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Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…

Despite progress in training neural networks for lossy image compression, current approaches fail to maintain both perceptual quality and abstract features at very low bitrates. Encouraged by recent success in learning discrete…

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…

We determine the resource scaling of machine learning-based quantum state reconstruction methods, in terms of inference and training, for systems of up to four qubits when constrained to pure states. Further, we examine system performance…

Neural network quantum states provide a novel representation of the many-body states of interacting quantum systems and open up a promising route to solve frustrated quantum spin models that evade other numerical approaches. Yet its…

Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the…

Quantum state tomography, a process that reconstructs a quantum state from measurements on an ensemble of identically prepared copies, plays a crucial role in benchmarking quantum devices. However, brute-force approaches to quantum state…

Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the…

Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…

In contrast to RNNs, which compress their history into a single hidden state, Transformers can attend to all past tokens directly. However, standard Transformers rely solely on the hidden state from the previous layer to represent the…

We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm…

The utility of solving the Fermi-Hubbard model has been estimated in the billions of dollars. Digital quantum computers can in principle address this task, but have so far been limited to quasi one-dimensional models. This is because of…

We introduce Variational State-Space Filters (VSSF), a new method for unsupervised learning, identification, and filtering of latent Markov state space models from raw pixels. We present a theoretically sound framework for latent state…

Effective human-robot interaction, such as in robot learning from human demonstration, requires the learning agent to be able to ground abstract concepts (such as those contained within instructions) in a corresponding high-dimensional…

Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…

Sparse autoencoders have become a standard tool for uncovering interpretable latent representations in neural networks. Yet salient concepts often span manifolds that current linear methods cannot capture without post hoc analysis. This…

Autoencoder-based structures have dominated recent learned image compression methods. However, the inherent information loss associated with autoencoders limits their rate-distortion performance at high bit rates and restricts their…

Most multilayer least squares (LS)-based neural networks are structured with two separate stages: unsupervised feature encoding and supervised pattern classification. Once the unsupervised learning is finished, the latent encoding would be…

In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…