The classical continuous time recurrent (Hopfield) network is considered and adapted to K -winner-take-all operation. The neurons are of sigmoidal type with a controllable gain G, an amplitude m and interconnected by the conductance p. The network is intended to process one by one a sequence of lists, each of them with N distinct elements, each of them squeezed to [0,I] admission interval, each of them having an imposed minimum separation between elements z_min. The network carries out: 1) a matching dynamic process between the order of list elements and the order of outputs, and 2) a binary type steady-state separation between K and K+1 outputs, the former surpassing a +ξ threshold and the later falling under the -ξ threshold. As a result, the machine will signal the ranks of the K largest elements of the list. To achieve 1), the initial condition of processing phase has to be placed in a computable θ -vicinity of zero-state. This requires a resetting procedure after each list. To achieve 2) the bias current M has to be within a certain interval computable from circuit parameters. In addition, the steady-state should be asymptotically stable. To these goals, we work with high gain and exploit the sigmoid properties and network symmetry. The various inequality type constraints between parameters are shown to be compatible and a neat synthesis procedure, simple and flexible, is given for the tanh sigmoid. It starts with the given parameters N, K, I, z_min, m and computes simple bounds of p, G, ξ, θ, and M. Numerical tests and comments reveal qualities and shortcomings of the method.

The identification of long-length impulse responses represents a challenge in the context of many applications, like echo cancellation. Recently, the problem has been addressed in the framework of low-rank systems, using a decomposition of the impulse response based on the nearest Kronecker product and low-rank approximations. As a result, the original system identification problem that involves a long-length finite impulse response filter is reshaped as a combination of two (much) shorter filters, which leads to significant advantages. In this context, the benchmark Wiener filter can be formulated in terms of an iterative algorithm, where the estimates of the two component filters are sequently updated. However, matrix inversion operations are required within this algorithm. In this article, we develop a new version of the decomposition-based iterative Wiener filter, which relies on the conjugate gradient (CG) method and avoids matrix inversion. Simulations performed in the framework of echo cancellation indicate the good performance of the proposed solution, which outperforms the conventional Wiener filter (implemented using CG updates) and inherits the advantages of the decomposition-based approach.

In linear system identification problems, the Wiener filter represents a popular tool and stands as an important benchmark. Nevertheless, it faces significant challenges when identifying long-length impulse responses. In order to address the related shortcomings, the solution presented in this paper is based on a third-order tensor decomposition technique, while the resulting sets of Wiener–Hopf equations are solved with the conjugate gradient (CG) method. Due to the decomposition-based approach, the number of coefficients (i.e., the parameter space of the filter) is greatly reduced, which results in operating with smaller data structures within the algorithm. As a result, improved robustness and accuracy can be achieved, especially in harsh scenarios (e.g., limited/incomplete sets of data and/or noisy conditions). Besides, the CG-based solution avoids matrix inversion operations, together with the related numerical and complexity issues. The simulation results are obtained in a network echo cancellation scenario and support the performance gain. In this context, the proposed iterative Wiener filter outperforms the conventional benchmark and also some previously developed counterparts that use matrix inversion or second-order tensor decompositions.

The paper shows rigorously how to build a KWTA selector from a classical neural Hopfield network in continuous time. The analytical relations between parameters result in a step-by-step accurate and flexible procedure to calculate the amplifiers gain, the processing and the resetting thresholds and the bias current.

Sensors in many applications must select the largest element in a sequence of currents. This can be performed in an analog way by the Winner-Take-All (WTA) circuit. This paper considers the classic version of the WTA Lazzaro circuit, working with MOS devices in a subthreshold regime. Since the separation of the gainer by analytically computable “decision levels” has recently been introduced, this paper aims to numerically verify and discuss these levels and their dependence on circuit and device parameters. For $V_T$, the threshold voltage of MOS devices, which is primarily responsible for differences between components (mismatch), its relationship with the output voltages is theoretically demonstrated and numerically checked.

The paper pioneers a thorough mathematical approach for the Lazzaro variant of the W(inner) T(ake) A(ll) maximum rank and amplitude analog selector. Two exact levels of output which split the maximum and determine the resolution, are found for the first time. At the input, a list of currents $$\left( I_{1},I_{2},\ldots ,I_{N}\right) $$I1,I2,…,IN from a large family $${{\mathcal {L}}}$$L with smallest relative distance $$\Delta $$Δ on a $$\left[ 0,I_{M}\right] $$0,IM scale is applied. To distinguish the largest current $$I_{w}$$Iw (the winner) from the second largest $$I_{l}$$Il (the loser), the paper proposes two decision levels, $${\overline{D}}$$D¯ and $${\underline{D}}$$D̲ , for the output voltage list $$\left( U_{1},U_{2},\ldots ,U_{N}\right) $$U1,U2,…,UN . The upper level $${\overline{D}}$$D¯ is surpassed only by the $$U_{w}$$Uw winner and encodes the winning rankw. All other ranks are placed under the lower level $${\underline{D}}$$D̲ . Two rigorously treated optimization problems with inequality constraints lead to the identification of two input lists that yield the levels $${\overline{D}}$$D¯ and $${\underline{D}}$$D̲ as outputs. They are valid for processing any list in the $${\mathcal {L}}$$L family. The index $$\left( {\overline{D}}-{\underline{D}}\right) /U_{M}$$D¯-D̲/UM —“the output resolution”—expresses how large the gap between the first and the second component on the $$\left[ 0,U_{M}\right] $$0,UM scale is. It exceeds “the input resolution,” i.e., the similar index $$\Delta /I_{M}$$Δ/IM at the input and the two depend monotonically on each other. Widely commented numerical examples are presented.