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One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…

The ultimate goal of all optimization methods is to solve real-world problems. For a successful project execution, knowledge about optimization and the application has to be pooled. As it is too inefficient to highly train one person in…

In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…

Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify…

Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…

We present a method for storing multiple models within a single set of parameters. Models can coexist in superposition and still be retrieved individually. In experiments with neural networks, we show that a surprisingly large number of…

Optimal control and sequential decision making are widely used in many complex tasks. Optimal control over a sequence of natural images is a first step towards understanding the role of vision in control. Here, we formalize this problem as…

Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…

Large language models (LLMs) have the potential to revolutionize how we design and implement compilers and code translation tools. However, existing LLMs struggle to handle long and complex programs. We introduce LEGO-Compiler, a novel…

New information technologies provide a lot of prospects for performance improvement. One of them is "Dynamic Source Code Generation and Compilation". This article shows how this way provides high performance for engineering problems.

What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…

A sup-interpretation is a tool which provides an upper bound on the size of a value computed by some symbol of a program. Sup-interpretations have shown their interest to deal with the complexity of first order functional programs. For…

The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…

Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into…

In high performance domains like image processing, physics simulation or machine learning, program performance is critical. Programmers called performance engineers are responsible for the challenging task of optimising programs. Two major…

Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…

Model merging has emerged as an efficient method to combine multiple single-task fine-tuned models. The merged model can enjoy multi-task capabilities without expensive training. While promising, merging into a single model often suffers…

Recent large-scale generative models learned on big data are capable of synthesizing incredible images yet suffer from limited controllability. This work offers a new generation paradigm that allows flexible control of the output image,…

Instruction tuning plays a pivotal role in Code Large Language Models (Code LLMs) for the task of program synthesis. Presently, two dominant paradigms for collecting tuning data are natural-instruct (human-written) and self-instruct…