The frequenciesf1, ...,fm quantify the oscillation rate of each component.

If the memory state can be addressed by its content, itisfurthermore called content-addressable.

Gating, as used in gated recurrent units (GRUs) [4] and long short-term memory (LSTM) networks [12], has become common-place in recurrent architectures. Gates facilitate the learning of longer term temporal relationships [12]. Furthermore, in the presence of noise in the input signal, gates can protect the cell state from undesired updates, thereby improving overall stability and convergence.

Knowing how the classifiers perform on unseen OOD data remains as a challenging task, owing tothetrain-test distribution divergence [3].

Wederiveinstance specific nonasymptotic and asymptotic lower bounds which generalize those of theIIDsetting.

Estimating a vector x from noisy linear measurements Ax + w often requires use of prior knowledge or structural constraints on x for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or "plug-in" denoiser function that can be designed in a modular manner based on the prior knowledge about x.

Whenconsidering networkdata,regularconvolutionsdonot hold since the data domain presents an irregular structure given by the network topology.

In particular, we will be interested in log-supermodular (LSM) potential functions as they encourage agreement between the variables upon which theyoperate.

Afundamental challenge indeep metric learning isthegeneralization capability of the feature embedding network model since the embedding network learned ontraining classes needtobeevaluated onnewtestclasses.

In addition, we present an alternative design that permits a near-optimal sublinear decoding timeofO(klog2k+klogn).