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The global economy relies on the flow of goods over supply chain networks, with nodes as firms and edges as transactions between firms. While we may observe these external transactions, they are governed by unseen production functions,…

Visual interpretability of Convolutional Neural Networks (CNNs) has gained significant popularity because of the great challenges that CNN complexity imposes to understanding their inner workings. Although many techniques have been proposed…

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…

We propose a new training method for a feedforward neural network having the activation functions with the geometric contraction property. The method consists of constructing a new functional that is less nonlinear in comparison with the…

Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…

Recurrent neural networks and sequence to sequence models require a predetermined length for prediction output length. Our model addresses this by allowing the network to predict a variable length output in inference. A new loss function…

We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these…

How do humans and animals perform trial-and-error learning when the space of possibilities is infinite? In a previous study, we used an interval timing production task and discovered an updating strategy in which the agent adjusted the…

Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…

Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually…

Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…

Loss function learning is a new meta-learning paradigm that aims to automate the essential task of designing a loss function for a machine learning model. Existing techniques for loss function learning have shown promising results, often…

Value function learning plays a central role in many state-of-the-art reinforcement-learning algorithms. Many popular algorithms like Q-learning do not optimize any objective function, but are fixed-point iterations of some variant of…

Cross entropy loss has served as the main objective function for classification-based tasks. Widely deployed for learning neural network classifiers, it shows both effectiveness and a probabilistic interpretation. Recently, after the…

Most of mathematic forgetting curve models fit well with the forgetting data under the learning condition of one time rather than repeated. In the paper, a convolution model of forgetting curve is proposed to simulate the memory process…

Dual-process theories play a central role in both psychology and neuroscience, figuring prominently in fields ranging from executive control to reward-based learning to judgment and decision making. In each of these domains, two mechanisms…

Given a valued graph, where both the nodes and the edges of the graph are associated with one or several values, any network function for a given node must be defined in terms of that node and its connected nodes in the graph. Generally,…

Neural networks used for multi-interaction trajectory reconstruction lack the ability to estimate the uncertainty in their outputs, which would be useful to better analyse and understand the systems they model. In this paper we extend the…

Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can…

Theoretical understanding of deep learning remains elusive despite its empirical success. In this study, we propose a novel "synaptic field theory" that describes the training dynamics of synaptic weights and biases in the continuum limit.…