Related papers: TropNNC: Structured Neural Network Compression Usi…
Convolutional neural networks (CNNs) have been used in many machine learning fields. In practical applications, the computational cost of convolutional neural networks is often high with the deepening of the network and the growth of data…
We propose an algebraic geometric framework to study the expressivity of linear activation neural networks. A particular quantity of neural networks that has been actively studied is the number of linear regions, which gives a…
We introduce a simple, easy to implement, and computationally efficient tropical convolutional neural network architecture that is robust against adversarial attacks. We exploit the tropical nature of piece-wise linear neural networks by…
This work tackles the problem of characterizing and understanding the decision boundaries of neural networks with piecewise linear non-linearity activations. We use tropical geometry, a new development in the area of algebraic geometry, to…
We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among…
Deep neural networks show great success when input vectors are in an Euclidean space. However, those classical neural networks show a poor performance when inputs are phylogenetic trees, which can be written as vectors in the tropical…
Tropical geometry has recently found several applications in the analysis of neural networks with piecewise linear activation functions. This paper presents a new look at the problem of tropical polynomial division and its application to…
In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our…
Convolutional neural networks have become increasingly deep and complex, leading to higher computational costs. While tropical convolutional neural networks (TCNNs) reduce multiplications, they underperform compared to standard CNNs. To…
We present a new, unifying approach following some recent developments on the complexity of neural networks with piecewise linear activations. We treat neural network layers with piecewise linear activations as tropical polynomials, which…
Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…
Recent advances in molecular representation learning have produced highly effective encodings of molecules for numerous cheminformatics and bioinformatics tasks. However, extracting general chemical insight while balancing predictive…
The state-of-the-art deep neural networks (DNNs) have been widely applied for various real-world applications, and achieved significant performance for cognitive problems. However, the increment of DNNs' width and depth in architecture…
This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…
Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against state-of-the-art attacks, including the Carlini-Wagner…
Wavelets are well known for data compression, yet have rarely been applied to the compression of neural networks. This paper shows how the fast wavelet transform can be used to compress linear layers in neural networks. Linear layers still…
The success of deep neural networks in many real-world applications is leading to new challenges in building more efficient architectures. One effective way of making networks more efficient is neural network compression. We provide an…
Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…
Compression is a standard procedure for making convolutional neural networks (CNNs) adhere to some specific computing resource constraints. However, searching for a compressed architecture typically involves a series of time-consuming…
The outstanding performance of large foundational models across diverse tasks, from computer vision to speech and natural language processing, has significantly increased their demand. However, storing and transmitting these models poses…