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Found 15 papers, 4 papers with code
Which Frequencies do CNNs Need? Emergent Bottleneck Structure in Feature Learning
We describe the emergence of a Convolution Bottleneck (CBN) structure in CNNs, where the network uses its first few layers to transform the input representation into a representation that is supported only along a few frequencies and channels, before using the last few layers to map back to the outputs.
Implicit bias of SGD in $L_{2}$-regularized linear DNNs: One-way jumps from high to low rank
The $L_{2}$-regularized loss of Deep Linear Networks (DLNs) with more than one hidden layers has multiple local minima, corresponding to matrices with different ranks.
Implicit Bias of Large Depth Networks: a Notion of Rank for Nonlinear Functions
We show that the representation cost of fully connected neural networks with homogeneous nonlinearities - which describes the implicit bias in function space of networks with $L_2$-regularization or with losses such as the cross-entropy - converges as the depth of the network goes to infinity to a notion of rank over nonlinear functions.
Feature Learning in $L_{2}$-regularized DNNs: Attraction/Repulsion and Sparsity
This second reformulation allows us to prove a sparsity result for homogeneous DNNs: any local minimum of the $L_{2}$-regularized loss can be achieved with at most $N(N+1)$ neurons in each hidden layer (where $N$ is the size of the training set).
Understanding Layer-wise Contributions in Deep Neural Networks through Spectral Analysis
Spectral analysis is a powerful tool, decomposing any function into simpler parts.
Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity
The dynamics of Deep Linear Networks (DLNs) is dramatically affected by the variance $\sigma^2$ of the parameters at initialization $\theta_0$.
DNN-Based Topology Optimisation: Spatial Invariance and Neural Tangent Kernel
We study the Solid Isotropic Material Penalisation (SIMP) method with a density field generated by a fully-connected neural network, taking the coordinates as inputs.
Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances
For a two-layer overparameterized network of width $ r^*+ h =: m $ we explicitly describe the manifold of global minima: it consists of $ T(r^*, m) $ affine subspaces of dimension at least $ h $ that are connected to one another.
Kernel Alignment Risk Estimator: Risk Prediction from Training Data
Under a natural universality assumption (that the KRR moments depend asymptotically on the first two moments of the observations) we capture the mean and variance of the KRR predictor.
Implicit Regularization of Random Feature Models
We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR).
The asymptotic spectrum of the Hessian of DNN throughout training
The dynamics of DNNs during gradient descent is described by the so-called Neural Tangent Kernel (NTK).
Order and Chaos: NTK views on DNN Normalization, Checkerboard and Boundary Artifacts
Moving the network into the chaotic regime prevents checkerboard patterns; we propose a graph-based parametrization which eliminates border artifacts; finally, we introduce a new layer-dependent learning rate to improve the convergence of DC-NNs.
Disentangling feature and lazy training in deep neural networks
Two distinct limits for deep learning have been derived as the network width $h\rightarrow \infty$, depending on how the weights of the last layer scale with $h$.
Scaling description of generalization with number of parameters in deep learning
At this threshold, we argue that $\|f_{N}\|$ diverges.
Neural Tangent Kernel: Convergence and Generalization in Neural Networks
While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training.
