Synthetic Image Detection via Spectral Gaps of QC-RBIM Nishimori Bethe-Hessian Operators

The rapid advance of deep generative models such as GANs and diffusion networks now produces images that are virtually indistinguishable from genuine photographs, undermining media forensics and biometric security. Supervised detectors quickly lose effectiveness on unseen generators or after adversarial post-processing, while existing unsupervised methods that rely on low-level statistical cues remain fragile. We introduce a physics-inspired, model-agnostic detector that treats synthetic-image identification as a community-detection problem on a sparse weighted graph. Image features are first extracted with pretrained CNNs and reduced to 32 dimensions, each feature vector becomes a node of a Multi-Edge Type QC-LDPC graph. Pairwise similarities are transformed into edge couplings calibrated at the Nishimori temperature, producing a Random Bond Ising Model (RBIM) whose Bethe-Hessian spectrum exhibits a characteristic gap when genuine community structure (real images) is present. Synthetic images violate the Nishimori symmetry and therefore lack such gaps. We validate the approach on binary tasks cat versus dog and male versus female using real photos from Flickr-Faces-HQ and CelebA and synthetic counterparts generated by GANs and diffusion models. Without any labeled synthetic data or retraining of the feature extractor, the detector achieves over 94% accuracy. Spectral analysis shows multiple well separated gaps for real image sets and a collapsed spectrum for generated ones. Our contributions are threefold: a novel LDPC graph construction that embeds deep image features, an analytical link between Nishimori temperature RBIM and the Bethe-Hessian spectrum providing a Bayes optimal detection criterion; and a practical, unsupervised synthetic image detector robust to new generative architectures. Future work will extend the framework to video streams and multi-class anomaly detection.

Natural Image Classification via Quasi-Cyclic Graph Ensembles and Random-Bond Ising Models at the Nishimori Temperature

We present a unified framework combining statistical physics, coding theory, and algebraic topology for efficient multi-class image classification. High-dimensional feature vectors from a frozen MobileNetV2 backbone are interpreted as spins on a sparse Multi-Edge Type quasi-cyclic LDPC (MET-QC-LDPC) graph, forming a Random-Bond Ising Model (RBIM). We operate this RBIM at its Nishimori temperature, $\beta_N$, where the smallest eigenvalue of the Bethe-Hessian matrix vanishes, maximizing class separability. Our theoretical contribution establishes a correspondence between local trapping sets in the code's graph and topological invariants (Betti numbers, bordism classes) of the feature manifold. A practical algorithm estimates $\beta_N$ efficiently with a quadratic interpolant and Newton correction, achieving a six-fold speed-up over bisection. Guided by topology, we design spherical and toroidal MET-QC-LDPC graph ensembles, using permanent bounds to suppress harmful trapping sets. This compresses 1280-dimensional features to 32 or 64 dimensions for ImageNet-10 and -100 subsets. Despite massive compression (40x fewer parameters), we achieve 98.7% accuracy on ImageNet-10 and 82.7% on ImageNet-100, demonstrating that topology-guided graph design yields highly efficient, physics-inspired embeddings with state-of-the-art performance.