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Interpretable regression models are important for many application domains, as they allow experts to understand relations between variables from sparse data. Symbolic regression addresses this issue by searching the space of all possible…

Differentiable vector graphics have enabled powerful gradient-based optimization of vector primitives directly from raster images. However, existing frameworks formulate this as a flat optimization problem, forcing hundreds to thousands of…

Large transformers are powerful architectures used for self-supervised data analysis across various data types, including protein sequences, images, and text. In these models, the semantic structure of the dataset emerges from a sequence of…

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the…

Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…

Modular reconfigurable manipulators enable quick adaptation and versatility to address different application environments and tailor to the specific requirements of the tasks. Task performance significantly depends on the manipulator's…

This paper pertains to an emerging machine learning paradigm: learning higher-order functions, i.e. functions whose inputs are functions themselves, $\textit{particularly when these inputs are Neural Networks (NNs)}$. With the growing…

The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…

The usage-based constructionist (UCx) approach to language posits that language comprises a network of learned form-meaning pairings (constructions) whose use is largely determined by their meanings or functions, requiring them to be graded…

The practical deployment of learning-based autonomous systems would greatly benefit from tools that flexibly obtain safety guarantees in the form of certificate functions from data. While the geometrical properties of such certificate…

This paper introduces a new mapping of geometrical transformation on the MorphoSys (M1) reconfigurable computing (RC) system. New mapping techniques for some linear algebraic functions are recalled. A new mapping for geometrical…

This paper proposes a novel learning architecture for acquiring generalizable high-level symbolic skills from a few unlabeled low-level skill trajectory demonstrations. The architecture involves neural networks for symbol discovery and…

The transformer architecture has demonstrated remarkable capabilities in modern artificial intelligence, among which the capability of implicitly learning an internal model during inference time is widely believed to play a key role in the…

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The…

Gradient boosting still dominates Transformers on tabular benchmarks. Our tokenizer uses a deliberately simplistic discretized vocabulary so we can highlight how even basic tokenization unlocks the power of attention on tabular features,…

The convergence rate of various first-order optimization algorithms is a pivotal concern within the numerical optimization community, as it directly reflects the efficiency of these algorithms across different optimization problems. Our…

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of…

We describe an implementation of gradient boosting and neural guidance of saturation-style automated theorem provers that does not depend on consistent symbol names across problems. For the gradient-boosting guidance, we manually create…

Large language models (LLMs) are increasingly used to complete complex tasks by selecting and coordinating external tools across multiple steps. This requires aligning tool choices with subtask intent while satisfying directional execution…

We derive extrinsic GJMS operators and $Q$-curvatures associated to a submanifold of a conformal manifold. The operators are conformally covariant scalar differential operators on the submanifold with leading part a power of the Laplacian…