We study the properties of alignment, a form of implicit regularization, in linear neural networks under gradient descent. We define alignment for fully connected networks with multidimensional outputs and show that it is a natural extension of alignment in networks with 1-dimensional outputs as defined by Ji and Telgarsky, 2018. While in fully connected networks, there always exists a global minimum corresponding to an aligned solution, we analyze alignment as it relates to the training process. Namely, we characterize when alignment is an invariant of training under gradient descent by providing necessary and sufficient conditions for this invariant to hold. In such settings, the dynamics of gradient descent simplify, thereby allowing us to provide an explicit learning rate under which the network converges linearly to a global minimum. We then analyze networks with layer constraints such as convolutional networks. In this setting, we prove that gradient descent is equivalent to projected gradient descent, and that alignment is impossible with sufficiently large datasets.
Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider NTK regime wide neural networks as a possible model of biological neural networks. Leveraging NTK theory, we show theoretically that gradient descent drives layerwise weight updates that are aligned with their input activity correlations weighted by error, and demonstrate empirically that the result also holds in finite-width wide networks. The alignment res…
Mila, Université de Montréal（蒙特利尔大学米拉研究所）；Microsoft Research（微软研究院）；Canada CIFAR AI chair（加拿大高级研究所加拿大人工智能主席项目）
We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a regularization effect induced by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small number of task-relevant directions. This can be interpreted as a combined mechanism of feature selection and compression. By extrapolating a new analysis of Rademacher complexity bounds for linear models, we motivate and study a heuristic complexity measure that captures this phenomenon, in terms of sequences of tangent kernel classes along optimization path…
Technion - Israel Institute of Technology（以色列理工学院）
Expressiveness and generalization of deep models was recently addressed via the connection between neural networks (NNs) and kernel learning, where first-order dynamics of NN during a gradient-descent (GD) optimization were related to gradient similarity kernel, also known as Neural Tangent Kernel (NTK). In the majority of works this kernel is considered to be time-invariant, with its properties being defined entirely by NN architecture and independent of the learning task at hand. In contrast, in this paper we empirically explore these properties along the optimization and show that in practi…
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
This paper introduces the notion of ``Initial Alignment'' (INAL) between a neural network at initialization and a target function. It is proved that if a network and a Boolean target function do not have a noticeable INAL, then noisy gradient descent on a fully connected network with normalized i.i.d. initialization will not learn in polynomial time. Thus a certain amount of knowledge about the target (measured by the INAL) is needed in the architecture design. This also provides an answer to an open problem posed in [AS20]. The results are based on deriving lower-bounds for descent algorithms…
Mila Institute（米拉研究所）；Saint Mary’s University（圣玛丽大学）；Université de Montréal（蒙特利尔大学）
We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rates for deep linear networks for both continuous and discrete dynamics. Additionally, we study incremental learning phenomena for shallow linear networks. Interestingly, certain specific initializations imply that negligible components are learned before the principal ones, thus potentially negatively affecting the effectiveness of such a learning algorithm; a phenomenon we classify as implicit anti-regularization. We…
VinAI Research（VinAI研究院）；Hanoi University of Science and Technology（河内科技大学）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Monash University（莫纳什大学）
Layer-wise model fusion via optimal transport, named OTFusion, applies soft neuron association for unifying different pre-trained networks to save computational resources. While enjoying its success, OTFusion requires the input networks to have the same number of layers. To address this issue, we propose a novel model fusion framework, named CLAFusion, to fuse neural networks with a different number of layers, which we refer to as heterogeneous neural networks, via cross-layer alignment. The cross-layer alignment problem, which is an unbalanced assignment problem, can be solved efficiently usi…
Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks
SISSA Trieste, Italy（意大利特里斯特SISSA研究所）；Theoretical and Scientific Data Science (TSDS) group at the International School for Advanced Studies (SISSA)（国际先进研究学院（SISSA）理论与科学数据科学（TSDS）小组）；Condensed Matter and Statistical Physics section at the International Centre for Theoretical Physics (ICTP)（国际理论物理中心（ICTP）凝聚态与统计物理部门）
We tackle here the problem of multimodal image non-rigid registration, which is of prime importance in remote sensing and medical imaging. The difficulties encountered by classical registration approaches include feature design and slow optimization by gradient descent. By analyzing these methods, we note the significance of the notion of scale. We design easy-to-train, fully-convolutional neural networks able to learn scale-specific features. Once chained appropriately, they perform global registration in linear time, getting rid of gradient descent schemes by predicting directly the deformat…
In this study, we show that landmark detection or face alignment task is not a single and independent problem. Instead, its robustness can be greatly improved with auxiliary information. Specifically, we jointly optimize landmark detection together with the recognition of heterogeneous but subtly correlated facial attributes, such as gender, expression, and appearance attributes. This is non-trivial since different attribute inference tasks have different learning difficulties and convergence rates. To address this problem, we formulate a novel tasks-constrained deep model, which not only lear…
Boston University（波士顿大学）；Google AI（谷歌人工智能）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Distribution alignment has many applications in deep learning, including domain adaptation and unsupervised image-to-image translation. Most prior work on unsupervised distribution alignment relies either on minimizing simple non-parametric statistical distances such as maximum mean discrepancy or on adversarial alignment. However, the former fails to capture the structure of complex real-world distributions, while the latter is difficult to train and does not provide any universal convergence guarantees or automatic quantitative validation procedures. In this paper, we propose a new distribut…
Center for Brain Science, Harvard University（哈佛大学脑科学中心）；School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）
The training dynamics and generalization properties of neural networks (NN) can be precisely characterized in function space via the neural tangent kernel (NTK). Structural changes to the NTK during training reflect feature learning and underlie the superior performance of networks outside of the static kernel regime. In this work, we seek to theoretically understand kernel alignment, a prominent and ubiquitous structural change that aligns the NTK with the target function. We first study a toy model of kernel evolution in which the NTK evolves to accelerate training and show that alignment na…
Multiple sequences alignment (MSA) is a traditional and challenging task for time-series analyses. The MSA problem is formulated as a discrete optimization problem and is typically solved by dynamic programming. However, the computational complexity increases exponentially with respect to the number of input sequences. In this paper, we propose neural time warping (NTW) that relaxes the original MSA to a continuous optimization and obtains the alignments using a neural network. The solution obtained by NTW is guaranteed to be a feasible solution for the original discrete optimization problem u…
Neural networks in the lazy training regime converge to kernel machines. Can neural networks in the rich feature learning regime learn a kernel machine with a data-dependent kernel? We demonstrate that this can indeed happen due to a phenomenon we term silent alignment, which requires that the tangent kernel of a network evolves in eigenstructure while small and before the loss appreciably decreases, and grows only in overall scale afterwards. We show that such an effect takes place in homogenous neural networks with small initialization and whitened data. We provide an analytical treatment of…
School of Electrical Engineering（电气工程学院）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院（KAIST））；Daejeon, Republic of Korea（大邱，韩国）
There were many algorithms to substitute the back-propagation (BP) in the deep neural network (DNN) training. However, they could not become popular because their training accuracy and the computational efficiency were worse than BP. One of them was direct feedback alignment (DFA), but it showed low training performance especially for the convolutional neural network (CNN). In this paper, we overcome the limitation of the DFA algorithm by combining with the conventional BP during the CNN training. To improve the training stability, we also suggest the feedback weight initialization method by a…
University of Alberta（阿尔伯塔大学）；University of Michigan（密歇根大学）
It is now a standard for neural network representations to be trained on large, publicly available datasets, and used for new problems. The reasons for why neural network representations have been so successful for transfer, however, are still not fully understood. In this paper we show that, after training, neural network representations align their top singular vectors to the targets. We investigate this representation alignment phenomenon in a variety of neural network architectures and find that (a) alignment emerges across a variety of different architectures and optimizers, with more ali…
Word alignments identify translational correspondences between words in a parallel sentence pair and is used, for instance, to learn bilingual dictionaries, to train statistical machine translation systems , or to perform quality estimation. In most areas of natural language processing, neural network models nowadays constitute the preferred approach, a situation that might also apply to word alignment models. In this work, we study and comprehensively evaluate neural models for unsupervised word alignment for four language pairs, contrasting several variants of neural models. We show that in …
LightOn；Laboratoire de Physique de l’ENS（巴黎高等师范学院物理实验室）；Université PSL（巴黎文理研究大学）；CNRS（法国国家科学研究中心）；Sorbonne Université（索邦大学）
The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods -where the error gradient is only roughly approximated - have garnered interest. These methods not only better portray how biological brains are learning, but also open new computational possibilities, such as updating layers asynchronously. Even so, they have failed to scale past simple tasks like MNIST or CIFAR-10. This is in part due to a lack of standards…
The University of Sydney（悉尼大学）；CSIRO Data61（联邦科学与工业研究组织数据61研究所）
We present ChromAlignNet, a deep learning model for alignment of peaks in Gas Chromatography-Mass Spectrometry (GC-MS) data. In GC-MS data, a compound's retention time (RT) may not stay fixed across multiple chromatograms. To use GC-MS data for biomarker discovery requires alignment of identical analyte's RT from different samples. Current methods of alignment are all based on a set of formal, mathematical rules. We present a solution to GC-MS alignment using deep learning neural networks, which are more adept at complex, fuzzy data sets. We tested our model on several GC-MS data sets of vario…
The most common tools for word-alignment rely on a large amount of parallel sentences, which are then usually processed according to one of the IBM model algorithms. The training data is, however, the same as for machine translation (MT) systems, especially for neural MT (NMT), which itself is able to produce word-alignments using the trained attention heads. This is convenient because word-alignment is theoretically a viable byproduct of any attention-based NMT, which is also able to provide decoder scores for a translated sentence pair. We summarize different approaches on how word-alignment…
Graph neural networks (GNNs) have been widely investigated in the field of semi-supervised graph machine learning. Most methods fail to exploit adequate graph information when labeled data is limited, leading to the problem of oversmoothing. To overcome this issue, we propose the Graph Alignment Neural Network (GANN), a simple and effective graph neural architecture. A unique learning algorithm with three alignment rules is proposed to thoroughly explore hidden information for insufficient labels. Firstly, to better investigate attribute specifics, we suggest the feature alignment rule to alig…
Recently, considerable effort has been devoted to deep domain adaptation in computer vision and machine learning communities. However, most of existing work only concentrates on learning shared feature representation by minimizing the distribution discrepancy across different domains. Due to the fact that all the domain alignment approaches can only reduce, but not remove the domain shift. Target domain samples distributed near the edge of the clusters, or far from their corresponding class centers are easily to be misclassified by the hyperplane learned from the source domain. To alleviate th…
Tsinghua University（清华大学）；The University of Hong Kong（香港大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Shanghai University of Finance and Economics（上海财经大学）
Despite its original goal to jointly learn to align and translate, prior researches suggest that Transformer captures poor word alignments through its attention mechanism. In this paper, we show that attention weights DO capture accurate word alignments and propose two novel word alignment induction methods Shift-Att and Shift-AET. The main idea is to induce alignments at the step when the to-be-aligned target token is the decoder input rather than the decoder output as in previous work. Shift-Att is an interpretation method that induces alignments from the attention weights of Transformer and…
Word alignments identify translational correspondences between words in a parallel sentence pair and are used, for instance, to learn bilingual dictionaries, to train statistical machine translation systems or to perform quality estimation. Variational autoencoders have been recently used in various of natural language processing to learn in an unsupervised way latent representations that are useful for language generation tasks. In this paper, we study these models for the task of word alignment and propose and assess several evolutions of a vanilla variational autoencoders. We demonstrate th…
Ongoing studies have identified similarities between neural representations in biological networks and in deep artificial neural networks. This has led to renewed interest in developing analogies between the backpropagation learning algorithm used to train artificial networks and the synaptic plasticity rules operative in the brain. These efforts are challenged by biologically implausible features of backpropagation, one of which is a reliance on symmetric forward and backward synaptic weights. A number of methods have been proposed that do not rely on weight symmetry but, thus far, these have…
Unsupervised domain adaptation leverages rich information from a labeled source domain to model an unlabeled target domain. Existing methods attempt to align the cross-domain distributions. However, the statistical representations of the alignment of the two domains are not well addressed. In this paper, we propose deep least squares alignment (DLSA) to estimate the distribution of the two domains in a latent space by parameterizing a linear model. We further develop marginal and conditional adaptation loss to reduce the domain discrepancy by minimizing the angle between fitting lines and inte…
Bidirectional Long Short-Term Memory (LSTM) is a special kind of Recurrent Neural Network (RNN) architecture which is designed to model sequences and their long-range dependencies more precisely than RNNs. This paper proposes to use deep bidirectional LSTM for sequence modeling as an approach to perform locality-sensitive hashing (LSH)-based sequence alignment. In particular, we use the deep bidirectional LSTM to learn features of LSH. The obtained LSH is then can be utilized to perform sequence alignment. We demonstrate the feasibility of the modeling sequences using the proposed LSTM-based m…
Real-world face detection and alignment demand an advanced discriminative model to address challenges by pose, lighting and expression. Illuminated by the deep learning algorithm, some convolutional neural networks based face detection and alignment methods have been proposed. Recent studies have utilized the relation between face detection and alignment to make models computationally efficiency, however they ignore the connection between each cascade CNNs. In this paper, we propose an structure to propose higher quality training data for End-to-End cascade network training, which give compute…
Michigan State University（密歇根州立大学）；HRL Laboratories（HRL实验室）
Network alignment, in general, seeks to discover the hidden underlying correspondence between nodes across two (or more) networks when given their network structure. However, most existing network alignment methods have added assumptions of additional constraints to guide the alignment, such as having a set of seed node-node correspondences across the networks or the existence of side-information. Instead, we seek to develop a general network alignment algorithm that makes no additional assumptions. Recently, network embedding has proven effective in many network analysis tasks, but embeddings…
Liulishuo AI Lab（流利说人工智能实验室）；University of British Columbia（不列颠哥伦比亚大学）；Disney Research（迪士尼研究院）
The alignment of heterogeneous sequential data (video to text) is an important and challenging problem. Standard techniques for this task, including Dynamic Time Warping (DTW) and Conditional Random Fields (CRFs), suffer from inherent drawbacks. Mainly, the Markov assumption implies that, given the immediate past, future alignment decisions are independent of further history. The separation between similarity computation and alignment decision also prevents end-to-end training. In this paper, we propose an end-to-end neural architecture where alignment actions are implemented as moving data be…
Relative Geometry of Neural Forecasters: Linking Accuracy and Alignment in Learned Latent Geometry
Max Planck Institute for Human Cognitive and Brain Sciences（马克斯·普朗克人类认知与脑科学研究所）；School of Embedded Composite Artificial Intelligence (SECAI)（嵌入式复合人工智能学院）；Leipzig University（莱比锡大学）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学研究院）
UiT The Arctic University of Norway（挪威北极大学）；Norwegian Computing Center（挪威计算中心）；University of Copenhagen（哥本哈根大学）
Self-supervised learning is a central component in recent approaches to deep multi-view clustering (MVC). However, we find large variations in the development of self-supervision-based methods for deep MVC, potentially slowing the progress of the field. To address this, we present DeepMVC, a unified framework for deep MVC that includes many recent methods as instances. We leverage our framework to make key observations about the effect of self-supervision, and in particular, drawbacks of aligning representations with contrastive learning. Further, we prove that contrastive alignment can negati…
NTT Communication Science Laboratories（日本电报电话通信科学实验室）
In this paper, we propose a method of improving temporal Convolutional Neural Networks (CNN) by determining the optimal alignment of weights and inputs using dynamic programming. Conventional CNN convolutions linearly match the shared weights to a window of the input. However, it is possible that there exists a more optimal alignment of weights. Thus, we propose the use of Dynamic Time Warping (DTW) to dynamically align the weights to the input of the convolutional layer. Specifically, the dynamic alignment overcomes issues such as temporal distortion by finding the minimal distance matching o…
Despite being the workhorse of deep learning, the backpropagation algorithm is no panacea. It enforces sequential layer updates, thus preventing efficient parallelization of the training process. Furthermore, its biological plausibility is being challenged. Alternative schemes have been devised; yet, under the constraint of synaptic asymmetry, none have scaled to modern deep learning tasks and architectures. Here, we challenge this perspective, and study the applicability of Direct Feedback Alignment to neural view synthesis, recommender systems, geometric learning, and natural language proces…
Prior to deep learning the semantic parsing community has been interested in understanding and modeling the range of possible word alignments between natural language sentences and their corresponding meaning representations. Sequence-to-sequence models changed the research landscape suggesting that we no longer need to worry about alignments since they can be learned automatically by means of an attention mechanism. More recently, researchers have started to question such premise. In this work we investigate whether seq2seq models can handle both simple and complex alignments. To answer this …
Recently, several optimization methods have been successfully applied to the hyperparameter optimization of deep neural networks (DNNs). The methods work by modeling the joint distribution of hyperparameter values and corresponding error. Those methods become less practical when applied to modern DNNs whose training may take a few days and thus one cannot collect sufficient observations to accurately model the distribution. To address this challenging issue, we propose a method that learns to transfer optimal hyperparameter values for a small source dataset to hyperparameter values with compar…
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电子信息与电气工程学院）
The wide application of deep learning techniques is boosting the regulation of deep learning models, especially deep neural networks (DNN), as commercial products. A necessary prerequisite for such regulations is identifying the owner of deep neural networks, which is usually done through the watermark. Current DNN watermarking schemes, particularly white-box ones, are uniformly fragile against a family of functionality equivalence attacks, especially the neuron permutation. This operation can effortlessly invalidate the ownership proof and escape copyright regulations. To enhance the robustne…
Feature, Alignment, and Supervision in Category Learning: A Comparative Approach with Children and Neural Networks
Department of Psychology, University of Southern California（南加州大学心理学系）；Department of Statistics and Data Science, University of California, Los Angeles（加州大学洛杉矶分校统计与数据科学系）
Queen Mary University of London（伦敦玛丽女王大学）；Institute for Research and Coordination in Acoustics/Music（声学/音乐研究与协调研究所）
The identification of structural differences between a music performance and the score is a challenging yet integral step of audio-to-score alignment, an important subtask of music information retrieval. We present a novel method to detect such differences between the score and performance for a given piece of music using progressively dilated convolutional neural networks. Our method incorporates varying dilation rates at different layers to capture both short-term and long-term context, and can be employed successfully in the presence of limited annotated data. We conduct experiments on audi…
University of Georgia（佐治亚大学）；The Pennsylvania State University（宾夕法尼亚州立大学）
Standard methods for differentially private training of deep neural networks replace back-propagated mini-batch gradients with biased and noisy approximations to the gradient. These modifications to training often result in a privacy-preserving model that is significantly less accurate than its non-private counterpart. We hypothesize that alternative training algorithms may be more amenable to differential privacy. Specifically, we examine the suitability of direct feedback alignment (DFA). We propose the first differentially private method for training deep neural networks with DFA and show t…
Arbitrary style transfer is an important problem in computer vision that aims to transfer style patterns from an arbitrary style image to a given content image. However, current methods either rely on slow iterative optimization or fast pre-determined feature transformation, but at the cost of compromised visual quality of the styled image; especially, distorted content structure. In this work, we present an effective and efficient approach for arbitrary style transfer that seamlessly transfers style patterns as well as keep content structure intact in the styled image. We achieve this by alig…
University of Bonn（波恩大学）；L3S Research Center, Leibniz Universität Hannover（汉诺威莱布尼茨大学L3S研究中心）
OpenStreetMap (OSM) is one of the richest openly available sources of volunteered geographic information. Although OSM includes various geographical entities, their descriptions are highly heterogeneous, incomplete, and do not follow any well-defined ontology. Knowledge graphs can potentially provide valuable semantic information to enrich OSM entities. However, interlinking OSM entities with knowledge graphs is inherently difficult due to the large, heterogeneous, ambiguous, and flat OSM schema and the annotation sparsity. This paper tackles the alignment of OSM tags with the corresponding kn…
University of Maryland（马里兰大学）；Institute for Adv. Computer Studies（高级计算机研究所）
Deep Reservoir Computing has emerged as a new paradigm for deep learning, which is based around the reservoir computing principle of maintaining random pools of neurons combined with hierarchical deep learning. The reservoir paradigm reflects and respects the high degree of recurrence in biological brains, and the role that neuronal dynamics play in learning. However, one issue hampering deep reservoir network development is that one cannot backpropagate through the reservoir layers. Recent deep reservoir architectures do not learn hidden or hierarchical representations in the same manner as d…
