Related papers: Pebble-Depth
We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
In Heintz-Schnorr (1982), the authors introduced the notion of correct test sequence and since then it has been widely used to design probabilistic algorithms for Polynomial Equality Test. The aim of this manuscript is to study the…
We analyse the size evolution of pebbles accreted into the gaseous envelope of a protoplanet growing in a protoplanetary disc, taking into account collisions driven by the relative sedimentation speed as well as the convective gas motion.…
Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we investigated this question for deep ReLU networks with a…
Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…
Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the…
When a fluid is constrained to a fixed, finite volume, the conditions for liquid-vapor equilibrium are different from the infinite volume or constant pressure cases. There is even a range of densities for which no bubble can form, and the…
Recent works have indicated redundancy across transformer blocks, prompting the research of depth compression to prune less crucial blocks. However, current ways of entire-block pruning suffer from risks of discarding meaningful cues…
Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order,…
We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a…
In this work, we build a generic architecture of Convolutional Neural Networks to discover empirical properties of neural networks. Our first contribution is to introduce a state-of-the-art framework that depends upon few hyper parameters…
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…
Embeddings are functions that map raw input data to low-dimensional vector representations, while preserving important semantic information about the inputs. Pre-training embeddings on a large amount of unlabeled data and fine-tuning them…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
Entanglement depth characterizes the minimal number of particles in a system that are mutually entangled. For symmetric states, we show that there is a dichotomy for entanglement depth: an $N$-particle symmetric state is either fully…
Let L be a link in the 3-sphere that is in thin position but not in bridge position and let P be a thin level sphere. We generalize a result of Wu by giving a bound on the number of disjoint irreducible compressing disks that P can have,…
Within the coexistence region between liquid and vapor the equilibrium pressure of a simulated fluid exhibits characteristic jumps and plateaus when plotted as a function of density at constant temperature. These features exclusively…
We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the…
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…