To learn reliable rules that can generalize to novel situations, the brain must be capable of imposing some form of regularization. Here we suggest, through theoretical and computational arguments, that the combination of noise with synchronization provides a plausible mechanism for regularization in the nervous system. The functional role of regularization is considered in a general context in which coupled computational systems receive inputs corrupted by correlated noise. Noise on the inputs is shown to impose regularization, and when synchronization upstream induces time-varying correlations across noise variables, the degree of regularization can be calibrated over time. The resulting qualitative behavior matches experimental data from visual cortex.

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by nonideal biological building blocks that can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error, which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. We discuss range of situations in which the mechanisms we model arise in brain science and draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.

A goal of central importance in the study of hierarchical models for object recognition -- and indeed the visual cortex -- is that of understanding quantitatively the trade-off between invariance and selectivity, and how invariance and discrimination properties contribute towards providing an improved representation useful for learning from data. In this work we provide a general group-theoretic framework for characterizing and understanding invariance in a family of hierarchical models. We show that by taking an algebraic perspective, one can provide a concise set of conditions which must be met to establish invariance, as well as a constructive prescription for meeting those conditions. Analyses in specific cases of particular relevance to computer vision and text processing are given, yielding insight into how and when invariance can be achieved. We find that the minimal sets of transformations intrinsic to the hierarchical model needed to support a particular invariance can be clearly described, thereby encouraging efficient computational implementations.

Drawing on recent progress in auditory neuroscience, we present a novel speech feature analysis technique based on localized spectro- temporal cepstral analysis of speech. We proceed by extracting localized 2D patches from the spectrogram and project onto a 2D discrete cosine (2D-DCT) basis. For each time frame, a speech feature vector is then formed by concatenating low-order 2D- DCT coefficients from the set of corresponding patches. We argue that our framework has significant advantages over standard one- dimensional MFCC features. In particular, we find that our features are more robust to noise, and better capture temporal modulations important for recognizing plosive sounds. We evaluate the performance of the proposed features on a TIMIT classification task in clean, pink, and babble noise conditions, and show that our feature analysis outperforms traditional features based on MFCCs.

We present a method that de-modulates a narrowband magnitude spectrogram S(f, t) into a frequency modulation term cos(Φ)(f,t)) which represents the underlying harmonic carrier, and an amplitude modulation term A(f,t) which represents the spectral envelope. Our method operates by performing a two-dimensional local patch analysis of the spectrogram, in which each patch is factored into a local carrier term and a local amplitude envelope term using a Max-Gabor analysis. We demonstrate the technique over a wide variety of speakers, and show how the spectrograms in each case may be adequately reconstructed as S(f, t) = A(f, t)cos(Φ(f, t)).

We perform phonetic classification with an architecture whose elements are binary classifiers trained via linear regularized least squares (RLS). RLS is a simple yet powerful regularization algorithm with the desirable property that a good value of the regularization parameter can be found efficiently by minimizing leave-one-out error on the training set. Our system achieves state-of-the-art single classifier performance on the TIMIT phonetic classification task, (slightly) beating other recent systems. We also show that in the presence of additive noise, our model is much more robust than a well-trained Gaussian mixture model.

We present a 2-D spectro-temporal Gabor filterbank based on the 2-D Fast Fourier Transform, and show how it may be used to analyze localized patches of a spectrogram. We argue that the 2-D Gabor filterbank has the capacity to decompose a patch into its underlying dominant spectro-temporal components, and we illustrate the response of our filterbank to different speech phenomena such as harmonicity, formants, vertical onsets/offsets, noise, and overlapping simultaneous speakers. Index Terms: speech analysis, spectro-temporal filterbanks, 2-D Gabor

We present an algorithm for reconstructing a time-domain signal from the magnitude of a short-time Fourier transform (STFT). In contrast to existing algorithms based on alternating projections, we offer a novel approach involving numerical root-finding combined with explicit smoothness assumptions. Our technique produces high-quality reconstructions that have lower signal-to-noise ratios when compared to other existing algorithms. If there is little redundancy in the given STFT, in particular, the algorithm can produce signals which also sound significantly better perceptually, as compared to existing work. Index Terms: signal reconstruction, phase retrieval. 1.

We present a method that analyzes a two-dimensional magnitude spectrogram S(f, t) into its local constituent spectro-temporal amplitudes A(f,t), frequencies F(f, t), orientations Θ(f, t), and phases φ(f, t). The method operates by performing a twodimensional local Gabor-like analysis of the spectrogram, retaining only the parameters of the 2D-Gabor filter with maximal amplitude response within the local region. We demonstrate the technique over a wide variety of speakers, and show how the spectrograms in each case may be adequately reconstructed using the parameters of the Max-Gabor analysis. Finally, we discuss the nature of the extracted Max-Gabor parameters. Index Terms: spectrogram analysis, spectrogram reconstruction, two-dimensional Gabor, spectro-temporal frequency, spectrotemporal orientation. 1.