arXiv research

Deep learning aids ADMM-based decoding for binary linear codes.

In this paper, we model Density Evolution (DE) using Recurrent Neural Networks (RNNs) with the aim of designing capacity-approaching Irregular Low-Density Parity-Check (LDPC) codes for binary erasure channels. In particular, we present a method for determining the coefficients of the degree distributions, characterizin…

We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, hyperbolic manifolds, as first suggested by Guth and Lubotzky. The main contr…

This paper considers the problem of implementing large-scale gradient descent algorithms in a distributed computing setting in the presence of {\em straggling} processors. To mitigate the effect of the stragglers, it has been previously proposed to encode the data with an erasure-correcting code and decode at the maste…

In this work, a deep learning-based method for log-likelihood ratio (LLR) lossy compression and quantization is proposed, with emphasis on a single-input single-output uncorrelated fading communication setting. A deep autoencoder network is trained to compress, quantize and reconstruct the bit log-likelihood ratios cor…

New fault-tolerant quantum gates for homological LDPC codes with constant or almost-constant rate.

New quantum code breaks distance barrier with transversal non-Clifford gates.

A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, with…

Low-density parity-check codes, a class of capacity-approaching linear codes, are particularly recognized for their efficient decoding scheme. The decoding scheme, known as the sum-product, is an iterative algorithm consisting of passing messages between variable and check nodes of the factor graph. The sum-product alg…

Topological theory for qLDPC codes enables non-Clifford gates and magic state injection.

Let ${\mathcal S}_m$ be the set of all $m\times m$ density matrices (Hermitian positively semi-definite matrices of unit trace). Consider a problem of estimation of an unknown density matrix $ρ\in {\mathcal S}_m$ based on outcomes of $n$ measurements of observables $X_1,\dots, X_n\in {\mathbb H}_m$ (${\mathbb H}_m$ bei…

Transformers solve parity problems efficiently with step-by-step reasoning.

This study analyzes how one-layer transformers learn regular language recognition tasks.

Optimal sample complexity for autoregressive chain-of-thought learning proven.

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density functio…

Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problem…

This paper provides a neural approach to represent option implied information.

In this paper, a neural network-aided bit-interleaved coded modulation (NN-BICM) receiver is designed to mitigate the nonlinear clipping distortion in the LDPC coded direct currentbiased optical orthogonal frequency division multiplexing (DCOOFDM) systems. Taking the cross-entropy as loss function, a feed forward netwo…

Enhances fairness in multi-output models using optimal transport.

The paper examines bias in ML models using the Adult dataset.

The currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the …

Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models leverage the power of neural networks to implicitly learn and represent probability …

This research simplifies verification of machine learning systems using reparameterization.

We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8πl);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2πl)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.

This work improves fair tensor decomposition using a kernel criterion.

Parity functors assign labels to knot diagrams based on crossing parity.

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance $n^ε$. Their rate is evaluated via Euler characteristic arguments and their distance using $\mathbb{Z}_2$-systolic geometry. This construction answers …

The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect small erroneous deviations in reconstructed density matrices, which c…

Parity defined for based matrices, a new example of virtual knot parity.

A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^α)$, scales sub-linearly in $N$ for some $0 < α< 1$. Assuming a random support model for the non-zero transform domain…

The index theorem connects anomalies on a domain wall to global integrals.

Improved error correction using neural networks and belief propagation.

We introduce the 2-colour parity. It is a theory of parity for a large class of virtual links, defined using the interaction between orientations of the link components and a certain type of colouring. The 2-colour parity is an extension of the Gaussian parity, to which it reduces on virtual knots. We show that the 2-c…

In the present paper, we develop the parity theory invented in \cite{ManSb}; we construct new parities for two-component (virtual and free) links. New parities significantly depend on geometrical properties of diagrams; in particular, they are mutation-sensitive. New parities can be used practically in all problems, wh…

Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the class…

In \cite {FrKn,Sbornik} it was shown that in some knot theories the crucial role is played by {\em parity}, i.e.\ a function on crossings valued in $\{0,1\}$ and behaving nicely with respect to Reidemeister moves. Any parity allows one to construct functorial mappings from knots to knots, to refine many invariants and …

We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We show that conditional parity is amenable to statistical analysis by studying ran…

Universal Gaussian parity proven for 2D knots.

New parities defined on virtual knots linked to crossing indices.

There has recently been a steady increase in the number iterative approaches to density estimation. However, an accompanying burst of formal convergence guarantees has not followed; all results pay the price of heavy assumptions which are often unrealistic or hard to check. The Generative Adversarial Network (GAN) lite…

Efficiently clusters large datasets using low-density hyperplanes.

Study how past radiation determines present matter in Penrose's cyclic cosmology.

This paper tackles fair Bayes-optimal classifiers under predictive parity, proving their limitations and proposing a new algorithm.

Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit models. The gradient-free algorithm, presented as a sequence of exactly solvable …

Proposes a neural density estimator that adapts to low-dimensional structures and integrates into generative models.

A machine-checked Itô calculus for Brownian motion on $[0,T]$

Parity calibration aims to predict increase-decrease events, not values.

We use crossing parity to construct a generalization of biquandles for virtual knots which we call Parity Biquandles. These structures include all biquandles as a standard example referred to as the even parity biquandle. Additionally, we find all Parity Biquandles arising from the Alexander Biquandle and Quaternionic …