Related papers: On the similarities between generalized rank and H…
We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…
Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with…
Machine learning systems often do not share the same inductive biases as humans and, as a result, extrapolate or generalize in ways that are inconsistent with our expectations. The trade-off between exemplar- and rule-based generalization…
We propose a method combining relational-logic representations with neural network learning. A general lifted architecture, possibly reflecting some background domain knowledge, is described through relational rules which may be handcrafted…
We study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the second part, we propose a new family of algebraic geometric LRC…
Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…
While sentence anomalies have been applied periodically for testing in NLP, we have yet to establish a picture of the precise status of anomaly information in representations from NLP models. In this paper we aim to fill two primary gaps,…
Proving capacity for networks without feedback or cooperation usually involves two fundamental random coding techniques: superposition coding and binning. Although conceptually very different, these two techniques often achieve the same…
Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${\cal C}$, identify…
Generative models have recently been explored for synthesizing neural network weights. These approaches take neural network checkpoints as training data and aim to generate high-performing weights during inference. In this work, we examine…
Weight norm $\|w\|$ and margin $\gamma$ participate in learning theory via the normalized margin $\gamma/\|w\|$. Since standard neural net optimizers do not control normalized margin, it is hard to test whether this quantity causally…
Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in…
Transfer learning is a useful technique for achieving improved performance and reducing training costs by leveraging the knowledge gained from source tasks and applying it to target tasks. Assessing the effectiveness of transfer learning…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Humans represent scenes and objects in rich feature spaces, carrying information that allows us to generalise about category memberships and abstract functions with few examples. What determines whether a neural network model generalises…
Rank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscross error correction, and post-quantum cryptography. Recent…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of…
Embedding is a common technique for analyzing multi-dimensional data. However, the embedding projection cannot always form significant and interpretable visual structures that foreshadow underlying data patterns. We propose an approach that…
The generalized Hamming weight (GHW) $d_r(C)$ of linear codes $C$ is a natural generalization of the minimum Hamming distance $d(C)(=d_1(C))$ and has become one of important research objects in coding theory since Wei's originary work [23]…