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While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
To drive progress in science and engineering, large language models (LLMs) must be able to process large amounts of numerical data and solve long calculations efficiently. This is currently only possible through the use of external tools or…
Numerical analysis has no satisfactory method for the more realistic optimization models. However, with constraint programming one can compute a cover for the solution set to arbitrarily close approximation. Because the use of constraint…
Dealing with the shear size and complexity of today's massive data sets requires computational platforms that can analyze data in a parallelized and distributed fashion. A major bottleneck that arises in such modern distributed computing…
As a blockchain platform that has developed vigorously in recent years, Ethereum is different from Bitcoin in that it introduces smart contracts into blockchain.Solidity is one of the most mature and widely used smart contract programming…
Stochastic constraints, which incorporate both deterministic parameters and random variables, extend classical deterministic constraints by explicitly accounting for uncertainty. These constraints are increasingly prevalent in data science,…
Large Language Models (LLMs) as stochastic systems may generate numbers that deviate from available data, a failure known as \emph{numeric hallucination}. Existing safeguards -- retrieval-augmented generation, citations, and uncertainty…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Researchers in answer set programming and constraint programming have spent significant efforts in the development of hybrid languages and solving algorithms combining the strengths of these traditionally separate fields. These efforts…
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical representations, where the integer appears as an explicit…
Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…
We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…
Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…
Training Large Language Models (LLMs) for chain-of-thought reasoning presents a significant challenge: supervised fine-tuning on a single "golden" rationale hurts generalization as it penalizes equally valid alternatives, whereas…
Recent studies in neuro-symbolic learning have explored the integration of logical knowledge into deep learning via encoding logical constraints as an additional loss function. However, existing approaches tend to vacuously satisfy logical…
Identifying robust designs for multi-energy systems is computationally challenging. As rigorous approaches are often computationally intractable, heuristics are employed to generate candidate designs. One example is the feasibility…
Structured output prediction problems (e.g., sequential tagging, hierarchical multi-class classification) often involve constraints over the output label space. These constraints interact with the learned models to filter infeasible…
Automated reasoning and theorem proving have recently become major challenges for machine learning. In other domains, representations that are able to abstract over unimportant transformations, such as abstraction over translations and…
We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1)…
We introduce a notion of \emph{efficient stability} for finite presentations of groups. Informally, a finite presentation using generators $S$ and relations $R$ is \emph{stable} if any map from $S$ to unitaries that approximately satisfies…