Related papers: The Filtration of the split-words process
Generalizations of Bell's framework to causal networks have yielded new foundational insights and applications, including the use of interventions to enhance the detection of nonclassicality in scenarios with communication. Such…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…
We consider a discrete-time process adapted to some filtration which lives on a (typically countable) subset of $\mathbb{R}^d$, $d\geq 2$. For this process, we assume that it has uniformly bounded jumps, is uniformly elliptic (can advance…
Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving…
In this paper, we investigate the distillation of time series reasoning capabilities into small, instruction-tuned language models as a step toward building interpretable time series foundation models. Leveraging a synthetic dataset of…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
Can stochastic gradient methods track a moving target? We study the problem of tracking multidimensional time-varying parameters under noisy observations and possible model misspecification. Gradient-based filters update the time-varying…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
A sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last $n$ symbols. If the algorithm is randomized, then at each time instant it produces an incorrect…
In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for…
The separating time for two probability measures on a filtered space is an extended stopping time which captures the phase transition between equivalence and singularity. More specifically, two probability measures are equivalent before…
Word embeddings have been demonstrated to benefit NLP tasks impressively. Yet, there is room for improvement in the vector representations, because current word embeddings typically contain unnecessary information, i.e., noise. We propose…
Large Language Models (LLMs) have recently been shown to produce estimates of psycholinguistic norms, such as valence, arousal, or concreteness, for words and multiword expressions, that correlate with human judgments. These estimates are…
The aim of this paper is to obtain estimates for the density of the law of a specific nonlinear diffusion process at any positive bounded time. This process is issued from kinetic theory and is called Landau process, by analogy with the…
Given a regular language $L$, we study the language of words $\mathsf{D}(L)$, that distinguish between pairs of different left-quotients of $L$. We characterize this distinguishability operation, show that its iteration has always a fixed…
Time-reversal symmetry breaking is a key feature of nearly all natural sounds, caused by the physics of sound production. While attention has been paid to the response of the auditory system to "natural stimuli," very few psychophysical…