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Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the…
Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…
Few-shot fine-grained visual categorization (FS-FGVC) focuses on identifying various subcategories within a common superclass given just one or few support examples. Most existing methods aim to boost classification accuracy by enriching…
Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the pre-selection and the post-selection should…
We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight…
Standard weak measurement (SWM) has been proved to be a useful ingredient for measuring small longitudinal phase shifts. [Phys. Rev. Lett. 111, 033604 (2013)]. In this letter, we show that with specfic pre-coupling and postselection,…
Transformer has been very successful in various computer vision tasks and understanding the working mechanism of transformer is important. As touchstones, weakly-supervised semantic segmentation (WSSS) and class activation map (CAM) are…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
Intravoxel incoherent motion (IVIM) imaging allows contrast-agent free in vivo perfusion quantification with magnetic resonance imaging (MRI). However, its use is limited by typically low accuracy due to low signal-to-noise ratio (SNR) at…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
In this work, using Moreau envelopes, we define a complete metric for the set of proper lower semicontinuous convex functions. Under this metric, the convergence of each sequence of convex functions is epi-convergence. We show that the set…
The stellar initial mass function (IMF) describes the distribution of stellar masses that form in a given star formation event. The long main-sequence lifetimes of low-mass stars mean that the IMF in this regime (below $\sim 1…
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…
When proxies (external instruments) used to identify target structural shocks are weak, inference in proxy-SVARs (SVAR-IVs) is nonstandard and the construction of asymptotically valid confidence sets for the impulse responses of interest…
The rapid development of deep learning has driven significant progress in image semantic segmentation - a fundamental task in computer vision. Semantic segmentation algorithms often depend on the availability of pixel-level labels (i.e.,…
Low-rank inducing unitarily invariant norms have been introduced to convexify problems with low-rank/sparsity constraint. They are the convex envelope of a unitary invariant norm and the indicator function of an upper bounding rank…
We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \; \{f(Ax) + h(x)\}.\] As Bach showed in [{\em SIAM J. Optim.},…
[abridged] We aim to constrain the stellar initial mass function (IMF) during the epoch of reionization. To this purpose, we build up a semi-empirical model for the reionization history of the Universe, based on various ingredients: the…
In this paper we discuss how to define an appropriate notion of weak topology in the Wasserstein space $(\mathcal{P}_2(H),W_2)$ of Borel probability measures with finite quadratic moment on a separable Hilbert space $H$. We will show that…
We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for…