We consider a class of learning problem of point estimation for modeling high-dimensional nonlinear functions, whose learning dynamics is guided by model training dataset, while the estimated parameter in due course provides an acceptable prediction accuracy on a different model validation dataset. Here, we establish an evidential connection between such a learning problem and a hierarchical optimal control problem that provides a framework how to account appropriately for both generalization and regularization at the optimization stage. In particular, we consider the following two objectives: (i) The first one is a controllability-type problem, i.e., generalization, which consists of guaranteeing the estimated parameter to reach a certain target set at some fixed final time, where such a target set is associated with model validation dataset. (ii) The second one is a regularization-type problem ensuring the estimated parameter trajectory to satisfy some regularization property over a certain finite time interval. First, we partition the control into two control strategies that are compatible with two abstract agents, namely, a leader, which is responsible for the controllability-type problem and that of a follower, which is associated with the regularization-type problem. Using the notion of Stackelberg's optimization, we provide conditions on the existence of admissible optimal controls for such a hierarchical optimal control problem under which the follower is required to respond optimally to the strategy of the leader, so as to achieve the overall objectives that ultimately leading to an optimal parameter estimate. Moreover, we provide a nested algorithm, arranged in a hierarchical structure-based on successive approximation methods, for solving the corresponding optimal control problem. Finally, we present some numerical results for a typical nonlinear regression problem.

Multi-dimensional time series data, such as matrix and tensor-variate time series, are increasingly prevalent in fields such as economics, finance, and climate science. Traditional Transformer models, though adept with sequential data, do not effectively preserve these multi-dimensional structures, as their internal operations in effect flatten multi-dimensional observations into vectors, thereby losing critical multi-dimensional relationships and patterns. To address this, we introduce the Tensor-Augmented Transformer (TEAFormer), a novel method that incorporates tensor expansion and compression within the Transformer framework to maintain and leverage the inherent multi-dimensional structures, thus reducing computational costs and improving prediction accuracy. The core feature of the TEAFormer, the Tensor-Augmentation (TEA) module, utilizes tensor expansion to enhance multi-view feature learning and tensor compression for efficient information aggregation and reduced computational load. The TEA module is not just a specific model architecture but a versatile component that is highly compatible with the attention mechanism and the encoder-decoder structure of Transformers, making it adaptable to existing Transformer architectures. Our comprehensive experiments, which integrate the TEA module into three popular time series Transformer models across three real-world benchmarks, show significant performance enhancements, highlighting the potential of TEAFormers for cutting-edge time series forecasting.

Generative models, as a powerful technique for generation, also gradually become a critical tool for recognition tasks. However, in skeleton-based action recognition, the features obtained from existing pre-trained generative methods contain redundant information unrelated to recognition, which contradicts the nature of the skeleton's spatially sparse and temporally consistent properties, leading to undesirable performance. To address this challenge, we make efforts to bridge the gap in theory and methodology and propose a novel skeleton-based idempotent generative model (IGM) for unsupervised representation learning. More specifically, we first theoretically demonstrate the equivalence between generative models and maximum entropy coding, which demonstrates a potential route that makes the features of generative models more compact by introducing contrastive learning. To this end, we introduce the idempotency constraint to form a stronger consistency regularization in the feature space, to push the features only to maintain the critical information of motion semantics for the recognition task. Our extensive experiments on benchmark datasets, NTU RGB+D and PKUMMD, demonstrate the effectiveness of our proposed method. On the NTU 60 xsub dataset, we observe a performance improvement from 84.6% to 86.2%. Furthermore, in zero-shot adaptation scenarios, our model demonstrates significant efficacy by achieving promising results in cases that were previously unrecognizable. Our project is available at https://github.com/LanglandsLin/IGM.

Photoplethysmography (PPG) is the most widely used non-invasive technique for monitoring biosignals and cardiovascular health, with applications in both clinical settings and consumer health through wearable devices. Current machine learning models trained on PPG signals are mostly task-specific and lack generalizability. Previous works often used single-device datasets, did not explore out-of-domain generalization, or did not release their models, hindering reproducibility and further research. We introduce PaPaGei, the first open foundation model for PPG signals. PaPaGei is pre-trained on more than 57,000 hours of 20 million unlabeled segments of PPG signals using publicly available datasets exclusively. We evaluate against popular time-series foundation models and other benchmarks on 20 tasks of 10 diverse datasets spanning cardiovascular health, sleep disorders, pregnancy monitoring, and wellbeing assessment. Our architecture incorporates novel representation learning approaches that leverage differences in PPG signal morphology across individuals, enabling it to capture richer representations than traditional contrastive learning methods. Across 20 tasks, PaPaGei improves classification and regression performance by an average of 6.3% and 2.9%, respectively, compared to other competitive time-series foundation models in at least 14 tasks. PaPaGei is more data- and parameter-efficient than other foundation models or methods, as it outperforms 70x larger models. Beyond accuracy, we also investigate robustness against different skin tones, establishing a benchmark for bias evaluations of future models. Notably, PaPaGei can be used out of the box as both a feature extractor and an encoder for other multimodal models, opening up new opportunities for multimodal health monitoring

3D semantic occupancy prediction is an essential part of autonomous driving, focusing on capturing the geometric details of scenes. Off-road environments are rich in geometric information, therefore it is suitable for 3D semantic occupancy prediction tasks to reconstruct such scenes. However, most of researches concentrate on on-road environments, and few methods are designed for off-road 3D semantic occupancy prediction due to the lack of relevant datasets and benchmarks. In response to this gap, we introduce WildOcc, to our knowledge, the first benchmark to provide dense occupancy annotations for off-road 3D semantic occupancy prediction tasks. A ground truth generation pipeline is proposed in this paper, which employs a coarse-to-fine reconstruction to achieve a more realistic result. Moreover, we introduce a multi-modal 3D semantic occupancy prediction framework, which fuses spatio-temporal information from multi-frame images and point clouds at voxel level. In addition, a cross-modality distillation function is introduced, which transfers geometric knowledge from point clouds to image features.

Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this work, we explore the potential of deliberately designing force fields for Hamiltonian ODEs, introducing Hamiltonian velocity predictors (HVPs) as a tool for score matching and generative models. We present two innovations constructed with HVPs: Hamiltonian Score Matching (HSM), which estimates score functions by augmenting data via Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments validate our theoretical insights about HSM as a novel score matching metric and demonstrate that HGFs rival leading generative modeling techniques.

Deep learning models often suffer from a lack of interpretability due to polysemanticity, where individual neurons are activated by multiple unrelated semantics, resulting in unclear attributions of model behavior. Recent advances in monosemanticity, where neurons correspond to consistent and distinct semantics, have significantly improved interpretability but are commonly believed to compromise accuracy. In this work, we challenge the prevailing belief of the accuracy-interpretability tradeoff, showing that monosemantic features not only enhance interpretability but also bring concrete gains in model performance. Across multiple robust learning scenarios-including input and label noise, few-shot learning, and out-of-domain generalization-our results show that models leveraging monosemantic features significantly outperform those relying on polysemantic features. Furthermore, we provide empirical and theoretical understandings on the robustness gains of feature monosemanticity. Our preliminary analysis suggests that monosemanticity, by promoting better separation of feature representations, leads to more robust decision boundaries. This diverse evidence highlights the generality of monosemanticity in improving model robustness. As a first step in this new direction, we embark on exploring the learning benefits of monosemanticity beyond interpretability, supporting the long-standing hypothesis of linking interpretability and robustness. Code is available at \url{https://github.com/PKU-ML/Beyond_Interpretability}.

One of the major difficulties in machine learning methods is categorizing datasets that are imbalanced. This problem may lead to biased models, where the training process is dominated by the majority class, resulting in inadequate representation of the minority class. Universum twin support vector machine (UTSVM) produces a biased model towards the majority class, as a result, its performance on the minority class is often poor as it might be mistakenly classified as noise. Moreover, UTSVM is not proficient in handling datasets that contain outliers and noises. Inspired by the concept of incorporating prior information about the data and employing an intuitionistic fuzzy membership scheme, we propose intuitionistic fuzzy universum twin support vector machines for imbalanced data (IFUTSVM-ID). We use an intuitionistic fuzzy membership scheme to mitigate the impact of noise and outliers. Moreover, to tackle the problem of imbalanced class distribution, data oversampling and undersampling methods are utilized. Prior knowledge about the data is provided by universum data. This leads to better generalization performance. UTSVM is susceptible to overfitting risks due to the omission of the structural risk minimization (SRM) principle in their primal formulations. However, the proposed IFUTSVM-ID model incorporates the SRM principle through the incorporation of regularization terms, effectively addressing the issue of overfitting. We conduct a comprehensive evaluation of the proposed IFUTSVM-ID model on benchmark datasets from KEEL and compare it with existing baseline models. Furthermore, to assess the effectiveness of the proposed IFUTSVM-ID model in diagnosing Alzheimer's disease (AD), we applied them to the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. Experimental results showcase the superiority of the proposed IFUTSVM-ID models compared to the baseline models.

Given two sets of elements (such as cell types and drug compounds), researchers typically only have access to a limited subset of their interactions. The task of causal imputation involves using this subset to predict unobserved interactions. Squires et al. (2022) have proposed two estimators for this task based on the synthetic interventions (SI) estimator: SI-A (for actions) and SI-C (for contexts). We extend their work and introduce a novel causal imputation estimator, generalized synthetic interventions (GSI). We prove the identifiability of this estimator for data generated from a more complex latent factor model. On synthetic and real data we show empirically that it recovers or outperforms their estimators.

Abstract: Non-negative Matrix Factorization (NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization (CF) algorithm extends matrix factorization to single non-linear kernel space, improving learning ability and adaptability of matrix factorization. In unsupervised environment, to design or select proper kernel function for specific dataset, a new algorithm called Globalized Multiple Kernel CF (GMKCF) was proposed. Multiple candidate kernel functions were input in the same time and learned in the CF framework based on global linear fusion, obtaining a clustering result with high quality and stability and solving the problem of kernel function selection that the CF faced. The convergence of the proposed algorithm was verified by solving the model with alternate iteration. The experimental results on several real databases show that the proposed algorithm outperforms comparison algorithms in data clustering, such as Kernel K-Means (KKM), Spectral Clustering (SC), Kernel CF (KCF), Co-regularized multi-view spectral clustering (Coreg), and Robust Multiple KKM (RMKKM).