Search Results for « Gradient Estimation »

Abstract A real-time population receptive field mapping procedure based on gradient descent is proposed. Model-free receptive fields produced by the algorithm are evaluated in context of simulated data exhibiting different levels of temporally autocorrelated noise and spatial point spread. As with any model-free approach, the exact shape of receptive fields produced by the real-time algorithm depends on the stimulus. Nevertheless, estimated receptive fields show good correspondence with ground-truth receptive fields in terms of both position and size. Furthermore, fitting a parametric model to the previously obtained estimates approximates the exact shape of the true underlying receptive fields well.

Simplified spiking neuron models such as the Adaptive Exponential Integrate-and-Fire (AdEx) model reproduce the firing behaviour of diverse neuron types at a fraction of the cost of biophysically detailed models, making them attractive for large-scale brain simulation. Fitting their parameters to recordings, however, still relies on derivative-free search such as grid search or evolutionary algorithms, because the discrete spike-and-reset mechanism renders these models non-differentiable. Surrogate gradients, used in deep spiking networks, replace the spike derivative with a smooth approximation on the backward pass. Whether they also enable efficient gradient-based parameter estimation for single simplified neurons is untested. We implement a differentiable AdEx model with a surrogate-gradient variant in the Jaxley framework. The implementation is on par with target-compiled C++ Brian2 code while remaining end-to-end differentiable, vmap-batchable and GPU/TPU-portable. It is 200 times faster than Brian2’s default runtime mode. Across a recovery-radius benchmark of 2,700 paired runs, gradient-based fitting never matched a gradient-free Nelder–Mead baseline. At sub-threshold levels, gradient descent instead beats Nelder–Mead. The obstacle is therefore the spike mechanism and the loss geometry it induces, not gradient descent itself.

Abstract In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove its fast convergence. We also prove the local convergence of the Newton method under the assumption of strong convexity. Our proposed methods offer a more efficient and effective approach, particularly for \textmd{$L_1$} regularization and group regularization problems, as they involve variable selection with each update. Through numerical experiments, we demonstrate the efficiency of our methods in solving problems encountered in sparse estimation. Our contributions include theoretical guarantees and practical applications for various problems.

Abstract Polarization of alkali vapor is a key parameter in the atomic magnetometer's response to the applied magnetic field. In this paper, estimating polarization is used by studying the transmission behavior of the pump beam as a function of intensity. In our study, the transmission of circularly polarized light exhibits nontrivial features such as nonlinear absorption and relaxation. The advantages of this method are its simplicity for characterizing polarization and its accuracy. The intensity and wavelength of the pumping laser are considered for studying polarization changes and polarization gradient. This method could apply directly to the quantum computing in devices like memory, gate, clock, and for reference cell. Also, this method is fast, reliable and accurate and doesn't need on resonance detection which makes it more suitable for ZULF NMR detection.