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Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this ...

We define an extension of classical additive splines for multivariate function approximation that we call hierarchical splines. We show that the case of hierarchical, additive, piece-wise linear splines includes present-day ...

The properties of a representation, such as smoothness, adaptability, generality, equivari- ance/invariance, depend on restrictions imposed during learning. In this paper, we propose using data symmetries, in the sense of ...

We study the average CVloo stability of kernel ridge-less regression and derive corresponding risk bounds. We show that the interpolating solution with minimum norm has the best CVloo stability, which in turn is controlled ...

THIS MEMO IS REPLACED BY CBMM MEMO 90 A main puzzle of deep networks revolves around the absence of overfitting despite overparametrization and despite the large capacity demonstrated by zero training error on randomly ...

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn ...

We extend i-theory to incorporate not only pooling but also rectifying nonlinearities in an extended HW module (eHW) designed for supervised learning. The two operations roughly correspond to invariance and selectivity, ...

[formerly titled "Why and When Can Deep – but Not Shallow – Networks Avoid the Curse of Dimensionality: a Review"] The paper reviews and extends an emerging body of theoretical results on deep learning including the ...

Recognition of speech, and in particular the ability to generalize and learn from small sets of labelled examples like humans do, depends on an appropriate representation of the acoustic input. We formulate the problem of ...

Deep learning networks with convolution, pooling and subsampling are a special case of hierar- chical architectures, which can be represented by trees (such as binary trees). Hierarchical as well as shallow networks can ...