Surface electromyography (sEMG) has been commonly used to register the activation of the peripheral nervous system and as part of non-invasive neural interfaces. More specifically, s-EMG has gained attention due to the increasing use of AI-powered human-computer interfaces (HCI) requiring hand gesture recognition (HGR).These interfaces have a range of applications, including the control of extended reality, agile prosthetics, and exoskeletons. However, the natural variability of sEMG among individuals and across multiple days has led researchers to focus on subject-specific and single-day solutions. In this dissertation, we address the robustness challenges of sEMG-based HGR, meaning that we propose and develop HGR systems that can be easily calibrated to be applicable to multiple subjects and across multiple days. We start by considering the subject generalization of sEMG-based HGR and show that by leveraging a common concept in natural language processing (NLP), namely "Embeddings", we can design a HGR system that can be efficiently and accurately calibrated to be used for a new subject with minimal required data. Next, we move on to solve the multiday generalization challenge of sEMG-based inference and use the concept of "Transformers" to facilitate system calibration across multiple days. Inspired by the superior performance of embeddings and transformers for HGR, we extend these models to address the finger kinematics tracking problem. In other words, we re-purpose the Vision Transformer architecture to forecast finger joint angles from 100 ms up to 1.5 seconds ahead of time. We show that our model significantly outperforms state of the art in terms of evaluation metrics and also visual quality of tracking. In this work we also study the theoretical properties of estimation of embeddings in high-dimensions. I.e. , we consider estimating factors of a low-rank matrix when the matrix is observed through a noisy channel with possibly unknown biases. We use a class of approximation algorithms called approximate message passing (AMP) to quantify the accuracy of the estimation in certain high-dimensional limits and show the relations of key parameters of the model. Finally, inspired by the applications of embeddings in sEMG-base inference and noting the data availability challenges of such problems, we analyze the problem of Few Shot Learning, where a few samples of data are used to calibrate a model to a downstream task. We propose a two step estimation framework to apply to such problems and we provide rigorous theoretical analysis for a bilinear model. We show that our proposed framework significantly outperforms a regular baseline training scheme when sufficient data is not available. For future directions of research we propose to investigate the following: (1) addressing the generalization of the joint angles tracking problem to new subjects and across multiple days. (2) Extending our theoretical results to address not only linear and bilinear cases, but also models that include deep neural networks as their components.