Hans-Andrea Loeliger

This letter explores the capability of continuous-time recurrent neural networks to store and recall precisely timed scores of spike trains. We show (by numerical experiments) that this is indeed possible: within some range of parameters, any random score of spike trains (for all neurons in the network) can be robustly memorized and autonomously reproduced with stable accurate relative timing of all spikes, with probability close to one. We also demonstrate associative recall under noisy conditions. In these experiments, the required synaptic weights are computed offline to satisfy a template that encourages temporal stability.

The paper considers the calibration of control-bounded analog-to-digital converters. It is demonstrated that variations of the analog frontend can be addressed by calibrating the digital estimation filter. In simulations (both behavioral and transistor level) of a leapfrog analog frontend, the proposed calibration method restores essentially the nominal performance. Moreover, with digital-filter calibration in mind, the paper reformulates the design problem of control-bounded converters and thereby clarifies the role of sampling, desired filter shape, and nominal conversion error.

The article explores a new approach to model predictive control (MPC) where both discrete-level input constraints and state constraints are expressed in terms of Gaussian variables with unknown variances. The computations boil down to repeating Kalman-type recursions, with linear complexity in the prediction horizon. In consequence, the proposed approach can handle long prediction horizons with both discrete-level input constraints and state constraints, which has been a largely unresolved problem. The article demonstrates and evaluates the application of this approach by applying it to the control problem of a three-level power converter with an $LC$ filter. In this application, long horizons are mandatory to obtain low harmonic current distortions, and certain state constraints must be imposed to prevent damage to the converter. The proposed controller can easily handle 100 or more time steps and is shown to perform remarkably well, not only in the steady state, but also in transients and in the case of a phase-to-ground fault.

This paper introduces the partial-inverse problem for linearized polynomials and develops its application to decoding Gabidulin codes and lifted Gabidulin codes in linear random network coding. The proposed approach is a natural generalization of its counterpart for ordinary polynomials, thus providing a unified perspective on Reed–Solomon codes for the Hamming metric and for the rank metric. The basic algorithm for solving the partial-inverse problem is a common parent algorithm of a Berlekamp–Massey algorithm, a Euclidean algorithm, and yet another algorithm, all of which are obtained as easy variations of the basic algorithm. Decoding Gabidulin codes can be reduced to the partial-inverse problem via a key equation with a new converse. This paper also develops new algorithms for interpolating crisscross erasures and for joint decoding of errors, erasures, and deviations in random network coding.

Variations of L1-regularization including, in particular, total variation regularization, have hugely improved computational imaging. However, sharper edges and fewer staircase artifacts can be achieved with convex-concave regularizers. We present a new class of such regularizers using normal priors with unknown variance (NUV), which include smoothed versions of the logarithm function and smoothed versions of L_p norms with p ≤ 1. All NUV priors allow variational representations that lead to efficient algorithms for image reconstruction by iterative reweighted descent. A preferred such algorithm is iterative reweighted coordinate descent, which has no parameters (in particular, no step size to control) and is empirically robust and efficient. The proposed priors and algorithms are demonstrated with applications to tomography. We also note that the proposed priors come with built-in edge detection, which is demonstrated by an application to image segmentation.

A control-bounded analog-to-digital converter consists of a linear analog system that is subject to digital control, and a digital filter that estimates the analog input signal from the digital control signals. Such converters have many commonalities with delta–sigma converters, but they can use more general analog filters. The paper describes the operating principle, gives a transfer function analysis, and describes the digital filtering. In addition, the paper discusses two examples of such architectures. The first example is a cascade structure reminiscent of, but simpler than, a high-order MASH converter. The second example combines two attractive properties that have so far been considered incompatible. Its nominal conversion noise (assuming ideal components) essentially equals that of the first example. However, its analog filter is a fully connected network to which the input signal is fed in parallel, which potentially makes it more robust against nonidealities.

This paper studies the capability of a recurrent neural network model to memorize random dynamical firing patterns by a simple local learning rule. Two modes of learning/memorization are considered: The first mode is strictly online, with a single pass through the data, while the second mode uses multiple passes through the data. In both modes, the learning is strictly local (quasi-Hebbian): At any given time step, only the weights between the neurons firing (or supposed to be firing) at the previous time step and those firing (or supposed to be firing) at the present time step are modified. The main result of the paper is an upper bound on the probability that the single-pass memorization is not perfect. It follows that the memorization capacity in this mode asymptotically scales like that of the classical Hopfield model (which, in contrast, memorizes static patterns). However, multiple-rounds memorization is shown to achieve a higher capacity (with a nonvanishing number of bits per connection/synapse). These mathematical findings may be helpful for understanding the functions of short-term memory and long-term memory in neuroscience.

In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this paper, using quantum mass functions, we discuss the realization of measurements in terms of unitary interactions and marginalizations. It follows that classical measurement results strictly belong to local models, i.e., marginals of more detailed models. Classical variables that are created by marginalization do not exist in the unmarginalized model, and different marginalizations may yield incompatible classical variables. These observations are illustrated by the Frauchiger–Renner paradox, which is analyzed (and resolved) in terms of quantum mass functions. Throughout, the paper uses factor graphs to represent quantum systems/models with multiple measurements at different points in time.

In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this paper, using quantum mass functions, we discuss the realization of measurements in terms of unitary interactions and marginalizations. It follows that classical measurement results strictly belong to local models, i.e., marginals of more detailed models. Classical variables that are created by marginalization do not exist in the unmarginalized model, and different marginalizations may yield incompatible classical variables. These observations are illustrated by the Frauchiger-Renner paradox, which is analyzed (and resolved) in terms of quantum mass functions. Throughout, the paper uses factor graphs to represent quantum systems/models with multiple measurements at different points in time.