Abstract: Collaborative filtering systems based on variational autoencoders (VAEs) are provided. VAEs may be trained on row-wise data without necessarily training a paired VAE on column-wise data (or vice-versa), and may optionally be trained via minibatches. The row-wise VAE models the output of the corresponding column-based VAE as a set of parameters and uses these parameters in decoding. In some implementations, a paired VAE is provided which receives column-wise data and models row-wise parameters; each of the paired VAEs may bind their learned column- or row-wise parameters to the output of the corresponding VAE. The paired VAEs may optionally be trained via minibatches. Unobserved data may be explicitly modelled. Methods for performing inference with such VAE-based collaborative filtering systems are also disclosed, as are example applications to search and anomaly detection.

Abstract: Collaborative filtering systems based on variational autoencoders (VAEs) are provided. VAEs may be trained on row-wise data without necessarily training a paired VAE on column-wise data (or vice-versa), and may optionally be trained via minibatches. The row-wise VAE models the output of the corresponding column-based VAE as a set of parameters and uses these parameters in decoding. In some implementations, a paired VAE is provided which receives column-wise data and models row-wise parameters; each of the paired VAEs may bind their learned column- or row-wise parameters to the output of the corresponding VAE. The paired VAEs may optionally be trained via minibatches. Unobserved data may be explicitly modelled. Methods for performing inference with such VAE-based collaborative filtering systems are also disclosed, as are example applications to search and anomaly detection.

Abstract: A digital processor runs a machine learning algorithm in parallel with a sampling server. The sampling sever may continuously or intermittently draw samples for the machine learning algorithm during execution of the machine learning algorithm, for example on a given problem. The sampling server may run in parallel (e.g., concurrently, overlapping, simultaneously) with a quantum processor to draw samples from the quantum processor.

Abstract: A digital processor runs a machine learning algorithm in parallel with a sampling server. The sampling sever may continuously or intermittently draw samples for the machine learning algorithm during execution of the machine learning algorithm, for example on a given problem. The sampling server may run in parallel (e.g., concurrently, overlapping, simultaneously) with a quantum processor to draw samples from the quantum processor.

Abstract: Collaborative filtering systems based on variational autoencoders (VAEs) are provided. VAEs may be trained on row-wise data without necessarily training a paired VAE on column-wise data (or vice-versa), and may optionally be trained via minibatches. The row-wise VAE models the output of the corresponding column-based VAE as a set of parameters and uses these parameters in decoding. In some implementations, a paired VAE is provided which receives column-wise data and models row-wise parameters; each of the paired VAEs may bind their learned column- or row-wise parameters to the output of the corresponding VAE. The paired VAEs may optionally be trained via minibatches. Unobserved data may be explicitly modelled. Methods for performing inference with such VAE-based collaborative filtering systems are also disclosed, as are example applications to search and anomaly detection.

Abstract: A hybrid computer comprising a quantum processor can be operated to perform a scalable comparison of high-entropy samplers. Performing a scalable comparison of high-entropy samplers can include comparing entropy and KL divergence of post-processed samplers. A hybrid computer comprising a quantum processor generates samples for machine learning. The quantum processor is trained by matching data statistics to statistics of the quantum processor. The quantum processor is tuned to match moments of the data.

Abstract: Generative and inference machine learning models with discrete-variable latent spaces are provided. Discrete variables may be transformed by a smoothing transformation with overlapping conditional distributions or made natively reparametrizable by definition over a GUMBEL distribution. Models may be trained by sampling from different models in the positive and negative phase and/or sample with different frequency in the positive and negative phase. Machine learning models may be defined over high-dimensional quantum statistical systems near a phase transition to take advantage of long-range correlations. Machine learning models may be defined over graph-representable input spaces and use multiple spanning trees to form latent representations. Machine learning models may be relaxed via continuous proxies to support a greater range of training techniques, such as importance weighting. Example architectures for (discrete) variational autoencoders using such techniques are also provided.

Abstract: A hybrid computer comprising a quantum processor can be operated to perform a scalable comparison of high-entropy samplers. Performing a scalable comparison of high-entropy samplers can include comparing entropy and KL divergence of post-processed samplers. A hybrid computer comprising a quantum processor generates samples for machine learning. The quantum processor is trained by matching data statistics to statistics of the quantum processor. The quantum processor is tuned to match moments of the data.

Abstract: Generative machine learning models, such as variational autoencoders, with comparatively sparse latent spaces are provided. Continuous latent variables are activated and/or inactivated based on a state of the latent space. Activation may be controlled by corresponding binary latent variables and/or by rectification of probability distributions defined over the latent space. Sparsification may be supported by normalization of terms, such as providing an L1 or L2 prior.

Abstract: A hybrid computer comprising a quantum processor can be operated to perform a scalable comparison of high-entropy samplers. Performing a scalable comparison of high-entropy samplers can include comparing entropy and KL divergence of post-processed samplers. A hybrid computer comprising a quantum processor generates samples for machine learning. The quantum processor is trained by matching data statistics to statistics of the quantum processor. The quantum processor is tuned to match moments of the data.