2 citations · 5 across the 40 of their papers we have counts for
46 papers
Noisy-Label Calibration with Multiple Unreliable Labels
Keisuke Hanada, Futoshi Futami
In medical annotation and crowdsourcing, multiple annotators assign labels to each example, but these labels may be incorrect. Treating such noisy labels as ground truth can bias c…
UCP Extension in Dimension Three
James Tian
We show that every UCP extension problem for a finite dimensional operator system can be reduced to three dimensions after finite matrix amplification. The set of extensions is pre…
Normalized Orbit Frames and Essential Spectrum
James Tian
We characterize the essential spectra of normal operators admitting normalized orbit frames. These are exactly closed subsets of the unit circle with positive Haar measure.
The role of parameter Jacobians in the stability of network outputs
Halyun Jeong, Palle E. T. Jorgensen, Hyun-Kyoung Kwon +2
In the framework of network dynamics, learning models, and neural tangent kernels (NTK), we show that the corresponding linearized dynamics leads naturally to a semigroup formulati…
A finite-Point Schwarz-Pick Inequality
James Tian
We prove a finite-point version of the Schwarz-Pick inequality for holomorphic self-maps of the disk. The estimate compares Bergman Gram matrices built from several points and thei…
Tree Coordinates and Range Martingales for Positive Operator-Valued Measures
James Tian
Positive operator-valued measures on a tree admit intrinsic local coordinates coming from the way each cylinder value splits into its children. We show that these local splittings,…
Compression Covariance and Tangent kernels
James Tian
Let be self-adjoint on a Hilbert space , let , and let be an orthogonal projection. Relative to the decomposition , write \[ T…
Ordered POVMs and Residual Collapse
James Tian
Ordered realizations of discrete POVMs are studied through a residual transform generated by sequential tests. One application of the transform replaces each coordinate by the effe…
Bernoulli cylinder frame operators: filtration, Haar structure, and self-similarity
James Tian
We study the finite-rank frame operators generated by cylinder indicator functions for the Bernoulli Cantor measure . In the symmetric case , the natural Haar…
Classification in Active Dimension 2 for Weighted Residual Dynamics
James Tian
We study weighted residual dynamics associated with a rank-one projection in finite dimension. The iteration reduces, after finitely many steps, to a nonlinear recursion on a stabi…
Multipartite parity bounds and total correlation
James Tian
This paper studies multipartite observables formed from sums of local self-adjoint contractions on tensor product Hilbert spaces. The square of such a sum has a parity structure: a…
Tree Capacity and Splitting Isometries for Subinvariant Kernels
James Tian
Starting from a subinvariant positive definite kernel under a branching pullback, we attach to the resulting kernel sequence an electrical network on the word tree whose edge weigh…
Subinvariant kernel dynamics
James Tian
We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an incr…
Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning
Palle E. T. Jorgensen, Myung-Sin Song, James F. Tian
We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of "residuals" in general, and "telescopi…
Boundary Disintegration for Weighted Residual Energy Trees
James Tian
We study iterated weighted residual (WR) splittings generated by a positive operator and a finite family of contractions in $B\le…
Wavelet-Packet Content for Positive Operators
Myung-Sin Song, James Tian
We study positive operator decompositions associated with rooted trees of orthogonal projections. In this sense, the refinement tree induces an ``MRA in ''. To…
Random Frame Decompositions from Weighted Residual Flows
James Tian
We study the evolution of a positive operator under weighted residual maps determined by a finite family of orthogonal projections. Iterating these maps along the rooted tree of mu…
Alternating Weighted Residual Flows and the Non-Commutative Gap
James Tian
This work develops a nonlinear analogue of alternating projections on Hilbert space, based on iterating a weighted residual transformation that removes the portion of an operator d…
Shorting Dynamics and Structured Kernel Regularization
James Tian
This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced…
A Kernel Approach to the Stinespring and Kraus Representations
James Tian
We give a self-contained derivation of the Stinespring theorem for completely positive maps and the Kraus representation for normal completely positive maps using two scalar positi…
Residual-Weighted Decomposition of Positive Operators
James Tian
This paper investigates an iterative rank-one decomposition scheme for positive operators on a Hilbert space based on a residual-weighted congruence update. At each step the operat…
Universal Kernel Models for Iterated Completely Positive Maps
James Tian
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to a…
Graph Structured Operator Inequalities and Tsirelson-Type Bounds
James Tian
We establish operator norm bounds for bipartite tensor sums of self-adjoint contractions. The inequalities generalize the analytic structure underlying the Tsirelson and CHSH bound…
Stability of Maximum-Entropy Inference in Finite Dimensions
James Tian
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of…