Xiang Zhang, Yang Zhang, Lukas Mehl, Karlis Martins Briedis, Markus Gross, Christopher Schroers
Accurately modeling soft boundaries, e.g., hair and defocus blur, is a fundamental challenge in stereo conversion due to the ambiguous blending of foreground and background. Existing depth models primarily predict single-layer depth, leading to ambiguity in depth correspondence at soft boundaries. While matting techniques can capture opacity for layered modeling, they often struggle in complex scenes with multiple targets and usually require user intervention. This paper introduces αDepth, a layered representation that decomposes soft boundaries for high-fidelity stereo conversion. Specifically, we first resolve mixed color and depth ambiguity by estimating layered color and depth values at soft boundaries. Considering complex multi-target scenes, we design a Circular Alpha Representation (CAR) that shifts the paradigm from global target extraction to local boundary decomposition. Unlike prior matting methods restricted to a single foreground/background, CAR enables efficient scene-level inference without manual guidance. Extensive evaluations demonstrate that αDepth achieves state-of-the-art performance in stereo conversion, eliminating background bleeding and structural distortions at soft boundaries.
Quantum reservoir computers (QRCs) have emerged as a promising approach to quantum machine learning, since they utilize the natural dynamics of quantum systems for data processing and are simple to train. Here, we consider $n$-qubit quantum extreme learning machines (QELMs) with initial-state encoding and continuous-time reservoir dynamics. Applying the Pauli transfer matrix (PTM) formalism reveals the encoding-generated features and their linear transformation by quantum channels, and thereby provides a nonlinear vector autoregression model as an interpretable classical representation of a QELM. We show that the nonlinear information processing capacity of a QELM factorizes into the ability of the encoding to represent a given target function and the decodability of the relevant Pauli features after the effective PTM. Comparing geometric and statistical decodability reveals features that are algebraically hidden yet recoverable through data correlations. We relate the decodability of Pauli features to the spreading of measurement operators under Heisenberg evolution (Krylov growth). Focusing on the unitary channel, we discuss how structured Hamiltonians, when paired with certain observables, can impair model performance, as reflected in a low rank of the readout and the effective PTMs. We trace this effect to Hamiltonian symmetries and derive asymptotic rank estimates for symmetry-resolved observable families. Our decodability analysis disentangles the contributions of encoding, reservoir dynamics, and measurement observables, and thus provides interpretable diagnostics that can inform the design of QELMs and reduce reliance on exhaustive hyperparameter search. As a specific application, we consider forecasting nonlinear dynamical systems and show that the readout of a trained QELM closely matches the expression of the underlying flow map at leading orders.