Papers Polynomial Neural Networks
“Polynomial Neural Networks” 태그가 달린 논문 29편 · 필터 해제
Identifiability of Deep Polynomial Neural Networks
Polynomial Neural Networks (PNNs) possess a rich algebraic and geometric structure. However, their identifiability -- a key property for ensuring interpretability -- remains poorly understood. In this work, we present a …
DecoderPolynomial Neural NetworksLearning on a Razor's Edge: the Singularity Bias of Polynomial Neural Networks
Deep neural networks often infer sparse representations, converging to a subnetwork during the learning process. In this work, we theoretically analyze subnetworks and their bias through the lens of algebraic geometry. W…
Polynomial Neural NetworksA Training Framework for Optimal and Stable Training of Polynomial Neural Networks
By replacing standard non-linearities with polynomial activations, Polynomial Neural Networks (PNNs) are pivotal for applications such as privacy-preserving inference via Homomorphic Encryption (HE). However, training PN…
Audio ClassificationHomomorphic Encryption for Deep LearningHuman Activity RecognitionImage Classification+2A practical, fast method for solving sum-of-squares problems for very large polynomials
Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Progra…
Polynomial Neural NetworksActivation degree thresholds and expressiveness of polynomial neural networks
We study the expressive power of deep polynomial neural networks through the geometry of their neurovariety. We introduce the notion of the activation degree threshold of a network architecture to express when the dimens…
Polynomial Neural NetworksPNeRV: A Polynomial Neural Representation for Videos
Extracting Implicit Neural Representations (INRs) on video data poses unique challenges due to the additional temporal dimension. In the context of videos, INRs have predominantly relied on a frame-only parameterization,…
Polynomial Neural NetworksGeometry of Polynomial Neural Networks
We study the expressivity and learning process for polynomial neural networks (PNNs) with monomial activation functions. The weights of the network parametrize the neuromanifold. In this paper, we study certain neuromani…
Polynomial Neural NetworksBayesian polynomial neural networks and polynomial neural ordinary differential equations
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. Howe…
Bayesian InferencePolynomial Neural NetworksSymbolic RegressionVariational InferenceExtrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study
Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but it is incompl…
Generalization BoundsPolynomial Neural NetworksOn the Study of Sample Complexity for Polynomial Neural Networks
As a general type of machine learning approach, artificial neural networks have established state-of-art benchmarks in many pattern recognition and data analysis tasks. Among various kinds of neural networks architecture…
Face RecognitionImage GenerationPolynomial Neural NetworksPlant Species Recognition with Optimized 3D Polynomial Neural Networks and Variably Overlapping Time-Coherent Sliding Window
Recently, the EAGL-I system was developed to rapidly create massive labeled datasets of plants intended to be commonly used by farmers and researchers to create AI-driven solutions in agriculture. As a result, a publicly…
Polynomial Neural NetworksThe Spectral Bias of Polynomial Neural Networks
Polynomial neural networks (PNNs) have been recently shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies have revealed that neural n…
Face RecognitionImage GenerationPolynomial Neural NetworksConditional Generation Using Polynomial Expansions
Generative modeling has evolved to a notable field of machine learning. Deep polynomial neural networks (PNNs) have demonstrated impressive results in unsupervised image generation, where the task is to map an input vect…
AttributeImage GenerationImage-to-Image TranslationPolynomial Neural Networks+2Ladder Polynomial Neural Networks
Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polyno…
Polynomial Neural NetworksAugmenting Deep Classifiers with Polynomial Neural Networks
Deep neural networks have been the driving force behind the success in classification tasks, e.g., object and audio recognition. Impressive results and generalization have been achieved by a variety of recently proposed …
Audio ClassificationGeneral ClassificationImage ClassificationModel Compression+3CoPE: Conditional image generation using Polynomial Expansions
Generative modeling has evolved to a notable field of machine learning. Deep polynomial neural networks (PNNs) have demonstrated impressive results in unsupervised image generation, where the task is to map an input vect…
AttributeConditional Image GenerationImage GenerationImage-to-Image Translation+31-Dimensional polynomial neural networks for audio signal related problems
In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that…
Polynomial Neural NetworksPhysics-Based Deep Neural Networks for Beam Dynamics in Charged Particle Accelerators
This paper presents a novel approach for constructing neural networks which model charged particle beam dynamics. In our approach, the Taylor maps arising in the representation of dynamics are mapped onto the weights of …
Polynomial Neural NetworksDeep Polynomial Neural Networks
Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to…
Conditional Image GenerationFace IdentificationFace RecognitionFace Verification+4P-nets: Deep Polynomial Neural Networks
Deep Convolutional Neural Networks (DCNNs) is currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to …
Image GenerationPolynomial Neural Networks