Related papers: Intrinsic stationarity for vector quantization: Fo…
We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in…
By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
Vector-quantized networks (VQNs) have exhibited remarkable performance across various tasks, yet they are prone to training instability, which complicates the training process due to the necessity for techniques such as subtle…
We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a…
We present a novel second-order trajectory optimization algorithm based on Stein Variational Newton's Method and Maximum Entropy Differential Dynamic Programming. The proposed algorithm, called Stein Variational Differential Dynamic…
We propose a variation of the classical Hilbert scheme of points - the double nested Hilbert scheme of points - which parametrizes flags of zero-dimensional subschemes whose nesting is dictated by a Young diagram. Over a smooth…
Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing…
The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the…
Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been…
Learned image compression possesses a unique challenge when incorporating non-differentiable quantization into the gradient-based training of the networks. Several quantization surrogates have been proposed to fulfill the training, but they…
High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for…
Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based…
We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an approximate Delaunay graph on the output points. Our…
In this paper we obtain second- and first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints. In the necessary conditions we suppose that the objective…
Neural network quantization is becoming an industry standard to efficiently deploy deep learning models on hardware platforms, such as CPU, GPU, TPU, and FPGAs. However, we observe that the conventional quantization approaches are…
This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties…
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…
We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for…
With the increase of intermittent renewable generation resources feeding into the electrical grid, Distribution System Operators (DSOs) must find ways to incorporate these new actors and adapt the grid to ensure stability and enable…