We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

Very little is known about the cost landscape for parametrized Quantum Circuits (PQCs). Nevertheless, PQCs are employed in Quantum Neural Networks and Variational Quantum Algorithms, which may allow for near-term quantum advantage. Such applications require good optimizers to train PQCs. Recent works have focused on quantum-aware optimizers specifically tailored for PQCs. However, ignorance of the cost landscape could hinder progress towards such optimizers. In this work, we analytically prove two results for PQCs: (1) We find an exponentially large symmetry in PQCs, yielding an exponentially large degeneracy of the minima in the cost landscape. (2) We show that noise (specifically non-unital noise) can break these symmetries and lift the degeneracy of minima, making many of them local minima instead of global minima. Based on these results, we introduce an optimization method called Symmetry-based Minima Hopping (SYMH), which exploits the underlying symmetries in PQCs to hop between local minima in the cost landscape. The versatility of SYMH allows it to be combined with local optimizers (e.g., gradient descent) with minimal overhead. Our numerical simulations show that SYMH improves the overall optimizer performance.

Handwritten Digit Recognition is an interesting machine learning problem in which we have to identify the handwritten digits through various classification algorithms. There are a number of ways and algorithms to recognize handwritten digits, including Deep Learning/CNN, SVM, Gaussian Naive Bayes, KNN, Decision Trees, Random Forests, etc. In this article, we will deploy a variety of machine learning algorithms from the Sklearn's library on our dataset to classify the digits into their categories. We will use Sklearn's load_digits dataset, which is a collection of 8x8 images (64 features)of digits. The dataset contains a total of 1797 sample points.

This article was published as a part of the Data Science Blogathon. Many times we have come across this statement – Lasso regression causes sparsity while Ridge regression doesn't! But I'm pretty sure that most of us might not have understood how exactly this works. Let's try to understand this using calculus. First, let's understand what sparsity is.

Linear Regression is one of the most fundamental algorithms used to model relationships between a dependent variable and one or more independent variables. In simpler terms, it involves finding the'line of best fit' that represents two or more variables. The line of best fit is found by minimizing the squared distances between the points and the line of best fit -- this is known as minimizing the sum of squared residuals. A residual is simply equal to the predicted value minus the actual value. In case it doesn't make sense yet, consider the image above.

Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of stochastic ordinary differential equations. A solution to these equations is the joint probability density function (PDF) of neuron states. It can be used to calculate such information-theoretic quantities as the mutual information between the stochastic stimulus and various internal states of the neuron (e.g., membrane potential), as well as various spiking statistics. When random excitations are modeled as Gaussian white noise, the joint PDF of neuron states satisfies exactly a Fokker-Planck equation. However, most biologically plausible noise sources are correlated (colored). In this case, the resulting PDF equations require a closure approximation. We propose two methods for closing such equations: a modified nonlocal large-eddy-diffusivity closure and a data-driven closure relying on sparse regression to learn relevant features. The closures are tested for stochastic leaky integrate-and-fire (LIF) and FitzHugh-Nagumo (FHN) neurons driven by sine-Wiener noise. Mutual information and total correlation between the random stimulus and the internal states of the neuron are calculated for the FHN neuron.

The wide adaption of 3D point-cloud data in safety-critical applications such as autonomous driving makes adversarial samples a real threat. Existing adversarial attacks on point clouds achieve high success rates but modify a large number of points, which is usually difficult to do in real-life scenarios. In this paper, we explore a family of attacks that only perturb a few points of an input point cloud, and name them nudge attacks. We demonstrate that nudge attacks can successfully flip the results of modern point-cloud DNNs. We present two variants, gradient-based and decision-based, showing their effectiveness in white-box and grey-box scenarios. Our extensive experiments show nudge attacks are effective at generating both targeted and untargeted adversarial point clouds, by changing a few points or even a single point from the entire point-cloud input. We find that with a single point we can reliably thwart predictions in 12--80% of cases, whereas 10 points allow us to further increase this to 37--95%. Finally, we discuss the possible defenses against such attacks, and explore their limitations.

Processing sequential multi-sensor data becomes important in many tasks due to the dramatic increase in the availability of sensors that can acquire sequential data over time. Human Activity Recognition (HAR) is one of the fields which are actively benefiting from this availability. Unlike most of the approaches addressing HAR by considering predefined activity classes, this paper proposes a novel approach to discover the latent HAR patterns in sequential data. To this end, we employed Latent Dirichlet Allocation (LDA), which is initially a topic modelling approach used in text analysis. To make the data suitable for LDA, we extract the so-called "sensory words" from the sequential data. We carried out experiments on a challenging HAR dataset, demonstrating that LDA is capable of uncovering underlying structures in sequential data, which provide a human-understandable representation of the data. The extrinsic evaluations reveal that LDA is capable of accurately clustering HAR data sequences compared to the labelled activities.

Mixed membership community detection is a challenge problem in network analysis. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for short) to estimate the memberships. Mixed-RSC is an extension of the RSC method (Qin and Rohe, 2013) to deal with the mixed membership community detection problem. We show that the algorithm is asymptotically consistent under mild conditions. The approach is successfully applied to a small scale of simulations and substantial empirical networks with encouraging results compared to a number of benchmark methods.