Related papers: Neural Lattice Decoders
Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders…
Neural machine translation (NMT) takes deterministic sequences for source representations. However, either word-level or subword-level segmentations have multiple choices to split a source sequence with different word segmentors or…
We consider the root lattice $A_n$ and derive explicit formulae for the moments of its Voronoi cell. We then show that these formulae enable accurate prediction of the error probability of lattice codes constructed from $A_n$.
Sparse representations of images are useful in many computer vision applications. Sparse coding with an $l_1$ penalty and a learned linear dictionary requires regularization of the dictionary to prevent a collapse in the $l_1$ norms of the…
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…
Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on…
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…
We explain how data-driven quantization of a linear unit in a neural network corresponds to solving the closest vector problem for a certain lattice generated by input data. We prove that the GPTQ algorithm is equivalent to Babai's…
The advancement of deep learning has led to the development of neural decoders for low latency communications. However, neural decoders can be very complex which can lead to increased computation and latency. We consider iterative pruning…
Universal approximation theory offers a foundational framework to verify neural network expressiveness, enabling principled utilization in real-world applications. However, most existing theoretical constructions are established by…
We formulate sequence to sequence transduction as a noisy channel decoding problem and use recurrent neural networks to parameterise the source and channel models. Unlike direct models which can suffer from explaining-away effects during…
Despite the indispensable role of X-ray computed tomography (CT) in diagnostic medicine field, the associated ionizing radiation is still a major concern considering that it may cause genetic and cancerous diseases. Decreasing the exposure…
Data-enabled predictive control (DeePC) for linear systems utilizes data matrices of recorded trajectories to directly predict new system trajectories, which is very appealing for real-life applications. In this paper we leverage the…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
We introduce a convolutional neural network for inferring a compact disentangled graphical description of objects from 2D images that can be used for volumetric reconstruction. The network comprises an encoder and a twin-tailed decoder. The…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…
This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a…
Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning…
Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…