相关论文: Tropical Bisectors and Carlini-Wagner Attacks

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…

We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU activations using tropical geometry. By representing a network's output as a tropical rational function, TropNNC enables…

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…

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…

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…

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…

Convolutional neural networks (CNN) have achieved great success in analyzing tropical cyclones (TC) with satellite images in several tasks, such as TC intensity estimation. In contrast, TC structure, which is conventionally described by a…

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…

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…

Can algebraic geometry enhance the sharpness, robustness, and interpretability of modern neural reasoning models by equipping them with a mathematically grounded inductive bias? To answer this, we introduce Tropical Attention, an attention…

In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in…

Though Convolutional Neural Networks (CNNs) have surpassed human-level performance on tasks such as object classification and face verification, they can easily be fooled by adversarial attacks. These attacks add a small perturbation to the…

We investigate a canonical extension of a conventional combinatorial notion of reduced divisors to a notion of tropical projections, which can be defined as the unique minimizers of the so-called $B$-pseudonorms with respect to compact…

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…

Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to…

Convolutional neural networks (CNNs) are known for their good performance and generalization in vision-related tasks and have become state-of-the-art in both application and research-based domains. However, just like other neural network…

A new method for estimating tropical cyclone track uncertainty is presented and tested. This method uses a neural network to predict a bivariate normal distribution, which serves as an estimate for track uncertainty. We train the network…

To evaluate the robustness gain of Bayesian neural networks on image classification tasks, we perform input perturbations, and adversarial attacks to the state-of-the-art Bayesian neural networks, with a benchmark CNN model as reference.…

This thesis delves into the geometry of abstract tropical curves, exploring their complete linear system and associated tropical submodules. We establish a lower bound on the dimension of tropical submodules in terms of the Baker-Norine…