Related papers: Spherical perceptron as a storage memory with limi…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage…
It is shown that nested polar codes achieve the Shannon rate-distortion function for arbitrary (binary or non-binary) discrete memoryless sources and the Shannon capacity of arbitrary discrete memoryless channels.
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…
Reservoir computing is a machine learning paradigm that uses a high-dimensional dynamical system, or \emph{reservoir}, to approximate and predict time series data. The scale, speed and power usage of reservoir computers could be enhanced by…
Generation and prediction of time series is analyzed for the case of a Bit-Generator: a perceptron where in each time step the input units are shifted one bit to the right with the state of the leftmost input unit set equal to the output…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
Neural networks deliver impressive predictive performance across a variety of tasks, but they are often opaque in their decision-making processes. Despite a growing interest in mechanistic interpretability, tools for systematically…
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces…
This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…
Actual realisations of EPR experiments do {\em not} demonstrate non-locality. A model is presented that should enable non-specialists as well as specialists to understand how easy it is to find realistic explanations for the observations.…
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…
Reservoir computing promises a fast method for handling large amounts of temporal data. This hinges on constructing a good reservoir--a dynamical system capable of transforming inputs into a high-dimensional representation while remembering…
Although photons are robust, room-temperature carriers well suited to quantum machine learning, the absence of photon-photon interactions hinder the realization of memory functionalities that are critical for capturing long-range context.…
Phenomenon of stochastic separability was revealed and used in machine learning to correct errors of Artificial Intelligence (AI) systems and analyze AI instabilities. In high-dimensional datasets under broad assumptions each point can be…
The historical significance of the Stern-Gerlach experiment lies in its provision of the initial evidence for space quantization. Over time, its sequential form has evolved into an elegant paradigm that effectively illustrates the…
The weight space of the Ising perceptron in which a set of random patterns is stored is examined using the generating function of the partition function $\phi(n)=(1/N)\log [Z^n]$ as the dimension of the weight vector $N$ tends to infinity,…
Prior studies have shown that the retention time of the non-volatile spin-transfer torque RAM (STT-RAM) can be relaxed in order to reduce STT-RAM's write energy and latency. However, since different applications may require different…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms…