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Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula's structural…

Generalized circuits are an important tool in the study of the computational complexity of equilibrium approximation problems. However, in this paper, we reveal that they have a conceptual flaw, namely that the solution concept is not…

Efficiency and safety of Large Language Models (LLMs), among other factors, rely on the quality of tokenization. A good tokenizer not only improves inference speed and language understanding but also provides extra defense against jailbreak…

We consider the problem of image representation for the tasks of unsupervised learning and semi-supervised learning. In those learning tasks, the raw image vectors may not provide enough representation for their intrinsic structures due to…

We describe an algorithm for proving termination of programs abstracted to systems of monotonicity constraints in the integer domain. Monotonicity constraints are a non-trivial extension of the well-known size-change termination method.…

Neural text classification models typically treat output labels as categorical variables which lack description and semantics. This forces their parametrization to be dependent on the label set size, and, hence, they are unable to scale to…

Constraint satisfaction or optimisation models -- even if they are formulated in high-level modelling languages -- need to be reduced into an equivalent format before they can be solved by the use of Quantum Computing. In this paper we show…

Tokenizers are crucial for encoding information in Large Language Models, but their development has recently stagnated, and they contain inherent weaknesses. Major limitations include computational overhead, ineffective vocabulary use, and…

Recovering a globally accurate complex physics field from limited sensor is critical to the measurement and control in the aerospace engineering. General reconstruction methods for recovering the field, especially the deep learning with…

Classical planning problems are typically defined using lifted first-order representations, which offer compactness and generality. While most planners ground these representations to simplify reasoning, this can cause an exponential blowup…

Tokenizers act as a bridge between human language and the latent space of language models, influencing how language is represented in these models. Due to the immense popularity of English-Centric Large Language Models (LLMs), efforts are…

In the present paper, some aspects of the finite-dimensional theory of set-inclusive generalized equations are studied. Set-inclusive generalized equations are problems arising in several contexts of optimization and variational analysis,…

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…

The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…

Stickers have become a popular form of visual communication, yet understanding their semantic relationships remains challenging due to their highly diverse and symbolic content. In this work, we formally {define the Sticker Semantic…

Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…

Autoencoder-based learning has emerged as a staple for disciplining representations in unsupervised and semi-supervised settings. This paper analyzes a framework for improving generalization in a purely supervised setting, where the target…

Tokenization is a fundamental component of language models for code. It involves breaking down the input into units that are later passed to the language model stack to learn high-dimensional representations used in various contexts, from…

This paper presents Z-Code++, a new pre-trained language model optimized for abstractive text summarization. The model extends the state of the art encoder-decoder model using three techniques. First, we use a two-phase pre-training process…

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…