Related papers: Sinkhorn algorithms for entropic vector quantile r…
Vector quantization (VQ) is a method for deterministically learning features through discrete codebook representations. Recent works have utilized visual tokenizers to discretize visual regions for self-supervised representation learning.…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay…
The purpose of this work is to develop a framework to calibrate signed datasets so as to be consistent with specified marginals by suitably extending the Schr\"odinger-Fortet-Sinkhorn paradigm. Specifically, we seek to revise…
In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…
We present a new optimization method for small-to-intermediate scale variational algorithms on noisy near-term quantum processors which uses a Gaussian process surrogate model equipped with a classically-evaluated quantum kernel.…
In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the…
Vectorized quantum block encoding provides a way to embed classical data into Hilbert space, offering a pathway for quantum models, such as Quantum Transformers (QT), that replace classical self-attention with quantum circuit simulations to…
Modern neural networks are over-parametrized. In particular, each rectified linear hidden unit can be modified by a multiplicative factor by adjusting input and output weights, without changing the rest of the network. Inspired by the…
Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better…
Variational Quantum Algorithms (VQAs) are a class of hybrid quantum-classical algorithms that leverage on classical optimization tools to find the optimal parameters for a parameterized quantum circuit. One relevant application of VQAs is…
Developments in cooperative trajectory planning of connected autonomous vehicles (CAVs) have gathered considerable momentum and research attention. Generally, such problems present strong non-linearity and non-convexity, rendering great…
Vector quantization(VQ) is a lossy data compression technique from signal processing for which simple competitive learning is one standard method to quantize patterns from the input space. Extending competitive learning VQ to the domain of…
We propose a novel algorithm, TR-SVR, for solving unconstrained stochastic optimization problems. This method builds on the trust-region framework, which effectively balances local and global exploration in optimization tasks. TR-SVR…
Post-training quantization (PTQ) for vision transformers (ViTs) has received increasing attention from both academic and industrial communities due to its minimal data needs and high time efficiency. However, many current methods fail to…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix…
This paper proposes a novel matrix quantization method, Binary Quadratic Quantization (BQQ). In contrast to conventional first-order quantization approaches, such as uniform quantization and binary coding quantization, that approximate…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…