We address the problem of denoising data from a Gaussian mixture using a two-layer non-linear autoencoder with tied weights and a skip connection.

Diffusion MRI (dMRI) provides a distinctive means to probe the microstructural architecture of living tissue, facilitating applications such as brain connectivity analysis, modeling across multiple conditions, and the estimation of macrostructural features. Tractography, which emerged in the final years of the 20th century and accelerated in the early 21st century, is a technique for visualizing white matter pathways in the brain using dMRI. Most diffusion tractography methods rely on procedural streamline propagators or global energy minimization methods. Although recent advancements in deep learning have enabled tasks that were previously challenging, existing tractography approaches are often non-differentiable, limiting their integration in end-to-end learning frameworks. While progress has been made in representing streamlines in differentiable frameworks, no existing method offers fully differentiable propagation. In this work, we propose a fully differentiable solution that retains numerical fidelity with a leading streamline algorithm. The key is that our PyTorch-engineered streamline propagator has no components that block gradient flow, making it fully differentiable. We show that our method matches standard propagators while remaining differentiable. By translating streamline propagation into a differentiable PyTorch framework, we enable deeper integration of tractography into deep learning workflows, laying the foundation for a new category of macrostructural reasoning that is not only computationally robust but also scientifically rigorous.

Logic Tensor Networks (LTN) is a Neuro-Symbolic framework that effectively incorporates deep learning and logical reasoning. In particular, LTN allows defining a logical knowledge base and using it as the objective of a neural model. This makes learning by logical reasoning possible as the parameters of the model are optimized by minimizing a loss function composed of a set of logical formulas expressing facts about the learning task. The framework learns via gradient-descent optimization. Fuzzy logic, a relaxation of classical logic permitting continuous truth values in the interval [0,1], makes this learning possible. Specifically, the training of an LTN consists of three steps. Firstly, (1) the training data is used to ground the formulas. Then, (2) the formulas are evaluated, and the loss function is computed. Lastly, (3) the gradients are back-propagated through the logical computational graph, and the weights of the neural model are changed so the knowledge base is maximally satisfied. LTNtorch is the fully documented and tested PyTorch implementation of Logic Tensor Networks. This paper presents the formalization of LTN and how LTNtorch implements it. Moreover, it provides a basic binary classification example.

While effective, the backpropagation (BP) algorithm exhibits limitations in terms of biological plausibility, computational cost, and suitability for online learning. As a result, there has been a growing interest in developing alternative biologically plausible learning approaches that rely on local learning rules. This study focuses on the primarily unsupervised similarity matching (SM) framework, which aligns with observed mechanisms in biological systems and offers online, localized, and biologically plausible algorithms. i) To scale SM to large datasets, we propose an implementation of Convolutional Nonnegative SM using PyTorch. ii) We introduce a localized supervised SM objective reminiscent of canonical correlation analysis, facilitating stacking SM layers. iii) We leverage the PyTorch implementation for pre-training architectures such as LeNet and compare the evaluation of features against BP-trained models. This work combines biologically plausible algorithms with computational efficiency opening multiple avenues for further explorations.

Machine learning techniques have a long history of success in denoising tasks. The recent breakthrough of diffusionbased generation [1, 2] has further revived the interest in denoising networks, demonstrating how they can also be leveraged, beyond denoising, for generative tasks. However, this rapidly expanding range of applications stands in sharp contrast to the relatively scarce theoretical understanding of denoising neural networks, even for the simplest instance thereof - namely Denoising Auto Encoders (DAEs) [3]. Theoretical studies of autoencoders have hitherto almost exclusively focused on data compression tasks using Reconstruction Auto Encoders (RAEs), where the goal is to learn a concise latent representation of the data. A majority of this body of work addresses linear autoencoders [4-7]. The authors of [8, 9] analyze the gradient-based training of non-linear autoencoders with online stochastic gradient descent or in population, thus implicitly assuming the availability of an infinite number of training samples. Furthermore, two-layer RAEs were shown to learn to essentially perform Principal Component Analysis (PCA) [10-12], i.e. to learn a linear model. Ref. [13] shows that this is also true for infinite-width architectures. Learning in DAEs has been the object of theoretical investigations only in the linear case [14], while the case of non-linear DAEs remains theoretically largely unexplored.

Sometimes we want to put a threshold function at the output of a layer. This can be for a variety of reasons. One of them is that we want to summarize the activations into binary values. This binarization of activations can be useful in autoencoders. However, thresholding poses a problem during backpropagation. The derivative of threshold functions is zero.

Speech enhancement refers to techniques that aim to reduce distortions and improve one or more perceptual speech qualities. The enhanced speech is expected to be of superior quality with minimal or no noise in it. It is also known as an audio enhancement, denoiser, and noise reduction. Speech enhancement has wide applications including improving the quality of audio processing systems like speech recognition. Several past experiments have shown that this preprocessing has led to improved speech recognition.

A pytorch implementation of the text-to-3D model Dreamfusion, powered by the Stable Diffusion text-to-2D model. This project is a work-in-progress, and contains lots of differences from the paper. Also, many features are still not implemented now. The current generation quality cannot match the results from the original paper, and many prompts still fail badly! Important: To download the Stable Diffusion model checkpoint, you should provide your access token.

Here, the block_args for the first block is altered from'r1_k3_s111_e1_i32_o16_se0.25'