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We compare the maximum achievable rates in single-carrier and OFDM modulation schemes, under the practical assumptions of i.i.d. finite alphabet inputs and linear ISI with additive Gaussian noise. We show that the Shamai-Laroia approximation serves as a bridge between the two rates: while it is well known that this approximation is often a lower bound on… (More)

We use smoothed analysis techniques to provide guarantees on the training loss of Multilayer Neural Networks (MNNs) at differentiable local minima. Specifically, we examine MNNs with piecewise linear activation functions, quadratic loss and a single output, under mild over-parametrization. We prove that for a MNN with one hidden layer, the training error is… (More)

We consider the discrete-time intersymbol interference (ISI) channel model, with additive Gaussian noise and fixed i.i.d. inputs. In this setting, we investigate the expression put forth by Shamai and Laroia as a conjectured lower bound for the input-output mutual information after application of a MMSE-DFE receiver. A low-SNR expansion is used to prove… (More)

We investigate the existance of simple policies in finite discounted cost Markov Decision Processes, when the discount factor is not constant. We introduce a class called " exponentially representable " discount functions. Within this class we prove existence of optimal policies which are eventually stationary—from some time N onward, and provide an… (More)

—We consider mean squared estimation with lookahead of a continuous-time signal corrupted by additive white Gaussian noise. We investigate the connections between lookahead in estimation, and information under this model. We show that the mutual information rate function, i.e., the mutual information rate as function of the signal-to-noise ratio (SNR) does… (More)

We generalize the geometric discount of finite discounted cost Markov Decision Processes to " exponentially representable " discount functions, prove existence of optimal policies which are stationary from some time N onward, and provide an algorithm for their computation. Outside this class, optimal " N-stationary " policies in general do not exist.

We consider mean squared estimation with lookahead of a continuous-time signal corrupted by additive white Gaussian noise. We show that the mutual information rate function, i.e., the mutual information rate as function of the signal-to-noise ratio (SNR), does not, in general, determine the minimum mean squared error (MMSE) with fixed finite lookahead, in… (More)

—We consider mean squared estimation of a continuous-time signal corrupted by additive white Gaus-sian noise. We investigate the trade-off between lookahead and estimation-loss under this model. We study the class of continuous-time stationary Gauss-Markov processes (Ornstein-Uhlenbeck processes) as channel inputs, and explicitly characterize the behavior… (More)

- Yair Carmon, John C. Duchi, Oliver Hinder, Aaron Sidford
- ArXiv
- 2016

We present an accelerated gradient method for non-convex optimization problems with Lips-chitz continuous first and second derivatives. The method requires time O(−7/4 log(1//)) to find an-stationary point, meaning a point such that ∇f (x) ≤ , improving the O(−2) complexity of gradient descent. Furthermore, our method is Hessian-free, relying only on… (More)

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