DPF: Learning Dense Prediction Fields with Weak Supervision

Nowadays, many visual scene understanding problems are addressed by dense prediction networks. But pixel-wise dense annotations are very expensive (e.g., for scene parsing) or impossible (e.g., for intrinsic image decomposition), motivating us to leverage cheap point-level weak supervision. However, existing pointly-supervised methods still use the same architecture designed for full supervision. In stark contrast to them, we propose a new paradigm that makes predictions for point coordinate queries, as inspired by the recent success of implicit representations, like distance or radiance fields. As such, the method is named as dense prediction fields (DPFs). DPFs generate expressive intermediate features for continuous sub-pixel locations, thus allowing outputs of an arbitrary resolution. DPFs are naturally compatible with point-level supervision. We showcase the effectiveness of DPFs using two substantially different tasks: high-level semantic parsing and low-level intrinsic image decomposition. In these two cases, supervision comes in the form of single-point semantic category and two-point relative reflectance, respectively. As benchmarked by three large-scale public datasets PASCALContext, ADE20K and IIW, DPFs set new state-of-the-art performance on all of them with significant margins. Code can be accessed at https://github.com/cxx226/DPF

Helicity amplitudes in light-cone and Feynman-diagram gauges

Recently proposed Feynman-diagram (FD) gauge propagator for massless and massive gauge bosons is obtained from a light-cone (LC) gauge propagator, by choosing the gauge vector along the opposite direction of the gauge boson three-momentum. We implement a general LC gauge propagator for all the gauge bosons of the Standard Model (SM) in the HELicity Amplitude Subroutines (HELAS) codes, such that all the SM helicity amplitudes can be evaluated at the tree level in the LC gauge by using MadGraph. We confirm that our numerical codes produce physical helicity amplitudes which are consistent among all gauge choices. We then study interference patterns among Feynman amplitudes, for a few $2\to3$ scattering processes in QED and QCD, and the process $\gamma\gamma\to W^+W^-$ followed by the $W^\pm$ decays. We find that in a generic LC gauge, where all the gauge boson propagators share a common gauge vector, we cannot remove the off-shell current components which grow with their energy systematically from all the Feynman amplitudes in $2\to3$ processes. On the other hand, the $5\times5$ LC gauge propagator for the weak bosons removes components which grow with energy due to the longitudinal polarization mode of the external bi-fermion currents, and hence can give $2\to2$ weak boson scattering amplitudes which are free from subtle cancellation at high energies. The particular choice of the FD gauge vector has advantages over generic LC gauge, not only because all the terms which grow with energy of off-shell and on-shell currents are removed systematically from all the diagrams, but also because no artificial gauge vector direction dependence of individual amplitudes appears.Comment: 20 pages, 14 figures; references adde

Measurement uncertainty relation for three observables

In this work we establish rigorously a measurement uncertainty relation (MUR) for three unbiased qubit observables, which was previously shown to hold true under some presumptions. The triplet MUR states that the uncertainty, which is quantified by the total statistic distance between the target observables and the jointly implemented observables, is lower bounded by an incompatibility measure that reflects the joint measurement conditions. We derive a necessary and sufficient condition for the triplet MUR to be saturated and the corresponding optimal measurement. To facilitate experimental tests of MURs we propose a straightforward implementation of the optimal joint measurements. The exact values of incompatibility measure are analytically calculated for some symmetric triplets when the corresponding triplet MURs are not saturated. We anticipate that our work may enrich the understanding of quantum incompatibility in terms of MURs and inspire further applications in quantum information science. This work presents a complete theory relevant to a parallel work [Y.-L. Mao, et al., Testing Heisenberg's measurement uncertainty relation of three observables, arXiv:2211.09389] on experimental tests.Comment: arXiv admin note: substantial text overlap with arXiv:2211.0938