We introduce a new class of non-linear function-on-function regression models for functional data using neural networks. We propose a framework using a hidden layer consisting of continuous neurons, called a continuous hidden layer, for functional response modeling and give two model fitting strategies, Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN). Both are designed explicitly to exploit the structure inherent in functional data and capture the complex relations existing between the functional predictors and the functional response. We fit these models by deriving functional gradients and implement regularization techniques for more parsimonious results. We demonstrate the power and flexibility of our proposed method in handling complex functional models through extensive simulation studies as well as real data examples.
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Most conventional crowd counting methods utilize a fully-supervised learning framework to establish a mapping between scene images and crowd density maps. They usually rely on a large quantity of costly and time-intensive pixel-level annotations for training supervision. One way to mitigate the intensive labeling effort and improve counting accuracy is to leverage large amounts of unlabeled images. This is attributed to the inherent self-structural information and rank consistency within a single image, offering additional qualitative relation supervision during training. Contrary to earlier methods that utilized the rank relations at the original image level, we explore such rank-consistency relation within the latent feature spaces. This approach enables the incorporation of numerous pyramid partial orders, strengthening the model representation capability. A notable advantage is that it can also increase the utilization ratio of unlabeled samples. Specifically, we propose a Deep Rank-consistEnt pyrAmid Model (DREAM), which makes full use of rank consistency across coarse-to-fine pyramid features in latent spaces for enhanced crowd counting with massive unlabeled images. In addition, we have collected a new unlabeled crowd counting dataset, FUDAN-UCC, comprising 4,000 images for training purposes. Extensive experiments on four benchmark datasets, namely UCF-QNRF, ShanghaiTech PartA and PartB, and UCF-CC-50, show the effectiveness of our method compared with previous semi-supervised methods. The codes are available at //github.com/bridgeqiqi/DREAM.
Millimeter wave (mmWave) sensing is an emerging technology with applications in 3D object characterization and environment mapping. However, realizing precise 3D reconstruction from sparse mmWave signals remains challenging. Existing methods rely on data-driven learning, constrained by dataset availability and difficulty in generalization. We propose DiffSBR, a differentiable framework for mmWave-based 3D reconstruction. DiffSBR incorporates a differentiable ray tracing engine to simulate radar point clouds from virtual 3D models. A gradient-based optimizer refines the model parameters to minimize the discrepancy between simulated and real point clouds. Experiments using various radar hardware validate DiffSBR's capability for fine-grained 3D reconstruction, even for novel objects unseen by the radar previously. By integrating physics-based simulation with gradient optimization, DiffSBR transcends the limitations of data-driven approaches and pioneers a new paradigm for mmWave sensing.
Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach combines overdamped Langevin and birth-death dynamics, incorporating a "dominance potential" to steer particles toward global Pareto optimality. In contrast to previous methods, our method is able to relocate dominated particles, making it particularly adept at managing Pareto fronts of complicated geometries. Our method is also theoretically grounded as a Wasserstein-Fisher-Rao gradient flow with convergence guarantees. Extensive experiments confirm that our approach outperforms state-of-the-art methods on challenging synthetic and real-world datasets.
Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the LaSDI (Latent Space Dynamics Identification) algorithm, a recently developed data-driven reduced order modeling technique. We introduce a weak form-based version WLaSDI (Weak-form Latent Space Dynamics Identification). WLaSDI first compresses data, then projects onto the test functions and learns the local latent space models. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. With WLaSDI, the local latent space is obtained using weak-form equation learning techniques. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a fast, robust, and accurate simulation. We demonstrate the efficacy of WLaSDI vs. LaSDI on several common benchmark examples including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in the case of 1D inviscid Burgers' simulations with the addition of up to 100% Gaussian white noise, the relative error remains consistently below 6% for WLaSDI, while it can exceed 10,000% for LaSDI. Similarly, for radial advection simulations, the relative errors stay below 15% for WLaSDI, in stark contrast to the potential errors of up to 10,000% with LaSDI. Moreover, speedups of several orders of magnitude can be obtained with WLaSDI. For example applying WLaSDI to 1D Burgers' yields a 140X speedup compared to the corresponding full order model. Python code to reproduce the results in this work is available at (//github.com/MathBioCU/PyWSINDy_ODE) and (//github.com/MathBioCU/PyWLaSDI).
We propose GAN-Supervised Learning, a framework for learning discriminative models and their GAN-generated training data jointly end-to-end. We apply our framework to the dense visual alignment problem. Inspired by the classic Congealing method, our GANgealing algorithm trains a Spatial Transformer to map random samples from a GAN trained on unaligned data to a common, jointly-learned target mode. We show results on eight datasets, all of which demonstrate our method successfully aligns complex data and discovers dense correspondences. GANgealing significantly outperforms past self-supervised correspondence algorithms and performs on-par with (and sometimes exceeds) state-of-the-art supervised correspondence algorithms on several datasets -- without making use of any correspondence supervision or data augmentation and despite being trained exclusively on GAN-generated data. For precise correspondence, we improve upon state-of-the-art supervised methods by as much as $3\times$. We show applications of our method for augmented reality, image editing and automated pre-processing of image datasets for downstream GAN training.
Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling applications, in which various molecular representations with different symmetry properties and levels of abstraction exist. This review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction, and quantum chemistry. Emphasis is placed on the relevance of the learned molecular features and their complementarity to well-established molecular descriptors. This review provides an overview of current challenges and opportunities, and presents a forecast of the future of GDL for molecular sciences.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Current models for event causality identification (ECI) mainly adopt a supervised framework, which heavily rely on labeled data for training. Unfortunately, the scale of current annotated datasets is relatively limited, which cannot provide sufficient support for models to capture useful indicators from causal statements, especially for handing those new, unseen cases. To alleviate this problem, we propose a novel approach, shortly named CauSeRL, which leverages external causal statements for event causality identification. First of all, we design a self-supervised framework to learn context-specific causal patterns from external causal statements. Then, we adopt a contrastive transfer strategy to incorporate the learned context-specific causal patterns into the target ECI model. Experimental results show that our method significantly outperforms previous methods on EventStoryLine and Causal-TimeBank (+2.0 and +3.4 points on F1 value respectively).
Knowledge graphs (KGs) serve as useful resources for various natural language processing applications. Previous KG completion approaches require a large number of training instances (i.e., head-tail entity pairs) for every relation. The real case is that for most of the relations, very few entity pairs are available. Existing work of one-shot learning limits method generalizability for few-shot scenarios and does not fully use the supervisory information; however, few-shot KG completion has not been well studied yet. In this work, we propose a novel few-shot relation learning model (FSRL) that aims at discovering facts of new relations with few-shot references. FSRL can effectively capture knowledge from heterogeneous graph structure, aggregate representations of few-shot references, and match similar entity pairs of reference set for every relation. Extensive experiments on two public datasets demonstrate that FSRL outperforms the state-of-the-art.
This paper presents a new multi-objective deep reinforcement learning (MODRL) framework based on deep Q-networks. We propose the use of linear and non-linear methods to develop the MODRL framework that includes both single-policy and multi-policy strategies. The experimental results on two benchmark problems including the two-objective deep sea treasure environment and the three-objective mountain car problem indicate that the proposed framework is able to converge to the optimal Pareto solutions effectively. The proposed framework is generic, which allows implementation of different deep reinforcement learning algorithms in different complex environments. This therefore overcomes many difficulties involved with standard multi-objective reinforcement learning (MORL) methods existing in the current literature. The framework creates a platform as a testbed environment to develop methods for solving various problems associated with the current MORL. Details of the framework implementation can be referred to //www.deakin.edu.au/~thanhthi/drl.htm.
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