Related papers: Non-Archimedean analysis, T-functions, and cryptog…
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…
We continue the study of communication cost of computing functions when inputs are distributed among $k$ processors, each of which is located at one vertex of a network/graph called a terminal. Every other node of the network also has a…
Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…
We present a unified heterogeneous computing framework for real-time time-dependent density functional theory (RT-TDDFT) based on numerical atomic orbitals (NAOs), implemented in the ABACUS package. We introduce three co-designed…
In this paper, we study the relationship between algebraic manipulation detection (AMD) codes and highly nonlinear functions. As applications, on one hand, a generic construction for systematic AMD codes is introduced based on highly…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
Many modern solvers and program analyzers rely on non-monotone reasoning (e.g. negation-as-failure, speculative updates, backtracking) for which classical monotone fixed-point methods do not apply. The general problem of finding the fixed…
How can we find patterns and anomalies in a tensor, or multi-dimensional array, in an efficient and directly interpretable way? How can we do this in an online environment, where a new tensor arrives each time step? Finding patterns and…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Large-scale diffusion models have achieved state-of-the-art results on text-to-image synthesis (T2I) tasks. Despite their ability to generate high-quality yet creative images, we observe that attribution-binding and compositional…
cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exist many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash…
Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way…
Recent deep learning-based methods for lossy image compression achieve competitive rate-distortion performance through extensive end-to-end training and advanced architectures. However, emerging applications increasingly prioritize semantic…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
Predicting vulnerable source code helps to focus attention on those parts of the code that need to be examined with more scrutiny. Recent work proposed the use of function names as semantic cues that can be learned by a deep neural network…
Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…