Related papers: Not All Multi-Valued Partial CFL Functions Are Ref…
Connected component analysis (CCA) has been heavily used to label binary images and classify segments. However, it has not been well-exploited to segment multi-valued natural images. This work proposes a novel multi-value segmentation…
This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…
Research on refinable functions in wavelet theory is mostly focused to localized functions. However it is known, that polynomial functions are refinable, too. In our paper we investigate on conversions between refinement masks and…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
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…
A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
Federated learning (FL) is an emerging technique that trains massive and geographically distributed edge data while maintaining privacy. However, FL has inherent challenges in terms of fairness and computational efficiency due to the rising…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
Multiphase ranking functions (M$\Phi$RFs) are tuples $\langle f_1,\ldots,f_d \rangle$ of linear functions that are often used to prove termination of loops in which the computation progresses through a number of "phases". Our work provides…
Algorithms that exploit factored Markov decision processes are far more sample-efficient than factor-agnostic methods, yet they assume a factored representation is known a priori -- a requirement that breaks down when the agent sees only…
Federated Learning (FL) traditionally assumes homogeneous client tasks; however, in real-world scenarios, clients often specialize in diverse tasks, introducing task heterogeneity. To address this challenge, Many-Task FL (MaT-FL) has…
Mechanistic interpretability produces circuit-level causal analyses of neural network behaviour, but discovered circuits often remain isolated experimental artefacts: there is no shared formal representation for what circuits compute, how…
The design of plateaued functions over $GF(2)^n$, also known as 3-valued Walsh spectra functions (taking the values from the set $\{0, \pm 2^{\lceil \frac{n+s}{2} \rceil}\}$), has been commonly approached by specifying a suitable algebraic…
Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs (LNCS, Vol. 4588, Springer, Berlin, 2007, pp. 60-71), and they showed that multi-letter QFAs can accept with…
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
Polyregular functions are the class of string-to-string functions definable by pebble transducers, an extension of finite-state automata with outputs and multiple two-way reading heads (pebbles) with a stack discipline. If a polyregular…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Continual Federated Learning (CFL) combines Federated Learning (FL), the decentralized learning of a central model on a number of client devices that may not communicate their data, and Continual Learning (CL), the learning of a model from…