arXiv subjects

Mohammad Meysami

Publications and source records attributed to Mohammad Meysami.

4 recordsLinked to original sources

arXiv2026

A QUBO Formulation for Nowhere-Zero $k$-Flows

We consider the encoding of graph problems as Quadratic Unconstrained Binary Optimization (QUBO) problems, which are solvable by either quantum or classical annealers. Yet, the class of problems encoded as QUBO problems has not previously included nowhere-zero flows. Nowhere-zero flows are related to Tutte's $5$-flow conjecture and appear in many contexts in graph theory. We provide an encoding of nowhere-zero flows as a QUBO Hamiltonian and prove the correctness of the construction. Our construction yields a Hamiltonian $H_{\mathrm{mod},k}$ whose ground state has zero energy if and only if the graph $G$ has a nowhere-zero $\mathbb Z_k$-flow. By Tutte's equivalence theorem, zero ground energy is equivalent to $\varphi(G)\le k$, and the zero-energy degeneracy is given by the flow polynomial $F(G;k)$. In particular, when the ground-state energy is zero, this is also the ground-state degeneracy. The construction uses one-hot variables to represent the edge flow residues modulo $k$ and auxiliary variables to represent the per-vertex modular quotient. We prove that the correctness of the construction is independent of the choice of orientation, root vertex, and positive penalty weights. We verify the construction on $59$ examples of graphs and values of $k$ that include both yes-instances and no-instances. We exhaustively sweep orientations and root choices on selected robustness instances and test a finite suite of positive penalty weights. The resulting Hamiltonian is implemented using the dimod.BinaryQuadraticModel class, which is compatible with the D-Wave Ocean SDK. Quantum-hardware runs and claims about potential speedup using these devices are left to follow-up work.

quant-ph↗

arXiv2026

The Normalized Difference Layer: A Differentiable Spectral Index Formulation for Deep Learning

Normalized difference indices have been a staple in remote sensing for decades. They stay reliable under lighting changes produce bounded values and connect well to biophysical signals. Even so, they are usually treated as a fixed pre processing step with coefficients set to one, which limits how well they can adapt to a specific learning task. In this study, we introduce the Normalized Difference Layer that is a differentiable neural network module. The proposed method keeps the classical idea but learns the band coefficients from data. We present a complete mathematical framework for integrating this layer into deep learning architectures that uses softplus reparameterization to ensure positive coefficients and bounded denominators. We describe forward and backward pass algorithms enabling end to end training through backpropagation. This approach preserves the key benefits of normalized differences, namely illumination invariance and outputs bounded to $[-1,1]$ while allowing gradient descent to discover task specific band weightings. We extend the method to work with signed inputs, so the layer can be stacked inside larger architectures. Experiments show that models using this layer reach similar classification accuracy to standard multilayer perceptrons while using about 75\% fewer parameters. They also handle multiplicative noise well, at 10\% noise accuracy drops only 0.17\% versus 3.03\% for baseline MLPs. The learned coefficient patterns stay consistent across different depths.

cs.CV↗

arXiv2025

Interpretable Machine Learning-Derived Spectral Indices for Vegetation Monitoring

Spectral indices such as NDVI have driven vegetation monitoring for decades, yet their design remains largely manual and ad hoc. Their usefulness stems not only from their empirical performance, but also from algebraic forms that remain compact and biologically interpretable. However, the space of possible algebraic expressions relating spectral bands is effectively infinite, making systematic search impractical without structural constraints. We introduce the Spectral Feature Polynomial (SFP) framework, a general pipeline that automatically discovers compact, interpretable spectral indices from labeled multispectral imagery. SFP constructs a library of ratio-based spectral features that inherit illumination invariance by construction. It then applies cross-validated feature selection and continuous coefficient optimization to produce a single closed-form equation per task, transparent to domain experts and deployable on any remote sensing platform without requiring standardization statistics. We validate the framework on two agricultural applications. For Kochia (Bassia scoparia) detection in Sentinel-2 imagery near Lucky Lake of Saskatchewan over three growing seasons, the same two-term equation emerged in 44 of 46 independent cross-validation folds, achieving 98.6% mean accuracy, more than 4 percentage points above the best established index under year-held-out evaluation. For wheat plant classification from UAV multispectral imagery, stage-specific indices achieved 99.5%, 97.2%, and 93.5% across three growth stages, compared to 78% or below for the best established index at late season when NIR-based contrasts lose discriminatory power as wheat senesces. In both applications, SFP yielded a single transparent equation that generalized across held-out regions and outperformed established indices.

cs.CV↗

arXiv2024

Probabilistic Analysis of Least Squares, Orthogonal Projection, and QR Factorization Algorithms Subject to Gaussian Noise

We consider the effect of Gaussian perturbations on least-squares residuals, orthogonal projections, and QR-type algorithms. The problem that motivated our investigations is as follows: suppose that a full column-rank matrix $B\in\mathbb{R}^{m\times n}$ has already been computed, and suppose that a new normalized column $q=(x+y)/\|x+y\|_2$ is to be appended to $B$, where $x\perp\operatorname{span}(B)$ is the ideal orthogonal component and $y$ represents the orthogonalization error. How large can the condition number $\kappa([B,q])$ of the resulting matrix $[B,q]$ become? While we provide a Weyl-type bound on the singular values of $[B,q]$, in terms of the extremal singular values of $B$ and the quantity $\|B^T y\|_2/\|x+y\|_2$, we also derive exact probability laws for norms and projection residuals under Gaussian perturbations. Finally, we use these probability laws to derive probabilistic condition-number bounds for QR-type processes with imperfect orthogonalization and exact normalization.

math.NA↗