13 accepted papers
In this paper we derive a novel iterative algorithm for learning kernel machines. Our algorithm, $\textsf{AxlePro}$, extends the $\textsf{EigenPro}$ family of algorithms via momentum-based acceleration. $\textsf{AxlePro}$ can be applied to train kernel machines with arbitrary positive semidefini…
Neural networks trained to solve modular arithmetic tasks exhibit grokking, a phenomenon where the test accuracy starts improving long after the model achieves 100% training accuracy in the training process. It is often taken as an example of "emergence", where model ability manifests sharply throug…
Classical kernel machines have historically faced significant challenges in scaling to large datasets and model sizes—a key ingredient that has driven the success of neural networks. In this paper, we present a new methodology for building kernel machines that can scale efficiently with both data si…
Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral preconditioning is an important tool to speed-up the convergence of suc…
Recent studies indicate that kernel machines can often perform similarly or better than deep neural networks (DNNs) on small datasets. The interest in kernel machines has been additionally bolstered by the discovery of their equivalence to wide neural networks in certain regimes. However, a key feat…
The practical success of overparameterized neural networks has motivated the recent scientific study of \emph{interpolating methods}-- learning methods which are able fit their training data perfectly. Empirically, certain interpolating methods can fit noisy training data without catastrophically ba…
Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the joint training of the generator and discriminator. This paper analyzes these joint dynamics when the true s…
Contemporary wisdom based on empirical studies suggests that standard recurrent neural networks (RNNs) do not perform well on tasks requiring long-term memory. However, RNNs’ poor ability to capture long-term dependencies has not been fully understood. This paper provides a rigorous explanation of t…
At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our understanding of their generalization capabilities is incomplete and…
We consider the problem of estimating the input and hidden variables of a stochastic multi-layer neural network from an observation of the output. The hidden variables in each layer are represented as matrices with statistical interactions along both rows as well as columns. This problem applies to…
We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises in learning interconnections of networks of dyn…
Estimating a vector $\mathbf{x}$ from noisy linear measurements $\mathbf{Ax+w}$ often requires use of prior knowledge or structural constraints on $\mathbf{x}$ for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or plug-in ``deno…
Structural segmentation of music involves identifying boundaries between homogenous regions where the homogeneity involves one or more musical dimensions, and therefore depends on the musical genre. In this work, we address the segmentation of Hindustani instrumental concert recordings at the highes…