieves state-of-the-art performance across all tasks. Our results further show that CSI-BERT2 generalizes effectively across varying sampling rates and robustly handles discontinuous CSI sequences caused by packet loss-challenges that conventional methods fail to address. The dataset and code are publicly available at https://github.com/RS2002/CSI-BERT2 .

cs.LG↗

arXiv2025

Confident RAG: Enhancing the Performance of LLMs for Mathematics Question Answering through Multi-Embedding and Confidence Scoring

Large Language Models (LLMs) hold significant promise for mathematics education, yet they often struggle with complex mathematical reasoning. While Retrieval-Augmented Generation (RAG) mitigates these issues by grounding LLMs in external knowledge, its effectiveness remains unstable, heavily dependent on the choice of a single embedding model. Moving beyond static RAG workflows, we draw on agentic workflow patterns, a paradigm that introduces structured task decomposition and collaboration to enhance system performance. We propose and examine two novel approaches that combine the benefits of multiple embedding models. While our Mixture-Embedding RAG approach (fusing retrieved documents) shows limited gains, our Confident RAG method (generating multiple answers and selecting the one with the highest confidence score) demonstrates significant improvement. Experimental results show that Confident RAG achieved average accuracy improvements of approximately 10% over vanilla LLMs and 5% over vanilla RAG. The consistent results across different LLMs and embedding models indicate that Confident RAG is an efficient plug-and-play solution for trustworthy mathematical AI assistants. Finally, we discuss how this work lays the groundwork for deploying Agentic RAG systems in educational settings, where autonomous planning and iterative refinement can be built upon our robust retrieval foundation.

cs.CL↗