Polynomial time constructive decision algorithm for multivariable quantum signal processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal operators corresponding to each variable with signal processing operators, which provides an efficient means to perform multivariable polynomial transformations. However, the necessary and sufficient condition for what types of polynomials can be constructed by M-QSP is unknown. In this paper, we propose a classical algorithm to determine whether a given pair of multivariable Laurent polynomials can be implemented by M-QSP, which returns True or False. As one of the most important properties of this algorithm, it returning True is the necessary and sufficient condition. The proposed classical algorithm runs in polynomial time in the number of variables and signal operators. Our algorithm also provides a constructive method to select the necessary parameters for implementing M-QSP. These findings offer valuable insights for identifying practical applications of M-QSP.

Head-Related Transfer Function Interpolation from Spatially Sparse Measurements Using Autoencoder with Source Position Conditioning

We propose a method of head-related transfer function (HRTF) interpolation from sparsely measured HRTFs using an autoencoder with source position conditioning. The proposed method is drawn from an analogy between an HRTF interpolation method based on regularized linear regression (RLR) and an autoencoder. Through this analogy, we found the key feature of the RLR-based method that HRTFs are decomposed into source-position-dependent and source-position-independent factors. On the basis of this finding, we design the encoder and decoder so that their weights and biases are generated from source positions. Furthermore, we introduce an aggregation module that reduces the dependence of latent variables on source position for obtaining a source-position-independent representation of each subject. Numerical experiments show that the proposed method can work well for unseen subjects and achieve an interpolation performance with only one-eighth measurements comparable to that of the RLR-based method.

Profiling based Out-of-core Hybrid Method for Large Neural Networks

GPUs are widely used to accelerate deep learning with NNs (NNs). On the other hand, since GPU memory capacity is limited, it is difficult to implement efficient programs that compute large NNs on GPU. To compute NNs exceeding GPU memory capacity, data-swapping method and recomputing method have been proposed in existing work. However, in these methods, performance overhead occurs due to data movement or increase of computation. In order to reduce the overhead, it is important to consider characteristics of each layer such as sizes and cost for recomputation. Based on this direction, we proposed Profiling based out-of-core Hybrid method (PoocH). PoocH determines target layers of swapping or recomputing based on runtime profiling. We implemented PoocH by extending a deep learning framework, Chainer, and we evaluated its performance. With PoocH, we successfully computed an NN requiring 50 GB memory on a single GPU with 16 GB memory. Compared with in-core cases, performance degradation was 38 \% on x86 machine and 28 \% on POWER9 machine.