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This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretised and discrete data, along with sample generation procedures. Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.

This paper proposes a novel unsupervised domain adaption (UDA) method based on contrastive bi-projector (CBP), which can improve the existing UDA methods. It is called CBPUDA here, which effectively promotes the feature extractors (FEs) to reduce the generation of ambiguous features for classification and domain adaption. The CBP differs from traditional bi-classifier-based methods at that these two classifiers are replaced with two projectors of performing a mapping from the input feature to two distinct features. These two projectors and the FEs in the CBPUDA can be trained adversarially to obtain more refined decision boundaries so that it can possess powerful classification performance. Two properties of the proposed loss function are analyzed here. The first property is to derive an upper bound of joint prediction entropy, which is used to form the proposed loss function, contrastive discrepancy (CD) loss. The CD loss takes the advantages of the contrastive learning and the bi-classifier. The second property is to analyze the gradient of the CD loss and then overcome the drawback of the CD loss. The result of the second property is utilized in the development of the gradient scaling (GS) scheme in this paper. The GS scheme can be exploited to tackle the unstable problem of the CD loss because training the CBPUDA requires using contrastive learning and adversarial learning at the same time. Therefore, using the CD loss with the GS scheme overcomes the problem mentioned above to make features more compact for intra-class and distinguishable for inter-class. Experimental results express that the CBPUDA is superior to conventional UDA methods under consideration in this paper for UDA and fine-grained UDA tasks.

This paper describes a way to improve the scalability of program synthesis by exploiting modularity: larger programs are synthesized from smaller programs. The key issue is to make each "larger-created-from-smaller" synthesis sub-problem be of a similar nature, so that the kind of synthesis sub-problem that needs to be solved--and the size of each search space--has roughly the same character at each level. This work holds promise for creating program-synthesis tools that have far greater capabilities than currently available tools, and opens new avenues for synthesis research: how synthesis tools should support modular system design, and how synthesis applications can best exploit such capabilities.

This paper uses symmetry to make Convolutional Neural Network classifiers (CNNs) robust against adversarial perturbation attacks. Such attacks add perturbation to original images to generate adversarial images that fool classifiers such as road sign classifiers of autonomous vehicles. Although symmetry is a pervasive aspect of the natural world, CNNs are unable to handle symmetry well. For example, a CNN can classify an image differently from its mirror image. For an adversarial image that misclassifies with a wrong label $l_w$, CNN inability to handle symmetry means that a symmetric adversarial image can classify differently from the wrong label $l_w$. Further than that, we find that the classification of a symmetric adversarial image reverts to the correct label. To classify an image when adversaries are unaware of the defense, we apply symmetry to the image and use the classification label of the symmetric image. To classify an image when adversaries are aware of the defense, we use mirror symmetry and pixel inversion symmetry to form a symmetry group. We apply all the group symmetries to the image and decide on the output label based on the agreement of any two of the classification labels of the symmetry images. Adaptive attacks fail because they need to rely on loss functions that use conflicting CNN output values for symmetric images. Without attack knowledge, the proposed symmetry defense succeeds against both gradient-based and random-search attacks, with up to near-default accuracies for ImageNet. The defense even improves the classification accuracy of original images.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.

This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN) for object classification, where each interpretable filter encodes features of a specific object part. Our method does not require additional annotations of object parts or textures for supervision. Instead, we use the same training data as traditional CNNs. Our method automatically assigns each interpretable filter in a high conv-layer with an object part of a certain category during the learning process. Such explicit knowledge representations in conv-layers of CNN help people clarify the logic encoded in the CNN, i.e., answering what patterns the CNN extracts from an input image and uses for prediction. We have tested our method using different benchmark CNNs with various structures to demonstrate the broad applicability of our method. Experiments have shown that our interpretable filters are much more semantically meaningful than traditional filters.

This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at //explained.ai

This paper proposes a method to modify traditional convolutional neural networks (CNNs) into interpretable CNNs, in order to clarify knowledge representations in high conv-layers of CNNs. In an interpretable CNN, each filter in a high conv-layer represents a certain object part. We do not need any annotations of object parts or textures to supervise the learning process. Instead, the interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. Our method can be applied to different types of CNNs with different structures. The clear knowledge representation in an interpretable CNN can help people understand the logics inside a CNN, i.e., based on which patterns the CNN makes the decision. Experiments showed that filters in an interpretable CNN were more semantically meaningful than those in traditional CNNs.

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.