Related papers: Dynamical Sampling for Shift-preserving Operators
This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of…
Task vectors capture how a model changes during fine-tuning by recording the difference between pre-trained and task-specific weights. The composition of task vectors, a key operator in task arithmetic, enables models to integrate knowledge…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
Multiplicatively invariant (MI) spaces are closed subspaces of $L^2(\Omega,\mathcal{H})$ that are invariant under multiplications of (some) functions in $L^{\infty}(\Omega)$. In this paper we work with MI spaces that are finitely generated.…
Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at…
In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…
In this article we develop a general technique which takes a known characterization of a property for weighted backward shifts and lifts it up to a characterization of that property for a large class of operators on $L^p(X)$. We call these…
We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
The video generation task can be formulated as a prediction of future video frames given some past frames. Recent generative models for videos face the problem of high computational requirements. Some models require up to 512 Tensor…
We present an operator learning approach for a class of evolution operators using a composition of a learned lift into the space of diffeomorphisms of the domain and the group action on the field space. In turn, this transforms the…
We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We…
We study translation preserving operators, that is operators commuting with translations by a closed subgroup of a locally compact abelian group. We show that there is a one to one correspondence between these operators and range operators.…
We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a…
Many video workflows benefit from a mixture of user controls with varying granularity, from exact 4D object trajectories and camera paths to coarse text prompts, while existing video generative models are typically trained for fixed input…
We consider a class of step skew product systems of interval diffeomorphisms over shift operators, as a means to study random compositions of interval diffeomorphisms. The class is chosen to present in a simplified setting intriguing…
We formulate the inverse problem in a Bayesian framework and aim to train a generative model that allows us to simulate (i.e., sample from the likelihood) and do inference (i.e., sample from the posterior). We review the use of triangular…
Dynamical Sampling of frames and tensor products are important topics in harmonic analysis. This paper combines the concepts of dynamical sampling of frames and the Carleson condition in the tensor product of Hardy spaces. Initially we…
In most of the transfer learning approaches to reinforcement learning (RL) the distribution over the tasks is assumed to be stationary. Therefore, the target and source tasks are i.i.d. samples of the same distribution. In the context of…