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Error backpropagation is a highly effective mechanism for learning high-quality hierarchical features in deep networks. Updating the features or weights in one layer, however, requires waiting for the propagation of error signals from…
This article contributes to the current statistical theory of deep neural networks (DNNs). It was shown that DNNs are able to circumvent the so--called curse of dimensionality in case that suitable restrictions on the structure of the…
Overparameterized models may have many interpolating solutions; implicit regularization refers to the hidden preference of a particular optimization method towards a certain interpolating solution among the many. A by now established line…
Continual learning can incrementally absorb new concepts without interfering with previously learned knowledge. Motivated by the characteristics of neural networks, in which information is stored in weights on connections, we investigated…
Feedforward neural networks with random hidden nodes suffer from a problem with the generation of random weights and biases as these are difficult to set optimally to obtain a good projection space. Typically, random parameters are drawn…
Intriguing empirical evidence exists that deep learning can work well with exoticschedules for varying the learning rate. This paper suggests that the phenomenon may be due to Batch Normalization or BN, which is ubiquitous and provides…
Neuron death is a complex phenomenon with implications for model trainability: the deeper the network, the lower the probability of finding a valid initialization. In this work, we derive both upper and lower bounds on the probability that…
Using multiple input streams simultaneously to train multimodal neural networks is intuitively advantageous but practically challenging. A key challenge is unimodal bias, where a network overly relies on one modality and ignores others…
The deep learning literature is continuously updated with new architectures and training techniques. However, weight initialization is overlooked by most recent research, despite some intriguing findings regarding random weights. On the…
Binary neural networks improve computationally efficiency of deep models with a large margin. However, there is still a performance gap between a successful full-precision training and binary training. We bring some insights about why this…
We introduce exact macroscopic on-line learning dynamics of two-layer neural networks with ReLU units in the form of a system of differential equations, using techniques borrowed from statistical physics. For the first experiments,…
Residual neural networks are state-of-the-art deep learning models. Their continuous-depth analog, neural ordinary differential equations (ODEs), are also widely used. Despite their success, the link between the discrete and continuous…
This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop…
Deep ResNets are recognized for achieving state-of-the-art results in complex machine learning tasks. However, the remarkable performance of these architectures relies on a training procedure that needs to be carefully crafted to avoid…
In recent years, deep learning has made remarkable progress in a wide range of domains, with a particularly notable impact on natural language processing tasks. One of the challenges associated with training deep neural networks in the…
In deep learning, it is common to use more network parameters than training points. In such scenarioof over-parameterization, there are usually multiple networks that achieve zero training error so that thetraining algorithm induces an…
In this paper, we first identify activation shift, a simple but remarkable phenomenon in a neural network in which the preactivation value of a neuron has non-zero mean that depends on the angle between the weight vector of the neuron and…
Early exiting is an effective paradigm for improving the inference efficiency of deep networks. By constructing classifiers with varying resource demands (the exits), such networks allow easy samples to be output at early exits, removing…
We develop a general duality between neural networks and compositional kernels, striving towards a better understanding of deep learning. We show that initial representations generated by common random initializations are sufficiently rich…
Deep neural networks have attained remarkable success across diverse classification tasks. Recent empirical studies have shown that deep networks learn features that are linearly separable across classes. However, these findings often lack…