Related papers: Symbolic Generation and Modular Embedding of High-…
Using ultrafilter techniques we show that in any partition of $\mathbb{N}$ into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind $a,b,a^b$ (with $a,b>1$). Also, we will show that any…
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
Induced representations of $\ast$-algebras by unbounded operators in Hilbert space are investigated. Conditional expectations of a $\ast$-algebra $\cA$ onto a unital $\ast$-subalgebra $\cB$ are introduced and used to define inner products…
For a PI-algebra R over a field of characteristic 0 let T(R) be the T-ideal of the polynomial identities of R and let c(R,t) be the codimension series of R (i.e., the generating function of the codimension sequence of R). Let A, B and R be…
We continue our work (started in ``Multiplicity-free representations of algebraic groups", arXiv:2101.04476), on the program of classifying triples $(X,Y,V)$, where $X,Y$ are simple algebraic groups over an algebraically closed field of…
Like the letters in the alphabet forming words, reusing components of a heterogeneous mixture is an efficient strategy for assembling a large number of target structures. Examples range from synthetic DNA origami to proteins self-assembling…
As machine learning models increase in scale and complexity, obtaining sufficient training data has become a critical bottleneck due to acquisition costs, privacy constraints, and data scarcity in specialised domains. While synthetic data…
Pretrained language models (LMs) are prone to arithmetic errors. Existing work showed limited success in probing numeric values from models' representations, indicating that these errors can be attributed to the inherent unreliability of…
We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps. Models achieve high accuracy even with very small…
We sketch a simplification of proofs of old results on the arithmeticity of the group generated by opposing integral unipotent radicals in higher rank arithmetic groups
This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic…
Extrinsic faulting has been discussed previously within the so called difference method and random walk calculation. In this contribution is revisited under the framework of computational mechanics, which allows to derive expressions for…
The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly not just via their n-tupel distributions. The generalized analysis of many…
Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the…
The unprecedented performance achieved by deep convolutional neural networks for image classification is linked primarily to their ability of capturing rich structural features at various layers within networks. Here we design a series of…
Generating primes is a fundamental problem in modern cryptography. Deterministic primality tests work well for special integers such as Mersenne or Proth primes, but these forms are quite restrictive. In this paper, we give a direct method…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
In this chapter we take a closer look at the distribution of symbolic regression models generated by genetic programming in the search space. The motivation for this work is to improve the search for well-fitting symbolic regression models…
Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I. It is shown that the minimal generators of Rs(I) are in one to one correspondence with…
In this paper, we discuss the generation of symbols (and alphabets) based on specific user requirements (medium, priorities, type of information that needs to be conveyed). A framework for the generation of alphabets is proposed, and its…