Related papers: Interval Translation Maps with Weakly Mixing Attra…
Intermittent maps of the interval are simple and widely-studied models for chaos with slow mixing rates, but have been notoriously resistant to numerical study. In this paper we present an effective framework to compute many ergodic…
We consider binary spatially coupled (SC) low density measurement matrices for low complexity reconstruction of sparse signals via the interval passing algorithm (IPA). The IPA is known to fail due to the presence of harmful sub-structures…
This paper utilizes well-designed item-item path modelling between consecutive items with attention mechanisms to sequentially model dynamic user-item evolutions on dynamic knowledge graph for explainable recommendations. Compared with…
A chaotic attractor is usually characterised by its multifractal spectrum which gives a geometric measure of its complexity. Here we present a characterisation using a minimal set of independant parameters which are uniquely determined by…
We study the asymptotic dynamics of piecewise contracting maps defined on a compact interval. For maps that are not necessarily injective, but have a finite number of local extrema and discontinuity points, we prove the existence of a…
Understanding how information propagates through Transformer models is a key challenge for interpretability. In this work, we study the effects of minimal token perturbations on the embedding space. In our experiments, we analyze the…
This text is an introduction to the author's cohomological approach, based on Hodge theory, to (effective) unique ergodicity and weak mixing of translation flows. Compared to earlier expositions, it emphasizes the analogy between the two…
We study a class of interval translation mappings introduced by Bruin and Troubetzkoy, describing a new renormalization scheme, inspired by the classical Rauzy induction for this class. We construct a measure, invariant under the…
Slow adaption processes, like synaptic and intrinsic plasticity, abound in the brain and shape the landscape for the neural dynamics occurring on substantially faster timescales. At any given time the network is characterized by a set of…
This paper introduces the class of "strongly endotactic networks", a subclass of the endotactic networks introduced by G. Craciun, F. Nazarov, and C. Pantea. The main result states that the global attractor conjecture holds for…
The influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics. Because influence matrices retain information only about the effective bath seen by local observables, they are expected to be…
In this note, continuous transitive maps $f$ on the interval $I$ are re-addressed, where $I$ denotes one of the intervals: $(-\infty, \infty)$, $(-\infty, a]$, $[b, \infty)$, $[a, b]$, where $a < b$ are real numbers. Such maps must have a…
For a finite group $G$, $G$-transfer systems are combinatorial objects which encode the homotopy category of $G$-$N_\infty$ operads, whose algebras in $G$-spectra are $E_\infty$ $G$-spectra with a specified collection of multiplicative…
Small perturbations in the input can severely distort intermediate representations and thus impact translation quality of neural machine translation (NMT) models. In this paper, we propose to improve the robustness of NMT models with…
We develop a definition of rate-induced tipping (R-tipping) in discrete-time dynamical systems (maps) and prove results giving conditions under which R-tipping will or will not happen. Specifically, we study (possibly non-invertible) maps…
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
Temporal gates play a significant role in modern recurrent-based neural encoders, enabling fine-grained control over recursive compositional operations over time. In recurrent models such as the long short-term memory (LSTM), temporal gates…
We introduce new models of very weakly coupled logistic and tent maps for which orbits of very long period are found. The length of these periods is far greater than one billion. The property of these models relatively to the distribution…
We consider the Ising model with inverse temperature beta and without external field on sequences of graphs G_n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weak converges to the…
The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one…