Related papers: On the scaling law for cortical magnification fact…
The sparse coding algorithm has served as a model for early processing in mammalian vision. It has been assumed that the brain uses sparse coding to exploit statistical properties of the sensory stream. We hypothesize that sparse coding…
Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such…
Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A task is usually composite hence can be decomposed into many…
Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists…
A steadily increasing body of evidence suggests that the brain performs probabilistic inference to interpret and respond to sensory input and that trial-to-trial variability in neural activity plays an important role. The neural sampling…
Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…
Theoretical proposals of scaling laws for the differential elastic scattering cross sections of protons are confronted with experimental data over a wide energy range. Different combinations of the transferred momentum and energy resulting…
A simple scaling theory for the sintering of fractal aerogels is presented. The densification at small scales is described by an increase of the lower cut-off length $a$ accompanied by a decrease of the upper cut-off length $\xi$, in order…
This paper presents a novel approach of representing dynamic visual scenes with static maps generated from video/image streams. Such representation allows easy visual assessment of motion in dynamic environments. These maps are 2D matrices…
If modern computers are sometimes superior to humans in some specialized tasks such as playing chess or browsing a large database, they can't beat the efficiency of biological vision for such simple tasks as recognizing and following an…
The flickering of the light of fluorescent lamps (FL), whose basic frequency, 100 Hz, is close to that of the micro-saccadic (the eye-muscles' tremor component) eye movement, is a severe problem for autists (autistic humans), a problem for…
Strong lensing has developed into an important astrophysical tool for probing both cosmology and galaxies (their structure, formation, and evolution). Using the gravitational lensing theory and cluster mass distribution model, we try to…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…
The correlation length $\xi$, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields…
The human nervous system utilizes synaptic plasticity to solve optimization problems. Previous studies have tried to add the plasticity factor to the training process of artificial neural networks, but most of those models require complex…
Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic…
With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here…
Gravitational lensing is the deflection of light rays due to the gravity of intervening masses. This phenomenon is observed in a variety of scales and configurations, involving any non-uniform mass such as planets, stars, galaxies, clusters…
Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…