Thegraphkernelfunction can be utilized toclassify graphs via standard kernel methods such assupport vector machines or k-nearest neighbors.

Converting an n-dimensional vector to a probability distribution over n objects isacommonly used component inmanymachine learning tasks likemulticlass classification,multilabelclassification,attentionmechanismsetc.

However, data annotation for training MLC models becomes much more labor-intensive due to the correlated (hence non-exclusive) labels and a potentially large and sparse label space.

Artificial intelligence (AI) systems in high-stakes domains raise concerns about proxy discrimination, unfairness, and explainability. Existing audits often fail to reveal why unfairness arises, particularly when rooted in structural bias. We propose a novel framework using formal abductive explanations to explain proxy discrimination in individual AI decisions. Leveraging background knowledge, our method identifies which features act as unjustified proxies for protected attributes, revealing hidden structural biases. Central to our approach is the concept of aptitude, a task-relevant property independent of group membership, with a mapping function aligning individuals of equivalent aptitude across groups to assess fairness substantively. As a proof of concept, we showcase the framework with examples taken from the German credit dataset, demonstrating its applicability in real-world cases.

Learning accurate prior knowledge of natural images is of great importance for single image super-resolution (SR).

We present LangToMo, a vision-language-action framework structured as a dual-system architecture that uses pixel motion forecasts as intermediate representations. Our high-level System 2, an image diffusion model, generates text-conditioned pixel motion sequences from a single frame to guide robot control. Pixel motion-a universal, interpretable, and motion-centric representation-can be extracted from videos in a weakly-supervised manner, enabling diffusion model training on any video-caption data. Treating generated pixel motion as learned universal representations, our low level System 1 module translates these into robot actions via motion-to-action mapping functions, which can be either hand-crafted or learned with minimal supervision. System 2 operates as a high-level policy applied at sparse temporal intervals, while System 1 acts as a low-level policy at dense temporal intervals. This hierarchical decoupling enables flexible, scalable, and generalizable robot control under both unsupervised and supervised settings, bridging the gap between language, motion, and action. Checkout https://kahnchana.github.io/LangToMo

Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory, statistical inference, and modern machine learning, including deep learning and large language models. By analyzing how techniques such as maximum likelihood estimation, Bayesian inference, and attention mechanisms address uncertainty, the paper illustrates that many AI methods are rooted in shared probabilistic principles. Through illustrative scenarios including system identification, image classification, and language generation, we show how increasingly complex models build upon these foundations to tackle practical challenges like overfitting, data sparsity, and interpretability. In other words, the work demonstrates that maximum likelihood, MAP estimation, Bayesian classification, and deep learning all represent different facets of a shared goal: inferring hidden causes from noisy and/or biased observations. It serves as both a theoretical synthesis and a practical guide for students and researchers navigating the evolving landscape of machine learning.