Behnam Asadi

Behnam Asadi

Automated photogrammetric inspection emits metric measurements from a 3D reconstruction whose own correctness is normally unknown without an external survey. Can a reconstruction estimate its own reliability with no ground truth? We formalise a track-leakage-free hold-out protocol: a deterministic subset of images is withheld and each re-localised against only 3D points seen by at least two retained images -- a track-level barrier so a view is never tested against structure it helped create -- aggregated into an mAA confidence. Held-out observations still entered the bundle adjustment that built the trusted structure, so we call it track-leakage-free (a stricter re-mapping variant confirms this at 3/5 deg). Across operational GNSS-referenced captures plus ETH3D, EuRoC and the IMC 2025 benchmark we report four findings. (i) The protocol is computationally well-posed: good reconstructions score millidegree self-consistency. (ii) Thresholded self-consistency saturates and does not track absolute accuracy: confidence stays near 1.00 while true RTK error swings up to 14x within a capture, and the per-capture correlation is sign-unstable across five captures (-0.57 to +0.98; pooled 95% CI spanning zero), so it cannot gate accuracy. (iii) It flags gross failure only when the failure destroys internal consistency: a fragmenting model drops confidence, but a single self-consistent, globally-distorted model evades it -- three of four captures gave one model wrong by 55-106 m at confidence 1.00. (iv) The same dichotomy holds on independent ETH3D and IMC 2025 ground truth. Track-leakage-free hold-out measures internal geometric consistency, not absolute accuracy: neither a substitute for control-point assessment nor a general gross-failure gate. We release the protocol and degradation harness.

Behnam Asadi

We revisit Gaussian Mixture Models (GMMs) as a lightweight, interpretable tool for anomaly detection and, in particular, for detecting distributional drift in data streams. We make three practical choices explicit and evaluate them on seven public benchmarks. First, the number of mixture components is selected automatically by the Bayesian Information Criterion, initialised by k-means, removing the need to fix it in advance. Second, individual observations are scored by their negative log-likelihood under a GMM fitted to normal data, with thresholds set at a target false-alarm rate using Extreme Value Theory. Third, the same interpretable model extends to distributional drift: each Gaussian component is a named "regime," and the fraction of a stream window that matches no regime -- its unexplained mass -- is a drift signal that is itself the explanation. We benchmark this against a model-free kernel two-sample test (Maximum Mean Discrepancy, MMD) and against two GMM-to-GMM divergences (a closed-form Cauchy-Schwarz divergence and a matching-based KL surrogate). Across seven benchmarks ranging from 3 to 64 dimensions and five random splits, the GMM point detector is competitive with -- though rarely more accurate than -- Isolation Forest, Local Outlier Factor, one-class SVM, ECOD, COPOD and an autoencoder, while uniquely yielding an interpretable model. For drift, MMD is the strongest pure detector, but the interpretable unexplained-mass statistic matches it when anomalies form novel regimes (and honestly fails, as MMD does not, when drift is a pure re-weighting of existing regimes). Every alarm is explainable: anomalies lie a median of 3-10 sigma outside their nearest regime vs. about 1 sigma for normal points, and a drift alarm reports the fraction of the window matching no known regime. All code and experiments are released.

Behnam Asadi, Hui Jiang

In this paper, we have extended the well-established universal approximator theory to neural networks that use the unbounded ReLU activation function and a nonlinear softmax output layer. We have proved that a sufficiently large neural network using the ReLU activation function can approximate any function in $L^1$ up to any arbitrary precision. Moreover, our theoretical results have shown that a large enough neural network using a nonlinear softmax output layer can also approximate any indicator function in $L^1$, which is equivalent to mutually-exclusive class labels in any realistic multiple-class pattern classification problems. To the best of our knowledge, this work is the first theoretical justification for using the softmax output layers in neural networks for pattern classification.