Related papers: Regularization of linear machine learning problems
Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…
We consider the computational complexity of training depth-2 neural networks composed of rectified linear units (ReLUs). We show that, even for the case of a single ReLU, finding a set of weights that minimizes the squared error (even…
Quantized Neural Networks (QNNs) are often used to improve network efficiency during the inference phase, i.e. after the network has been trained. Extensive research in the field suggests many different quantization schemes. Still, the…
Time series prediction is essential for human activities in diverse areas. A common approach to this task is to harness Recurrent Neural Networks (RNNs). However, while their predictions are quite accurate, their learning process is complex…
According to conventional neural network theories, the feature of single-hidden-layer feedforward neural networks(SLFNs) resorts to parameters of the weighted connections and hidden nodes. SLFNs are universal approximators when at least the…
Although weight and activation quantization is an effective approach for Deep Neural Network (DNN) compression and has a lot of potentials to increase inference speed leveraging bit-operations, there is still a noticeable gap in terms of…
Post-training quantization (PTQ) for vision transformers (ViTs) has garnered significant attention due to its efficiency in compressing models. However, existing methods typically overlook the relationship between a well-trained NN and the…
We present QNNRepair, the first method in the literature for repairing quantized neural networks (QNNs). QNNRepair aims to improve the accuracy of a neural network model after quantization. It accepts the full-precision and weight-quantized…
We present a weight similarity measure method that can quantify the weight similarity of non-convex neural networks. To understand the weight similarity of different trained models, we propose to extract the feature representation from the…
Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…
The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…
Linearized shallow neural networks that are constructed by fixing the hidden-layer parameters have recently shown strong performance in solving partial differential equations (PDEs). Such models, widely used in the random feature method…
Recurrent Neural Networks (RNNs) produce state-of-art performance on many machine learning tasks but their demand on resources in terms of memory and computational power are often high. Therefore, there is a great interest in optimizing the…
The success of deep neural networks is in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice, as they improve generalization…
We study the improper learning of multi-layer neural networks. Suppose that the neural network to be learned has $k$ hidden layers and that the $\ell_1$-norm of the incoming weights of any neuron is bounded by $L$. We present a kernel-based…
The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…
We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed…
Linear recurrent neural networks, such as State Space Models (SSMs) and Linear Recurrent Units (LRUs), have recently shown state-of-the-art performance on long sequence modelling benchmarks. Despite their success, their empirical…
We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…