The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in many real-world applications. In order to improve the comprehension and interpretability of deep neural networks, we here introduce a novel theoretical framework based on the compositional structure of piecewise linear activation functions. By defining a direct acyclic graph representing the composition of activation patterns through the network layers, it is possible to characterize the instances of the input data with respect to both the predicted label and the specific (linear) transformation used to perform predictions. Preliminary tests on the MNIST dataset show that our method can group input instances with regard to their similarity in the internal representation of the neural network, providing an intuitive measure of input complexity.
We utilize a connection between compositional kernels and branching processes via Mehler's formula to study deep neural networks. This new probabilistic insight provides us a novel perspective on the mathematical role of activation functions in compositional neural networks. We study the unscaled and rescaled limits of the compositional kernels and explore the different phases of the limiting behavior, as the compositional depth increases. We investigate the memorization capacity of the compositional kernels and neural networks by characterizing the interplay among compositional depth, sample …
University of Oxford（牛津大学）；Google DeepMind（谷歌DeepMind）
This paper aims to explore the effect of prior disambiguation on neural network- based compositional models, with the hope that better semantic representations for text compounds can be produced. We disambiguate the input word vectors before they are fed into a compositional deep net. A series of evaluations shows the positive effect of prior disambiguation for such deep models.
Beihang University（北京航空航天大学）；Tianjin Medical University（天津医科大学）
In recent years, deep learning has witnessed its blossom in the field of Electrocardiography (ECG) processing, outperforming traditional signal processing methods in various tasks, for example, classification, QRS detection, wave delineation. Although many neural architectures have been proposed in the literature, there is a lack of systematic studies and open-source libraries for ECG deep learning. In this paper, we propose a deep learning framework, named \texttt{torch\_ecg}, which gathers a large number of neural networks, both from literature and novel, for various ECG processing tasks. It…
Neuro-Cognitive Modeling Group, Eberhard Karls University Tübingen（图宾根大学神经认知建模小组）
When comparing human with artificial intelligence, one major difference is apparent: Humans can generalize very broadly from sparse data sets because they are able to recombine and reintegrate data components in compositional manners. To investigate differences in efficient learning, Joshua B. Tenenbaum and colleagues developed the character challenge: First an algorithm is trained in generating handwritten characters. In a next step, one version of a new type of character is presented. An efficient learning algorithm is expected to be able to re-generate this new character, to identify simila…
Indian Institute of Technology, Guwahati（印度理工学院古瓦哈提分校）
Generalization error defines the discriminability and the representation power of a deep model. In this work, we claim that feature space design using deep compositional function plays a significant role in generalization along with explicit and implicit regularizations. Our claims are being established with several image classification experiments. We show that the information loss due to convolution and max pooling can be marginalized with the compositional design, improving generalization performance. Also, we will show that learning rate decay acts as an implicit regularizer in deep model …
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；University of California, Irvine（加州大学欧文分校）
Hierarchy and compositionality are common latent properties in many natural and scientific datasets. Determining when a deep network's hidden activations represent hierarchy and compositionality is important both for understanding deep representation learning and for applying deep networks in domains where interpretability is crucial. However, current benchmark machine learning datasets either have little hierarchical or compositional structure, or the structure is not known. This gap impedes precise analysis of a network's representations and thus hinders development of new methods that can l…
University of Amsterdam（阿姆斯特丹大学）；Universitat Pompeu Fabra（庞培法布拉大学）
Recent findings in multi-agent deep learning systems point towards the emergence of compositional languages. These claims are often made without exact analysis or testing of the language. In this work, we analyze the emergent language resulting from two different cooperative multi-agent game with more exact measures for compositionality. Our findings suggest that solutions found by deep learning models are often lacking the ability to reason on an abstract level therefore failing to generalize the learned knowledge to out of the training distribution examples. Strategies for testing compositio…
Learning Sparse Compositional Functions with Norm-Constrained Neural Networks
Istituto Italiano di Tecnologia（意大利技术研究院）；Università degli Studi di Genova（热那亚大学）；MaLGa（MaLGa实验室）；DIBRIS（迪布里兹实验室）；CBMM（生物医学工程与机器人实验室）；Massachusetts Institute of Technology（麻省理工学院）
University of Tübingen（图宾根大学）；University of Bath（巴斯大学）；Electronic Arts（艺电公司）；Siemens AG（西门子股份公司）；TU Munich（慕尼黑工业大学）；University of Bristol（布里斯托尔大学）；Royal Society（皇家学会）
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a posterior distribution of compositions of multiple functions giving rise to the observations. However, exact Bayesian inference is intractable for DGPs, motivating the use of various approximations. We show that the application of simplifying mean-field assumptions across the hierarchy leads to the layers of a DGP collapsing to near-deterministic transforma…
Sri Sathya Sai Institute of Higher Learning（斯里萨特亚赛高等研究院）
A formal description of the compositionality of neural networks is associated directly with the formal grammar-structure of the objects it seeks to represent. This formal grammar-structure specifies the kind of components that make up an object, and also the configurations they are allowed to be in. In other words, objects can be described as a parse-tree of its components -- a structure that can be seen as a candidate for building connection-patterns among neurons in neural networks. We present a formal grammar description of convolutional neural networks and capsule networks that shows how c…
University of Colorado Boulder（科罗拉多大学博尔德分校）；MILA（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）
Standard methods in deep learning for natural language processing fail to capture the compositional structure of human language that allows for systematic generalization outside of the training distribution. However, human learners readily generalize in this way, e.g. by applying known grammatical rules to novel words. Inspired by work in neuroscience suggesting separate brain systems for syntactic and semantic processing, we implement a modification to standard approaches in neural machine translation, imposing an analogous separation. The novel model, which we call Syntactic Attention, subst…
We assume that a high-dimensional datum, like an image, is a compositional expression of a set of properties, with a complicated non-linear relationship between the datum and its properties. This paper proposes a factorial mixture prior for capturing latent properties, thereby adding structured compositionality to deep generative models. The prior treats a latent vector as belonging to Cartesian product of subspaces, each of which is quantized separately with a Gaussian mixture model. Some mixture components can be set to represent properties as observed random variables whenever labeled prope…
Georgia Tech（佐治亚理工学院）；Oregon State University（俄勒冈州立大学）；Facebook AI Research（Facebook人工智能研究院）
Recent work has studied the emergence of language among deep reinforcement learning agents that must collaborate to solve a task. Of particular interest are the factors that cause language to be compositional -- i.e., express meaning by combining words which themselves have meaning. Evolutionary linguists have found that in addition to structural priors like those already studied in deep learning, the dynamics of transmitting language from generation to generation contribute significantly to the emergence of compositionality. In this paper, we introduce these cultural evolutionary dynamics int…
As deep neural networks become more adept at traditional tasks, many of the most exciting new challenges concern multimodality---observations that combine diverse types, such as image and text. In this paper, we introduce a family of multimodal deep generative models derived from variational bounds on the evidence (data marginal likelihood). As part of our derivation we find that many previous multimodal variational autoencoders used objectives that do not correctly bound the joint marginal likelihood across modalities. We further generalize our objective to work with several types of deep gen…
Lawrence Livermore National Laboratories（劳伦斯利弗莫尔国家实验室）
This paper studies the problem of post-hoc calibration of machine learning classifiers. We introduce the following desiderata for uncertainty calibration: (a) accuracy-preserving, (b) data-efficient, and (c) high expressive power. We show that none of the existing methods satisfy all three requirements, and demonstrate how Mix-n-Match calibration strategies (i.e., ensemble and composition) can help achieve remarkably better data-efficiency and expressive power while provably maintaining the classification accuracy of the original classifier. Mix-n-Match strategies are generic in the sense that…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Johns Hopkins University（约翰斯·霍普金斯大学）
Is analogical reasoning a task that must be learned to solve from scratch by applying deep learning models to massive numbers of reasoning problems? Or are analogies solved by computing similarities between structured representations of analogs? We address this question by comparing human performance on visual analogies created using images of familiar three-dimensional objects (cars and their subregions) with the performance of alternative computational models. Human reasoners achieved above-chance accuracy for all problem types, but made more errors in several conditions (e.g., when relevant…
Methods of deep learning have become increasingly popular in recent years, but they have not arrived in compositional data analysis. Imputation methods for compositional data are typically applied on additive, centered or isometric log-ratio representations of the data. Generally, methods for compositional data analysis can only be applied to observed positive entries in a data matrix. Therefore one tries to impute missing values or measurements that were below a detection limit. In this paper, a new method for imputing rounded zeros based on artificial neural networks is shown and compared wi…
Institute of Mathematical Sciences, Claremont Graduate University（克莱蒙特研究生大学数学科学研究所）；Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology（麻省理工学院麦戈文脑科学研究所脑、心智与机器中心）
We show that deep networks are better than shallow networks at approximating functions that can be expressed as a composition of functions described by a directed acyclic graph, because the deep networks can be designed to have the same compositional structure, while a shallow network cannot exploit this knowledge. Thus, the blessing of compositionality mitigates the curse of dimensionality. On the other hand, a theorem called good propagation of errors allows to `lift' theorems about shallow networks to those about deep networks with an appropriate choice of norms, smoothness, etc. We illustr…
With the growth of adversarial attacks against machine learning models, several concerns have emerged about potential vulnerabilities in designing deep neural network-based intrusion detection systems (IDS). In this paper, we study the resilience of deep learning-based intrusion detection systems against adversarial attacks. We apply the min-max (or saddle-point) approach to train intrusion detection systems against adversarial attack samples in NSW-NB 15 dataset. We have the max approach for generating adversarial samples that achieves maximum loss and attack deep neural networks. On the othe…
Carnegie Mellon University（卡内基梅隆大学）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Boeing（波音公司）
As autonomy becomes prevalent in many applications, ranging from recommendation systems to fully autonomous vehicles, there is an increased need to provide safety guarantees for such systems. The problem is difficult, as these are large, complex systems which operate in uncertain environments, requiring data-driven machine-learning components. However, learning techniques such as Deep Neural Networks, widely used today, are inherently unpredictable and lack the theoretical foundations to provide strong assurance guarantees. We present a compositional approach for the scalable, formal verificat…
This study presents a novel, deep, fully convolutional architecture which is optimized for the task of EEG-based neonatal seizure detection. Architectures of different depths were designed and tested; varying network depth impacts convolutional receptive fields and the corresponding learned feature complexity. Two deep convolutional networks are compared with a shallow SVM-based neonatal seizure detector, which relies on the extraction of hand-crafted features. On a large clinical dataset, of over 800 hours of multichannel unedited EEG, containing 1389 seizure events, the deep 11-layer archite…
Despite achieving tremendous success, existing deep learning models have exposed limitations in compositional generalization, the capability to learn compositional rules and apply them to unseen cases in a systematic manner. To tackle this issue, we propose the Neural-Symbolic Stack Machine (NeSS). It contains a neural network to generate traces, which are then executed by a symbolic stack machine enhanced with sequence manipulation operations. NeSS combines the expressive power of neural sequence models with the recursion supported by the symbolic stack machine. Without training supervision o…
Position: A Theory of Deep Learning Must Include Compositional Sparsity
Center for Brains, Minds and Machines (CBMM), MIT, Cambridge, MA, USA（大脑、心智与机器中心（CBMM），麻省理工学院）；ETH Zurich, Zurich, Switzerland（苏黎世联邦理工学院）；University of Zurich, Zurich, Switzerland（苏黎世大学）；University of Milan, Milan, Italy（米兰大学）
We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated matrix-space models for compositionality, and show they are special cases of the multiplicative recurrent net. Our experiments show that these models perform comparably or better than Elman-type additive recurrent neural networks and outperform matrix-space models on a standard fine-grained sentiment analysis corpus. Furthermore, they yield comparable results to s…
We tackle a task where an agent learns to navigate in a 2D maze-like environment called XWORLD. In each session, the agent perceives a sequence of raw-pixel frames, a natural language command issued by a teacher, and a set of rewards. The agent learns the teacher's language from scratch in a grounded and compositional manner, such that after training it is able to correctly execute zero-shot commands: 1) the combination of words in the command never appeared before, and/or 2) the command contains new object concepts that are learned from another task but never learned from navigation. Our deep…
Center for Brains, Minds and Machines（脑、心智与机器中心）；Massachusetts Institute of Technology（麻省理工学院）
The main success stories of deep learning, starting with ImageNet, depend on deep convolutional networks, which on certain tasks perform significantly better than traditional shallow classifiers, such as support vector machines, and also better than deep fully connected networks; but what is so special about deep convolutional networks? Recent results in approximation theory proved an exponential advantage of deep convolutional networks with or without shared weights in approximating functions with hierarchical locality in their compositional structure. More recently, the hierarchical structur…
Massachusetts Institute of Technology（麻省理工学院）；Brown University（布朗大学）；Tel-Aviv University（特拉维夫大学）
In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including convolutional neural networks. These bounds differ from previous ones, as they consider the norms of the convolutional filters instead of the norms of the associated Toeplitz matrices, independently of weight sharing between neurons. As we show theoretically, these bounds may be orders of magnitude better than standard norm-based generalization bounds and empirically, t…
Center for Data Science（数据科学中心）；New York University（纽约大学）
We explore the benefits of augmenting state-of-the-art model-free deep reinforcement algorithms with simple object representations. Following the Frostbite challenge posited by Lake et al. (2017), we identify object representations as a critical cognitive capacity lacking from current reinforcement learning agents. We discover that providing the Rainbow model (Hessel et al.,2018) with simple, feature-engineered object representations substantially boosts its performance on the Frostbite game from Atari 2600. We then analyze the relative contributions of the representations of different types o…
Since first introduced, computer simulation has been an increasingly important tool in evolutionary linguistics. Recently, with the development of deep learning techniques, research in grounded language learning has also started to focus on facilitating the emergence of compositional languages without pre-defined elementary linguistic knowledge. In this work, we explore the emergence of compositional languages for numeric concepts in multi-agent communication systems. We demonstrate that compositional language for encoding numeric concepts can emerge through iterated learning in populations of…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated strong performance on novel applications, they sacrifice many of the functionalities of traditional software programs. With this as motivation, we take a modest first step towards improving deep learning programs by jointly training a generative model to constrain neural network activations to "decode" back to inputs. We call this design a Decodable Neural Networ…
Solving complex, temporally-extended tasks is a long-standing problem in reinforcement learning (RL). We hypothesize that one critical element of solving such problems is the notion of compositionality. With the ability to learn concepts and sub-skills that can be composed to solve longer tasks, i.e. hierarchical RL, we can acquire temporally-extended behaviors. However, acquiring effective yet general abstractions for hierarchical RL is remarkably challenging. In this paper, we propose to use language as the abstraction, as it provides unique compositional structure, enabling fast learning an…
University of Nebraska（内布拉斯加大学）；University of Nebraska-Lincoln（内布拉斯加大学林肯分校）；Georgia Institute of Technology（佐治亚理工学院）；Ford R&A（福特研究与创新中心）；German University in Cairo（开罗德国大学）
Understanding the per-layer learning dynamics of deep neural networks is of significant interest as it may provide insights into how neural networks learn and the potential for better training regimens. We investigate learning in Deep Convolutional Neural Networks (CNNs) by measuring the relative weight change of layers while training. Several interesting trends emerge in a variety of CNN architectures across various computer vision classification tasks, including the overall increase in relative weight change of later layers as compared to earlier ones.
University of Edinburgh（爱丁堡大学）；Sorbonne Université（索邦大学）；German Aerospace Center (DLR)（德国航空航天中心）
Deep Reinforcement Learning has shown great success in a variety of control tasks. However, it is unclear how close we are to the vision of putting Deep RL into practice to solve real world problems. In particular, common practice in the field is to train policies on largely deterministic simulators and to evaluate algorithms through training performance alone, without a train/test distinction to ensure models generalise and are not overfitted. Moreover, it is not standard practice to check for generalisation under domain shift, although robustness to such system change between training and te…
Compositional structures between parts and objects are inherent in natural scenes. Modeling such compositional hierarchies via unsupervised learning can bring various benefits such as interpretability and transferability, which are important in many downstream tasks. In this paper, we propose the first deep latent variable model, called RICH, for learning Representation of Interpretable Compositional Hierarchies. At the core of RICH is a latent scene graph representation that organizes the entities of a scene into a tree structure according to their compositional relationships. During inferenc…
Eligibility traces in reinforcement learning are used as a bias-variance trade-off and can often speed up training time by propagating knowledge back over time-steps in a single update. We investigate the use of eligibility traces in combination with recurrent networks in the Atari domain. We illustrate the benefits of both recurrent nets and eligibility traces in some Atari games, and highlight also the importance of the optimization used in the training.
Histone modifications play a critical role in gene regulation. Consequently, predicting gene expression from histone modification signals is a highly motivated problem in epigenetics. We build upon the work of DeepChrome by Singh et al. (2016), who trained classifiers that map histone modification signals to gene expression. We present a novel visualization technique for providing insight into combinatorial relationships among histone modifications for gene regulation that uses a generative adversarial network to generate histone modification signals. We also explore and compare various archit…
University of Zagreb Faculty of Electrical Engineering and Computing（萨格勒布大学电气工程与计算学院）
Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this thesis we build a category-theoretic formalism around a class of neural networks exemplified by CycleGAN. CycleGAN is a collection of neural networks, closed under composition, whose inductive bias is increased by enforcing composition invariants, i.e. cycle-consistencies. Inspired by Functorial Data Migration, we specify the interconnection of these networks us…
