arXiv subjects

Minxuan Duan

Publications and source records attributed to Minxuan Duan.

7 recordsLinked to original sources

arXiv2026

Efficiently Learning Branching Networks for Multitask Algorithmic Reasoning

Algorithmic reasoning -- the ability to perform step-by-step logical inference -- is a synthetic benchmark for evaluating multi-step reasoning abilities, designed for graph neural networks and also for transformer models. Prior work has evaluated reasoning for executing a single algorithmic task, whereas a more desirable objective is to perform multiple algorithmic reasoning tasks simultaneously. We start by noting that this is inherently difficult due to differences arising from the execution traces of the algorithms (such as depth- vs. breadth-first search), which cause interference when they are trained together. In this paper, we introduce {branching neural networks}, a new architecture for multitask algorithmic reasoning. The main idea is to search for a recursive tree-structured partition of $n$ algorithmic tasks into a $k$-ary tree (divided into $L$ layers). Naive search requires $O(k^{nL})$ complexity; we develop an algorithm that reduces this to $O(nL)$ by solving a convex relaxation at each layer to approximate an optimal partition. Our approach clusters these tasks using gradient-based affinity and can be used on top of any base model. We validate our approach on algorithmic reasoning benchmarks and their extensions with text descriptions. We show that gradient-based affinity scores help estimate true performance with less than 5% error, measured across eight different architectures with up to 34 billion parameters. On the CLRS benchmark, our approach outperforms existing graph neural networks by 3.7% and baselines by 1.2%, while reducing runtime by 48% and memory usage by 26%. The learned branching structure shows a hierarchical clustering of related algorithms. On three text-based graph reasoning benchmarks, our approach improves over baseline methods by 3.2%. Finally, we validate our approach for overlapping community detection.

cs.LG↗

arXiv2026

Learning Multimodal Embeddings for Traffic Accident Prediction and Causal Estimation

We consider analyzing traffic accident patterns using both road network data and satellite images aligned to road graph nodes. Previous work for predicting accident occurrences relies primarily on road network structural features while overlooking physical and environmental information from the road surface and its surroundings. In this work, we construct a large multimodal dataset spanning six U.S. states, containing nine million traffic accident records from official sources, and one million high-resolution satellite images for each node of the road network. Additionally, every node is annotated with features such as the region's weather statistics and road type (e.g., residential vs. motorway), and each edge is annotated with traffic volume information (i.e., Average Annual Daily Traffic). Utilizing this dataset, we conduct a comprehensive evaluation of multimodal learning methods that integrate both visual and network embeddings. Our findings show that integrating both data modalities improves prediction accuracy, achieving an average AUROC of $90.1\%$, a $3.7\%$ gain over graph neural network models that use only graph structures. With the improved embeddings, we conduct a causal analysis using a matching estimator to identify the key factors influencing traffic accidents. We find that accident rates rise by $24\%$ under higher precipitation, by $22\%$ on higher-speed roads such as motorways, and by $29\%$ due to seasonal patterns, after adjusting for other confounding factors. Ablation studies confirm that satellite imagery features are essential for achieving accurate prediction.

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arXiv2026

Efficient Estimation of Kernel Surrogate Models for Task Attribution

Modern AI agents such as large language models are trained on diverse tasks -- translation, code generation, mathematical reasoning, and text prediction -- simultaneously. A key question is how to quantify the influence of each individual training task on performance on a target task, a problem we refer to as task attribution. The direct approach, leave-one-out retraining, measures the effect of removing each task, but is computationally infeasible at scale. An alternative approach that builds surrogate models to predict the performance on a target task for any subset of training tasks has emerged in the recent literature. Prior work focuses on linear surrogate models, which capture first-order relationships but miss nonlinear interactions such as XOR-type effects. In this paper, we first consider a unified task-weighting framework for analyzing task-attribution methods and establish a new connection between linear surrogate models and influence functions via a second-order analysis. Then, we introduce kernel surrogate models, which more effectively represent second-order task interactions. To efficiently learn the kernel surrogate, we develop a gradient-based estimation procedure that leverages a first-order approximation of pretrained models; empirically, this yields accurate surrogate estimates with less than $2\%$ relative error without repeated retraining. Experiments across multiple settings -- including mathematical reasoning in transformers, in-context learning, and multi-objective reinforcement learning -- demonstrate the effectiveness of kernel surrogate models. They achieve a $25\%$ higher correlation with the leave-one-out ground truth than linear surrogates and influence-function baselines, enabling more accurate and scalable task attribution. When used for downstream data selection, kernel surrogate models further yield a $40\%$ improvement in the aforementioned settings.

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arXiv2026

Scalable Multi-Objective and Meta Reinforcement Learning via Gradient Estimation

We study the problem of efficiently estimating policies that simultaneously optimize multiple objectives in reinforcement learning (RL). Given $n$ objectives (or tasks), we seek the optimal partition of these objectives into $k \ll n$ groups, where each group comprises related objectives that can be trained together. This problem arises in applications such as robotics, control, and preference optimization in language models, where learning a single policy for all $n$ objectives is suboptimal as $n$ grows. We introduce a two-stage procedure -- meta-training followed by fine-tuning -- to address this problem. We first learn a meta-policy for all objectives using multitask learning. Then, we adapt the meta-policy to multiple randomly sampled subsets of objectives. The adaptation step leverages a first-order approximation property of well-trained policy networks, which is empirically verified to be accurate within a 2% error margin across various RL environments. The resulting algorithm, PolicyGradEx, efficiently estimates an aggregate task-affinity score matrix given a policy evaluation algorithm. Based on the estimated affinity score matrix, we cluster the $n$ objectives into $k$ groups by maximizing the intra-cluster affinity scores. Experiments on three robotic control and the Meta-World benchmarks demonstrate that our approach outperforms state-of-the-art baselines by 16% on average, while delivering up to $26\times$ faster speedup relative to performing full training to obtain the clusters. Ablation studies validate each component of our approach. For instance, compared with random grouping and gradient-similarity-based grouping, our loss-based clustering yields an improvement of 19%. Finally, we analyze the generalization error of policy networks by measuring the Hessian trace of the loss surface, which gives non-vacuous measures relative to the observed generalization errors.

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arXiv2024

Back to Bayesics: Uncovering Human Mobility Distributions and Anomalies with an Integrated Statistical and Neural Framework

Existing methods for anomaly detection often fall short due to their inability to handle the complexity, heterogeneity, and high dimensionality inherent in real-world mobility data. In this paper, we propose DeepBayesic, a novel framework that integrates Bayesian principles with deep neural networks to model the underlying multivariate distributions from sparse and complex datasets. Unlike traditional models, DeepBayesic is designed to manage heterogeneous inputs, accommodating both continuous and categorical data to provide a more comprehensive understanding of mobility patterns. The framework features customized neural density estimators and hybrid architectures, allowing for flexibility in modeling diverse feature distributions and enabling the use of specialized neural networks tailored to different data types. Our approach also leverages agent embeddings for personalized anomaly detection, enhancing its ability to distinguish between normal and anomalous behaviors for individual agents. We evaluate our approach on several mobility datasets, demonstrating significant improvements over state-of-the-art anomaly detection methods. Our results indicate that incorporating personalization and advanced sequence modeling techniques can substantially enhance the ability to detect subtle and complex anomalies in spatiotemporal event sequences.

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arXiv2022

The Nonequilibrium Mechanism of Noise Enhancer synergizing with Activator in HIV Latency Reactivation

Noise-modulating chemicals can synergize with transcriptional activators in reactivating latent HIV to eliminate latent HIV reservoirs. To understand the underlying biomolecular mechanism, we investigate a previous two-gene-state model and identify two necessary conditions for the synergy: an assumption of inhibition effect of transcription activators on noise enhancers; and frequent transitions to the gene non-transcription-permissive state. We then develop a loop-four-gene-state model with Tat transcription/translation and find that drug synergy is mainly determined by the magnitude and direction of energy input into the genetic regulatory kinetics of the HIV promoter. The inhibition effect of transcription activators is actually a phenomenon of energy dissipation in the nonequilibrium gene transition system. Overall, the loop-four-state model demonstrates that energy dissipation plays a crucial role in HIV latency reactivation, which might be useful for improving drug effects and identifying other synergies on lentivirus latency reactivation.

q-bio.SC↗

arXiv2020

C-SURE: Shrinkage Estimator and Prototype Classifier for Complex-Valued Deep Learning

The James-Stein (JS) shrinkage estimator is a biased estimator that captures the mean of Gaussian random vectors.While it has a desirable statistical property of dominance over the maximum likelihood estimator (MLE) in terms of mean squared error (MSE), not much progress has been made on extending the estimator onto manifold-valued data. We propose C-SURE, a novel Stein's unbiased risk estimate (SURE) of the JS estimator on the manifold of complex-valued data with a theoretically proven optimum over MLE. Adapting the architecture of the complex-valued SurReal classifier, we further incorporate C-SURE into a prototype convolutional neural network (CNN) classifier. We compare C-SURE with SurReal and a real-valued baseline on complex-valued MSTAR and RadioML datasets. C-SURE is more accurate and robust than SurReal, and the shrinkage estimator is always better than MLE for the same prototype classifier. Like SurReal, C-SURE is much smaller, outperforming the real-valued baseline on MSTAR (RadioML) with less than 1 percent (3 percent) of the baseline size

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