Coordinate-based Multi-Layer Perceptrons (MLPs) are known to have difficulty reconstructing high frequencies of the training data. A common solution to this problem is Positional Encoding (PE), which has become quite popular. However, PE has drawbacks. It has high-frequency artifacts and adds another hyper-hyperparameter, just like batch normalization and dropout do. We believe that under certain circumstances PE is not necessary, and a smarter construction of the network architecture together with a smart training method is sufficient to achieve similar results. In this paper, we show that very simple MLPs can quite easily output a frequency when given input of the half-frequency and quarter-frequency. Using this, we design a network architecture in blocks, where the input to each block is the output of the two previous blocks along with the original input. We call this a {\it Fibonacci Network}. By training each block on the corresponding frequencies of the signal, we show that Fibonacci Networks can reconstruct arbitrarily high frequencies.

Video Anomaly Detection (VAD) plays a crucial role in modern surveillance systems, aiming to identify various anomalies in real-world situations. However, current benchmark datasets predominantly emphasize simple, single-frame anomalies such as novel object detection. This narrow focus restricts the advancement of VAD models. In this research, we advocate for an expansion of VAD investigations to encompass intricate anomalies that extend beyond conventional benchmark boundaries. To facilitate this, we introduce two datasets, HMDB-AD and HMDB-Violence, to challenge models with diverse action-based anomalies. These datasets are derived from the HMDB51 action recognition dataset. We further present Multi-Frame Anomaly Detection (MFAD), a novel method built upon the AI-VAD framework. AI-VAD utilizes single-frame features such as pose estimation and deep image encoding, and two-frame features such as object velocity. They then apply a density estimation algorithm to compute anomaly scores. To address complex multi-frame anomalies, we add a deep video encoding features capturing long-range temporal dependencies, and logistic regression to enhance final score calculation. Experimental results confirm our assumptions, highlighting existing models limitations with new anomaly types. MFAD excels in both simple and complex anomaly detection scenarios.

Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one route (root-to-leaf) that is dependent on the input data. In this paper, we present DecisioNet (DN), a binary-tree structured neural network. We propose a systematic way to convert an existing DNN into a DN to create a lightweight version of the original model. DecisioNet takes the best of both worlds - it uses neural modules to perform representational learning and utilizes its tree structure to perform only a portion of the computations. We evaluate various DN architectures, along with their corresponding baseline models on the FashionMNIST, CIFAR10, and CIFAR100 datasets. We show that the DN variants achieve similar accuracy while significantly reducing the computational cost of the original network.

We present a stochastic clustering algorithm based on pairwise similarity ofdatapoints. Our method extends existing deterministic methods, including agglomerative algorithms, min-cut graph algorithms, andconnected components. Thus it provides a common framework for all these methods. Our graph-based method differs from existing stochastic methods which are based on analogy to physical systems. The stochastic nature of our method makes it more robust against noise, including accidental edges and small spurious clusters. We demonstrate the superiority of our algorithm using an example with 3 spiraling bands and a lot of noise. 1 Introduction Clustering algorithms can be divided into two categories: those that require a vectorial representationof the data, and those which use only pairwise representation. In the former case, every data item must be represented as a vector in a real normed space, while in the second case only pairwise relations of similarity or dissimilarity areused.

We present a stochastic clustering algorithm based on pairwise similarity of datapoints. Our method extends existing deterministic methods, including agglomerative algorithms, min-cut graph algorithms, and connected components. Thus it provides a common framework for all these methods. Our graph-based method differs from existing stochastic methods which are based on analogy to physical systems. The stochastic nature of our method makes it more robust against noise, including accidental edges and small spurious clusters. We demonstrate the superiority of our algorithm using an example with 3 spiraling bands and a lot of noise. 1 Introduction Clustering algorithms can be divided into two categories: those that require a vectorial representation of the data, and those which use only pairwise representation. In the former case, every data item must be represented as a vector in a real normed space, while in the second case only pairwise relations of similarity or dissimilarity are used.