In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the multidimensional simplex, where the classification depends on a multidimensional threshold. This change of perspective enables for any trained classification network an \textit{a posteriori} optimization of the classification score by means of threshold tuning, as usually carried out in the binary setting, thus allowing for a further refinement of the prediction capability of any network. Our experiments show indeed that multidimensional threshold tuning yields performance improvements across various networks and datasets. Moreover, we derive a multiclass ROC analysis based on \emph{ROC clouds} -- the attainable (FPR,TPR) operating points induced by a single multiclass threshold -- and summarize them via a \emph{Distance From Point} (DFP) score to $(0,1)$. This yields a coherent alternative to standard One-vs-Rest (OvR) curves and aligns with the observed tuning gains.

We consider the Threshold Bandit setting, a variant of the classical multi-armed bandit problem in which the reward on each round depends on a piece of side information known as a threshold value .

We will make this discussion more explicit.

In all cases, the training exploded, similar to the no-threshold vanilla arctanh (l.209,214-215). However in our case, in many of the units, the value explodes at infinity. In the paper (l.203), we ran BP experiments until Running without the absolute value is part of the ablation. Please see the ablation analysis (l.205-216) and note that: (i) hypernetworks allow us to adapt Arikan, "Polar codes: A pipelined implementation"), which makes use of the structure of polar GallagerB, MSA, SP A), while we learn the node activations from scratch. In both codes, our performance is better across all SNR. SNR=5.5 and SNR=6, we obtain a third of their bit error rate (

In this section, we report the testing results on Argoverse and ETH/UCY datasets and compare the results with other models in the literature.

This section provides parameter estimation equations in the MM procedure Eq. (13) for the baseline Below, we provide results for the exponential and power distributions. This section describes the details of the experiments. Dense10 data sets and the Python code to generate those as part of the final submission. Due to the stochastic nature, the total number of event instances cannot be controlled. See the attached code for the detail.

We present the complete algorithm for FixMatch in algorithm 1. Algorithm 1 FixMatch algorithm. Here, we provide a complete list of hyperparameters in table 4. Note that we did ablation As shown in table 5, when using small threshold values, most unlabeled examples' confidence is Consequently, they all contribute to the unlabeled loss in eq. SGD, but the difference was not significant. While the value 0.0005 appeared as a good default choice for WRN-28-2 across datasets, we find We report results over five random folds of labeled data. Runs are ordered by accuracy.

Rooftop 3D reconstruction using UAV-based photogrammetry offers a promising solution for infrastructure assessment, but existing methods often require high percentages of image overlap and extended flight times to ensure model accuracy when using autonomous flight paths. This study systematically evaluates key flight parameters-ground sampling distance (GSD) and image overlap-to optimize the 3D reconstruction of complex rooftop infrastructure. Controlled UAV flights were conducted over a multi-segment rooftop at Queen's University using a DJI Phantom 4 Pro V2, with varied GSD and overlap settings. The collected data were processed using Reality Capture software and evaluated against ground truth models generated from UAV-based LiDAR and terrestrial laser scanning (TLS). Experimental results indicate that a GSD range of 0.75-1.26 cm combined with 85% image overlap achieves a high degree of model accuracy, while minimizing images collected and flight time. These findings provide guidance for planning autonomous UAV flight paths for efficient rooftop assessments.