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Kun Zhu, Chunhui Zhao

Causal discovery under Granger causality framework has yielded widespread concerns in time series analysis task. Nevertheless, most previous methods are unaware of the underlying causality disappearing problem, that is, certain weak causalities are less focusable and may be lost during the modeling process, thus leading to biased causal conclusions. Therefore, we propose to introduce joint causal influences (i.e., causal influences from the union of multiple variables) as additional causal indication information to help identify weak causalities. Further, to break the limitation of existing methods that implicitly and coarsely model joint causal influences, we propose a novel hidden variable-driven causal hypergraph neural network to meticulously explore the locality and diversity of joint causal influences, and realize its explicit and fine-grained modeling. Specifically, we introduce hidden variables to construct a causal hypergraph for explicitly characterizing various fine-grained joint causal influences. Then, we customize a dual causal information transfer mechanism (encompassing a multi-level causal path and an information aggregation path) to realize the free diffusion and meticulous aggregation of joint causal influences and facilitate its adaptive learning. Finally, we design a multi-view collaborative optimization constraint to guarantee the characterization diversity of causal hypergraph and capture remarkable forecasting relationships (i.e., causalities). Experiments are conducted to demonstrate the superiority of the proposed model.

Zhe Zhao, Pengkun Wang, Haibin Wen, Yudong Zhang, Zhengyang Zhou, Yang Wang

Graph neural networks (GNNs) have achieved state-of-the-art results on many graph representation learning tasks by exploiting statistical correlations. However, numerous observations have shown that such correlations may not reflect the true causal mechanisms underlying the data and thus may hamper the ability of the model to generalize beyond the observed distribution. To address this problem, we propose an Information-based Causal Learning (ICL) framework that combines information theory and causality to analyze and improve graph representation learning to transform information relevance to causal dependence. Specifically, we first introduce a multi-objective mutual information optimization objective derived from information-theoretic analysis and causal learning principles to simultaneously extract invariant and interpretable causal information and reduce reliance on non-causal information in correlations. To optimize this multi-objective objective, we enable a causal disentanglement layer that effectively decouples the causal and non-causal information in the graph representations. Moreover, due to the intractability of mutual information estimation, we derive variational bounds that enable us to transform the above objective into a tractable loss function. To balance the multiple information objectives and avoid optimization conflicts, we leverage multi-objective gradient descent to achieve a stable and efficient transformation from informational correlation to causal dependency. Our approach provides important insights into modulating the information flow in GNNs to enhance their reliability and generalization. Extensive experiments demonstrate that our approach significantly improves the robustness and interpretability of GNNs across different distribution shifts. Visual analysis demonstrates how our method converts informative dependencies in representations into causal dependencies.

Qiao Zhang, Tao Xiang, Chunsheng Xin, Hongyi Wu

Privacy-preserving Machine Learning as a Service (MLaaS) enables the powerful cloud server to run its well-trained neural model upon the input from resource-limited client, with both of server's model parameters and client's input data protected. While computation efficiency is critical for the practical implementation of privacy-preserving MLaaS and it is inspiring to witness recent advances towards efficiency improvement, there still exists a significant performance gap to real-world applications. In general, state-of-the-art frameworks perform function-wise efficiency optimization based on specific cryptographic primitives. Although it is logical, such independent optimization for each function makes noticeable amount of expensive operations unremovable and misses the opportunity to further accelerate the performance by jointly considering privacy-preserving computation among adjacent functions. As such, we propose COIN: Conjunctive Optimization with Interleaved Nexus, which remodels mainstream computation for each function to conjunctive counterpart for composite function, with a series of united optimization strategies. Specifically, COIN jointly computes a pair of consecutive nonlinear-linear functions in the neural model by reconstructing the intermediates throughout the whole procedure, which not only eliminates the most expensive crypto operations without invoking extra encryption enabler, but also makes the online crypto complexity independent of filter size. Experimentally, COIN demonstrates 11.2x to 29.6x speedup over various function dimensions from modern networks, and 6.4x to 12x speedup on the total computation time when applied in networks with model input from small-scale CIFAR10 to large-scale ImageNet.

Hao-Kai Zhang, Chengkai Zhu, Geng Liu, Xin Wang

Quantum neural networks (QNNs) have become a leading paradigm for establishing near-term quantum applications in recent years. The trainability issue of QNNs has garnered extensive attention, spurring demand for a comprehensive analysis of QNNs in order to identify viable solutions. In this work, we propose a perspective that characterizes the trainability of QNNs based on their locality. We prove that the entire variation range of the loss function via adjusting any local quantum gate vanishes exponentially in the number of qubits with a high probability for a broad class of QNNs. This result reveals extra harsh constraints independent of gradients and unifies the restrictions on gradient-based and gradient-free optimizations naturally. We showcase the validity of our results with numerical simulations of representative models and examples. Our findings, as a fundamental property of random quantum circuits, deepen the understanding of the role of locality in QNNs and serve as a guideline for assessing the effectiveness of diverse training strategies for quantum neural networks.

Lei Zhai, Shuyuan Yang, Yitong Li, Zhixi Feng, Zhihao Chang, Quanwei Gao

Deep learning methods have achieved outstanding performance in various signal tasks. However, due to degraded signals in real electromagnetic environment, it is crucial to seek methods that can improve the representation of signal features. In this paper, a Singular Value decomposition-based Attention, SVA is proposed to explore structure of signal data for adaptively enhancing intrinsic feature. Using a deep neural network as a base model, SVA performs feature semantic subspace learning through a decomposition layer and combines it with an attention layer to achieve adaptive enhancement of signal features. Moreover, we consider the gradient explosion problem brought by SVA and optimize SVA to improve the stability of training. Extensive experimental results demon-strate that applying SVA to a generalized classification model can significantly improve its ability in representations, making its recognition performance competitive with, or even better than, the state-of-the-art task-specific models.

Nan Yin, Mengzhu Wang, Zhenghan Chen, Giulia De Masi, Huan Xiong, Bin Gu

The integration of Spiking Neural Networks (SNNs) and Graph Neural Networks (GNNs) is gradually attracting attention due to the low power consumption and high efficiency in processing the non-Euclidean data represented by graphs. However, as a common problem, dynamic graph representation learning faces challenges such as high complexity and large memory overheads. Current work often uses SNNs instead of Recurrent Neural Networks (RNNs) by using binary features instead of continuous ones for efficient training, which overlooks graph structure information and leads to the loss of details during propagation. Additionally, optimizing dynamic spiking models typically requires the propagation of information across time steps, which increases memory requirements. To address these challenges, we present a framework named Dynamic Spiking Graph Neural Networks (Dy-SIGN). To mitigate the information loss problem, Dy-SIGN propagates early-layer information directly to the last layer for information compensation. To accommodate the memory requirements, we apply the implicit differentiation on the equilibrium state, which does not rely on the exact reverse of the forward computation. While traditional implicit differentiation methods are usually used for static situations, Dy-SIGN extends it to the dynamic graph setting. Extensive experiments on three large-scale real-world dynamic graph datasets validate the effectiveness of Dy-SIGN on dynamic node classification tasks with lower computational costs.

Zhengqin Xu, Yulun Zhang, Chao Ma, Yichao Yan, Zelin Peng, Shoulie Xie, Shiqian Wu, Xiaokang Yang

A fundamental task in the realms of computer vision, Low-Rank Matrix Recovery (LRMR) focuses on the inherent low-rank structure precise recovery from incomplete data and/or corrupted measurements given that the rank is a known prior or accurately estimated. However, it remains challenging for existing rank estimation methods to accurately estimate the rank of an ill-conditioned matrix. Also, existing LRMR optimization methods are heavily dependent on the chosen parameters, and are therefore difficult to adapt to different situations. Addressing these issues, A novel LEarning-based low-rank matrix recovery with Rank Estimation (LERE) is proposed. More specifically, considering the characteristics of the Gerschgorin disk's center and radius, a new heuristic decision rule in the Gerschgorin Disk Theorem is significantly enhanced and the low-rank boundary can be exactly located, which leads to a marked improvement in the accuracy of rank estimation. According to the estimated rank, we select row and column sub-matrices from the observation matrix by uniformly random sampling. A 17-iteration feedforward-recurrent-mixed neural network is then adapted to learn the parameters in the sub-matrix recovery processing. Finally, by the correlation of the row sub-matrix and column sub-matrix, LERE successfully recovers the underlying low-rank matrix. Overall, LERE is more efficient and robust than existing LRMR methods. Experimental results demonstrate that LERE surpasses state-of-the-art (SOTA) methods. The code for this work is accessible at https://github.com/zhengqinxu/LERE.

Ke Xu, Zhongcheng Li, Shanshan Wang, Xingyi Zhang

The ability of model quantization with arbitrary bit-width to dynamically meet diverse bit-width requirements during runtime has attracted significant attention. Recent research has focused on optimizing large-scale training methods to achieve robust bit-width adaptation, which is a time-consuming process requiring hundreds of GPU hours. Furthermore, converting bit-widths requires recalculating statistical parameters of the norm layers, thereby impeding real-time switching of the bit-width. To overcome these challenges, we propose an efficient Post-Training Multi-bit Quantization (PTMQ) scheme that requires only a small amount of calibration data to perform block-wise reconstruction of multi-bit quantization errors. It eliminates the influence of statistical parameters by fusing norm layers, and supports real-time switching bit-widths in uniform quantization and mixed-precision quantization. To improve quantization accuracy and robustness, we propose a Multi-bit Feature Mixer technique (MFM) for fusing features of different bit-widths to enhance robustness across varying bit-widths. Moreover, we introduced the Group-wise Distillation Loss (GD-Loss) to enhance the correlation between different bit-width groups and further improve the overall performance of PTMQ. Extensive experiments demonstrate that PTMQ achieves comparable performance to existing state-of-the-art post-training quantization methods, while optimizing it speeds up by 100$\times$ compared to recent multi-bit quantization works. Code can be available at https://github.com/xuke225/PTMQ.

Xingrun Xing, Li Du, Xinyuan Wang, Xianlin Zeng, Yequan Wang, Zheng Zhang, Jiajun Zhang

Pretrained foundation models offer substantial benefits for a wide range of downstream tasks, which can be one of the most potential techniques to access artificial general intelligence. However, scaling up foundation transformers for maximal task-agnostic knowledge has brought about computational challenges, especially on resource-limited devices such as mobiles. This work proposes the first Binary Pretrained Foundation Transformer (BiPFT) for natural language understanding (NLU) tasks, which remarkably saves 56 times operations and 28 times memory. In contrast to previous task-specific binary transformers, BiPFT exhibits a substantial enhancement in the learning capabilities of binary neural networks (BNNs), promoting BNNs into the era of pre-training. Benefiting from extensive pretraining data, we further propose a data-driven binarization method. Specifically, we first analyze the binarization error in self-attention operations and derive the polynomials of binarization error. To simulate full-precision self-attention, we define binarization error as binarization residual polynomials, and then introduce low-rank estimators to model these polynomials. Extensive experiments validate the effectiveness of BiPFTs, surpassing task-specific baseline by 15.4% average performance on the GLUE benchmark. BiPFT also demonstrates improved robustness to hyperparameter changes, improved optimization efficiency, and reduced reliance on downstream distillation, which consequently generalize on various NLU tasks and simplify the downstream pipeline of BNNs. Our code and pretrained models are publicly available at https://github.com/Xingrun-Xing/BiPFT.

Chenghan Xie, Chenxi Li, Chuwen Zhang, Qi Deng, Dongdong Ge, Yinyu Ye

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general (L0, L1)-smoothness setting, which gains particular significance within the realms of deep neural networks and distributionally robust optimization (DRO). We demonstrate the significant advantage of trust region methods for stochastic nonconvex optimization under such generalized smoothness assumption. We show that first-order trust region methods can recover the normalized and clipped stochastic gradient as special cases and then provide a unified analysis to show their convergence to first-order stationary conditions. Motivated by the important application of DRO, we propose a generalized high-order smoothness condition, under which second-order trust region methods can achieve a complexity of O(epsilon(-3.5)) for convergence to second-order stationary points. By incorporating variance reduction, the second-order trust region method obtains an even better complexity of O(epsilon(-3)), matching the optimal bound for standard smooth optimization. To our best knowledge, this is the first work to show convergence beyond the first-order stationary condition for generalized smooth optimization. Preliminary experiments show that our proposed algorithms perform favorably compared with existing methods.

Yu Wang, Yuxuan Yin, Karthik Somayaji NS, Ján Drgoňa, Malachi Schram, Mahantesh Halappanavar, Frank Liu, Peng Li

Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary Differential Equations (NODE) have shown promising results by leveraging the expressive power of neural networks to model unknown dynamics. However, these approaches often suffer from limited labeled training data, leading to poor generalization and suboptimal predictions. On the other hand, semi-supervised algorithms can utilize abundant unlabeled data and have demonstrated good performance in classification and regression tasks. We propose TS-NODE, the first semi-supervised approach to modeling dynamical systems with NODE. TS-NODE explores cheaply generated synthetic pseudo rollouts to broaden exploration in the state space and to tackle the challenges brought by lack of ground-truth system data under a teacher-student model. TS-NODE employs an unified optimization framework that corrects the teacher model based on the student's feedback while mitigating the potential false system dynamics present in pseudo rollouts. TS-NODE demonstrates significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.

Luzhi Wang, Dongxiao He, He Zhang, Yixin Liu, Wenjie Wang, Shirui Pan, Di Jin, Tat-Seng Chua

Graph neural networks (GNNs) have found widespread application in modeling graph data across diverse domains. While GNNs excel in scenarios where the testing data shares the distribution of their training counterparts (in distribution, ID), they often exhibit incorrect predictions when confronted with samples from an unfamiliar distribution (out-of-distribution, OOD). To identify and reject OOD samples with GNNs, recent studies have explored graph OOD detection, often focusing on training a specific model or modifying the data on top of a well-trained GNN. Despite their effectiveness, these methods come with heavy training resources and costs, as they need to optimize the GNN-based models on training data. Moreover, their reliance on modifying the original GNNs and accessing training data further restricts their universality. To this end, this paper introduces a method to detect Graph Out-of-Distribution At Test-time (namely GOODAT), a data-centric, unsupervised, and plug-and-play solution that operates independently of training data and modifications of GNN architecture. With a lightweight graph masker, GOODAT can learn informative subgraphs from test samples, enabling the capture of distinct graph patterns between OOD and ID samples. To optimize the graph masker, we meticulously design three unsupervised objective functions based on the graph information bottleneck principle, motivating the masker to capture compact yet informative subgraphs for OOD detection. Comprehensive evaluations confirm that our GOODAT method outperforms state-of-the-art benchmarks across a variety of real-world datasets.

Théo Vincent, Alberto Maria Metelli, Boris Belousov, Jan Peters, Marcello Restelli, Carlo D'Eramo

Approximate value iteration (AVI) is a family of algorithms for reinforcement learning (RL) that aims to obtain an approximation of the optimal value function. Generally, AVI algorithms implement an iterated procedure where each step consists of (i) an application of the Bellman operator and (ii) a projection step into a considered function space. Notoriously, the Bellman operator leverages transition samples, which strongly determine its behavior, as uninformative samples can result in negligible updates or long detours, whose detrimental effects are further exacerbated by the computationally intensive projection step. To address these issues, we propose a novel alternative approach based on learning an approximate version of the Bellman operator rather than estimating it through samples as in AVI approaches. This way, we are able to (i) generalize across transition samples and (ii) avoid the computationally intensive projection step. For this reason, we call our novel operator projected Bellman operator (PBO). We formulate an optimization problem to learn PBO for generic sequential decision-making problems, and we theoretically analyze its properties in two representative classes of RL problems. Furthermore, we theoretically study our approach under the lens of AVI and devise algorithmic implementations to learn PBO in offline and online settings by leveraging neural network parameterizations. Finally, we empirically showcase the benefits of PBO w.r.t. the regular Bellman operator on several RL problems.

Johannes Schneider, Mohit Prabhushankar

The learning dynamics of deep neural networks are not well understood. The information bottleneck (IB) theory proclaimed separate fitting and compression phases. But they have since been heavily debated. We comprehensively analyze the learning dynamics by investigating a layer's reconstruction ability of the input and prediction performance based on the evolution of parameters during training. We empirically show the existence of three phases using common datasets and architectures such as ResNet and VGG: (i) near constant reconstruction loss, (ii) decrease, and (iii) increase. We also derive an empirically grounded data model and prove the existence of phases for single-layer networks. Technically, our approach leverages classical complexity analysis. It differs from IB by relying on measuring reconstruction loss rather than information theoretic measures to relate information of intermediate layers and inputs. Our work implies a new best practice for transfer learning: We show empirically that the pre-training of a classifier should stop well before its performance is optimal.

Yinuo Ren, Yiping Lu, Lexing Ying, Grant M. Rotskoff

Inferring a diffusion equation from discretely observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments. Assuming that the underlying dynamical process obeys a d-dimensional stochastic differential equation of the form dx_t = b(x_t)dt + \Sigma(x_t)dw_t, we propose neural network-based estimators of both the drift b and the spatially-inhomogeneous diffusion tensor D = \Sigma\Sigma^T/2 and provide statistical convergence guarantees when b and D are s-Hölder continuous. Notably, our bound aligns with the minimax optimal rate N^{-\frac{2s}{2s+d}} for nonparametric function estimation even in the presence of correlation within observational data, which necessitates careful handling when establishing fast-rate generalization bounds. Our theoretical results are bolstered by numerical experiments demonstrating accurate inference of spatially-inhomogeneous diffusion tensors.

Nisal Ranasinghe, Damith Senanayake, Sachith Seneviratne, Malin Premaratne, Saman Halgamuge

Traditional machine learning is generally treated as a black-box optimization problem and does not typically produce interpretable functions that connect inputs and outputs. However, the ability to discover such interpretable functions is desirable. In this work, we propose GINN-LP, an interpretable neural network to discover the form and coefficients of the underlying equation of a dataset, when the equation is assumed to take the form of a multivariate Laurent Polynomial. This is facilitated by a new type of interpretable neural network block, named the “power-term approximator block”, consisting of logarithmic and exponential activation functions. GINN-LP is end-to-end differentiable, making it possible to use backpropagation for training. We propose a neural network growth strategy that will enable finding the suitable number of terms in the Laurent polynomial that represents the data, along with sparsity regularization to promote the discovery of concise equations. To the best of our knowledge, this is the first model that can discover arbitrary multivariate Laurent polynomial terms without any prior information on the order. Our approach is first evaluated on a subset of data used in SRBench, a benchmark for symbolic regression. We first show that GINN-LP outperforms the state-of-the-art symbolic regression methods on datasets generated using 48 real-world equations in the form of multivariate Laurent polynomials. Next, we propose an ensemble method that combines our method with a high-performing symbolic regression method, enabling us to discover non-Laurent polynomial equations. We achieve state-of-the-art results in equation discovery, showing an absolute improvement of 7.1% over the best contender, by applying this ensemble method to 113 datasets within SRBench with known ground-truth equations.

Mincheol Park, Dongjin Kim, Cheonjun Park, Yuna Park, Gyeong Eun Gong, Won Woo Ro, Suhyun Kim

Channel pruning is widely accepted to accelerate modern convolutional neural networks (CNNs). The resulting pruned model benefits from its immediate deployment on general-purpose software and hardware resources. However, its large pruning granularity, specifically at the unit of a convolution filter, often leads to undesirable accuracy drops due to the inflexibility of deciding how and where to introduce sparsity to the CNNs. In this paper, we propose REPrune, a novel channel pruning technique that emulates kernel pruning, fully exploiting the finer but structured granularity. REPrune identifies similar kernels within each channel using agglomerative clustering. Then, it selects filters that maximize the incorporation of kernel representatives while optimizing the maximum cluster coverage problem. By integrating with a simultaneous training-pruning paradigm, REPrune promotes efficient, progressive pruning throughout training CNNs, avoiding the conventional train-prune-finetune sequence. Experimental results highlight that REPrune performs better in computer vision tasks than existing methods, effectively achieving a balance between acceleration ratio and performance retention.

Zherong Pan, Xifeng Gao, Kui Wu

Predicting the state evolution of ultra high-dimensional, time-reversible fluid dynamic systems is a crucial but computationally expensive task. Existing physics-informed neural networks either incur high inference cost or cannot preserve the time-reversible nature of the underlying dynamics system. We propose a model-based approach to identify low-dimensional, time reversible, nonlinear fluid dynamic systems. Our method utilizes the symplectic structure of reduced Eulerian fluid and use stochastic Riemann optimization to obtain a low-dimensional bases that minimize the expected trajectory-wise dimension-reduction error over a given distribution of initial conditions. We show that such minimization is well-defined since the reduced trajectories are differentiable with respect to the subspace bases over the entire Grassmannian manifold, under proper choices of timestep sizes and numerical integrators. Finally, we propose a loss function measuring the trajectory-wise discrepancy between the original and reduced models. By tensor precomputation, we show that gradient information of such loss function can be evaluated efficiently over a long trajectory without time-integrating the high-dimensional dynamic system. Through evaluations on a row of simulation benchmarks, we show that our method reduces the discrepancy by 50-90 percent over conventional reduced models and we outperform PINNs by exactly preserving the time reversibility.

Yongfan Lu, Bingdong Li, Aimin Zhou

Optimizing multiple conflicting black-box objectives simultaneously is a prevalent occurrence in many real-world applications, such as neural architecture search, and machine learning. These problems are known as expensive multi-objective optimization problems (EMOPs) when the function evaluations are computationally or financially costly. Multi-objective Bayesian optimization (MOBO) offers an efficient approach to discovering a set of Pareto optimal solutions. However, the data deficiency issue caused by limited function evaluations has posed a great challenge to current optimization methods. Moreover, most current methods tend to prioritize the quality of candidate solutions, while ignoring the quantity of promising samples. In order to tackle these issues, our paper proposes a novel multi-objective Bayesian optimization algorithm with a data augmentation strategy that provides ample high-quality samples for Pareto set learning (PSL). Specifically, it utilizes Generative Adversarial Networks (GANs) to enrich data and a dominance prediction model to screen out high-quality samples, mitigating the predicament of limited function evaluations in EMOPs. Additionally, we adopt the regularity model to expensive multi-objective Bayesian optimization for PSL. Experimental results on both synthetic and real-world problems demonstrate that our algorithm outperforms several state-of-the-art and classical algorithms.

Guy Lorberbom, Itai Gat, Yossi Adi, Alexander Schwing, Tamir Hazan

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.