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Recovering texture information from the aliasing regions has always been a major challenge for Single Image Super Resolution (SISR) task. These regions are often submerged in noise so that we have to restore texture details while…

The ability of overparameterized deep networks to interpolate noisy data, while at the same time showing good generalization performance, has been recently characterized in terms of the double descent curve for the test error. Common…

The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…

Removing the shape noise from the observed weak lensing field, i.e., denoising, enhances the potential of WL by accessing information at small scales where the shape noise dominates without denoising. We utilise two machine learning (ML)…

Deep networks achieve excellent results on large-scale clean data but degrade significantly when learning from noisy labels. To suppressing the impact of mislabeled data, this paper proposes a conceptually simple yet efficient training…

Sequential memory, the ability to form and accurately recall a sequence of events or stimuli in the correct order, is a fundamental prerequisite for biological and artificial intelligence as it underpins numerous cognitive functions (e.g.,…

We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…

Dictionary learning consists of finding a sparse representation from noisy data and is a common way to encode data-driven prior knowledge on signals. Alternating minimization (AM) is standard for the underlying optimization, where gradient…

We consider the problem of training a neural network to store a set of patterns with maximal noise robustness. A solution, in terms of optimal weights and state update rules, is derived by training each individual neuron to perform either…

We consider a three-layer Sejnowski machine and show that features learnt via contrastive divergence have a dual representation as patterns in a dense associative memory of order P=4. The latter is known to be able to Hebbian-store an…

A critical bottleneck of massive multiple-input multiple-output (MIMO) system is the huge training overhead caused by downlink transmission, like channel estimation, downlink beamforming and covariance observation. In this paper, we propose…

The problem of learning structural equation models (SEMs) from data is a fundamental problem in causal inference. We develop a new algorithm --- which is computationally and statistically efficient and works in the high-dimensional regime…

Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…

We study the problem of learning associative memory -- a system which is able to retrieve a remembered pattern based on its distorted or incomplete version. Attractor networks provide a sound model of associative memory: patterns are stored…

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…

Auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription) serve as a foundational framework for pattern recognition and associative memory in statistical mechanics. However, their…

While Magnetic Resonance Imaging (MRI) has played an essential role in infant brain analysis, segmenting MRI into a number of tissues such as gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) is crucial and complex due to…

A central goal in deep learning is to learn compact representations of features at every layer of a neural network, which is useful for both unsupervised representation learning and structured network pruning. While there is a growing body…

In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…

The generative process of Diffusion Models (DMs) has recently set state-of-the-art on many AI generation benchmarks. Though the generative process is traditionally understood as an "iterative denoiser", there is no universally accepted…