Hongjue Zhao

Xieting Chu, Hongjue Zhao, Enze Xu et al.

Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face scalability issues when dealing with complex equations involving multiple variables. To address this challenge, we propose ScaleSR, a scalable symbolic regression model that leverages control variables to enhance both accuracy and scalability. The core idea is to decompose multi-variable symbolic regression into a set of single-variable SR problems, which are then combined in a bottom-up manner. The proposed method involves a four-step process. First, we learn a data generator from observed data using deep neural networks (DNNs). Second, the data generator is used to generate samples for a certain variable by controlling the input variables. Thirdly, single-variable symbolic regression is applied to estimate the corresponding mathematical expression. Lastly, we repeat steps 2 and 3 by gradually adding variables one by one until completion. We evaluate the performance of our method on multiple benchmark datasets. Experimental results demonstrate that the proposed ScaleSR significantly outperforms state-of-the-art baselines in discovering mathematical expressions with multiple variables. Moreover, it can substantially reduce the search space for symbolic regression. The source code will be made publicly available upon publication.

Hongjue Zhao, Haosen Sun, Jiangtao Kong et al.

Activation steering, or representation engineering, offers a lightweight approach to align large language models (LLMs) by manipulating their internal activations at inference time. However, current methods suffer from two key limitations: \textit{(i)} the lack of a unified theoretical framework for guiding the design of steering directions, and \textit{(ii)} an over-reliance on \textit{one-step steering} that fail to capture complex patterns of activation distributions. In this work, we propose a unified ordinary differential equations (ODEs)-based \textit{theoretical} framework for activation steering in LLM alignment. We show that conventional activation addition can be interpreted as a first-order approximation to the solution of an ODE. Based on this ODE perspective, identifying a steering direction becomes equivalent to designing a \textit{barrier function} from control theory. Derived from this framework, we introduce ODESteer, a kind of ODE-based steering guided by barrier functions, which shows \textit{empirical} advancement in LLM alignment. ODESteer identifies steering directions by defining the barrier function as the log-density ratio between positive and negative activations, and employs it to construct an ODE for \textit{multi-step and adaptive} steering. Compared to state-of-the-art activation steering methods, ODESteer achieves consistent empirical improvements on diverse LLM alignment benchmarks, a notable $5.7\%$ improvement over TruthfulQA, $2.5\%$ over UltraFeedback, and $2.4\%$ over RealToxicityPrompts. Our work establishes a principled new view of activation steering in LLM alignment by unifying its theoretical foundations via ODEs, and validating it empirically through the proposed ODESteer method.

Hongjue Zhao, Yizhuo Chen, Yuchen Wang et al.

Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a theoretical foundation for understanding, analyzing, and improving DNNs. We organize the discussion around three guiding questions: i) how differential equations offer a principled understanding of DNN architectures, ii) how tools from differential equations can be used to improve DNN performance in a principled way, and iii) what real-world applications benefit from grounding DNNs in differential equations. We adopt a two-fold perspective spanning the model level, which interprets the whole DNN as a differential equation, and the layer level, which models individual DNN components as differential equations. From these two perspectives, we review how this framework connects model design, theoretical analysis, and performance improvement. We further discuss real-world applications, as well as key challenges and opportunities for future research.

Tomoyoshi Kimura, Denizhan Kara, Jinyang Li et al.

Internet of Things (IoT) systems continuously collect heterogeneous sensing signals from ubiquitous sensors to support intelligent applications such as human activity analysis, emotion monitoring, and environmental perception. These signals are inherently non-stationary and multi-scale, posing unique challenges for standard tokenization techniques. This paper proposes Dywave, a dynamic tokenization framework for IoT sensing signals that constructs compact input representations aligned with intrinsic temporal structures and underlying physical events. Dywave leverages wavelet-based hierarchical decomposition, identifies meaningful temporal boundaries corresponding to underlying semantic events, and adaptively compresses redundant intervals while preserving temporal coherence. Extensive evaluations on five real-world IoT sensing datasets across activity recognition, stress assessment, and nearby object detection demonstrate that Dywave outperforms state-of-the-art methods by up to 12% in accuracy, while improving computational efficiency by reducing input token lengths by up to 75% across mainstream sequence models. Moreover, Dywave exhibits improved robustness to domain shifts and varying sequence lengths.

Yuchen Wang, Hongjue Zhao, Haohong Lin et al.

This work aims to address the problem of long-term dynamic forecasting in complex environments where data are noisy and irregularly sampled. While recent studies have introduced some methods to improve prediction performance, these approaches still face a significant challenge in handling long-term extrapolation tasks under such complex scenarios. To overcome this challenge, we propose Phy-SSM, a generalizable method that integrates partial physics knowledge into state space models (SSMs) for long-term dynamics forecasting in complex environments. Our motivation is that SSMs can effectively capture long-range dependencies in sequential data and model continuous dynamical systems, while the incorporation of physics knowledge improves generalization ability. The key challenge lies in how to seamlessly incorporate partially known physics into SSMs. To achieve this, we decompose partially known system dynamics into known and unknown state matrices, which are integrated into a Phy-SSM unit. To further enhance long-term prediction performance, we introduce a physics state regularization term to make the estimated latent states align with system dynamics. Besides, we theoretically analyze the uniqueness of the solutions for our method. Extensive experiments on three real-world applications, including vehicle motion prediction, drone state prediction, and COVID-19 epidemiology forecasting, demonstrate the superior performance of Phy-SSM over the baselines in both long-term interpolation and extrapolation tasks. The code is available at https://github.com/511205787/Phy_SSM-ICML2025.

Yuchen Wang, Jiangtao Kong, Sizhe Wei et al.

Trajectory world models play a crucial role in robotic dynamics learning, planning, and control. While recent works have explored trajectory world models for diverse robotic systems, they struggle to scale to a large number of distinct system dynamics and overlook domain knowledge of physical structures. To address these limitations, we introduce WestWorld, a knoWledge-Encoded Scalable Trajectory World model for diverse robotic systems. To tackle the scalability challenge, we propose a novel system-aware Mixture-of-Experts (Sys-MoE) that dynamically combines and routes specialized experts for different robotic systems via a learnable system embedding. To further enhance zero-shot generalization, we incorporate domain knowledge of robot physical structures by introducing a structural embedding that aligns trajectory representations with morphological information. After pretraining on 89 complex environments spanning diverse morphologies across both simulation and real-world settings, WestWorld achieves significant improvements over competitive baselines in zero- and few-shot trajectory prediction. Additionally, it shows strong scalability across a wide range of robotic environments and significantly improves performance on downstream model-based control for different robots. Finally, we deploy our model on a real-world Unitree Go1, where it demonstrates stable locomotion performance (see our demo on the website: https://westworldrobot.github.io/). The code will be available upon publication.

Yizhuo Chen, Tianchen Wang, You Lyu et al.

We present SPAR, a framework for self-supervised placement-aware representation learning in distributed sensing. Distributed sensing spans applications where multiple spatially distributed and multimodal sensors jointly observe an environment, from vehicle monitoring to human activity recognition and earthquake localization. A central challenge shared by this wide spectrum of applications, is that observed signals are inseparably shaped by sensor placements, including their spatial locations and structural roles. However, existing pretraining methods remain largely placement-agnostic. SPAR addresses this gap through a unifying principle: the duality between signals and positions. Guided by this principle, SPAR introduces spatial and structural positional embeddings together with dual reconstruction objectives, explicitly modeling how observing positions and observed signals shape each other. Placement is thus treated not as auxiliary metadata but as intrinsic to representation learning. SPAR is theoretically supported by analyses from information theory and occlusion-invariant learning. Extensive experiments on three real-world datasets show that SPAR achieves superior robustness and generalization across various modalities, placements, and downstream tasks.

Viet Duong, Qiong Wu, Zhengyi Zhou et al.

As an emerging interpretable technique, Generalized Additive Models (GAMs) adopt neural networks to individually learn non-linear functions for each feature, which are then combined through a linear model for final predictions. Although GAMs can explain deep neural networks (DNNs) at the feature level, they require large numbers of model parameters and are prone to overfitting, making them hard to train and scale. Additionally, in real-world datasets with many features, the interpretability of feature-based explanations diminishes for humans. To tackle these issues, recent research has shifted towards concept-based interpretable methods. These approaches try to integrate concept learning as an intermediate step before making predictions, explaining the predictions in terms of human-understandable concepts. However, these methods require domain experts to extensively label concepts with relevant names and their ground-truth values. In response, we propose CAT, a novel interpretable Concept-bAsed Taylor additive model to simply this process. CAT does not have to require domain experts to annotate concepts and their ground-truth values. Instead, it only requires users to simply categorize input features into broad groups, which can be easily accomplished through a quick metadata review. Specifically, CAT first embeds each group of input features into one-dimensional high-level concept representation, and then feeds the concept representations into a new white-box Taylor Neural Network (TaylorNet). The TaylorNet aims to learn the non-linear relationship between the inputs and outputs using polynomials. Evaluation results across multiple benchmarks demonstrate that CAT can outperform or compete with the baselines while reducing the need of extensive model parameters. Importantly, it can explain model predictions through high-level concepts that human can understand.