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Found 20 papers, 9 papers with code
Multi-layer random features and the approximation power of neural networks
To achieve a certain approximation error the required number of neurons in each layer is defined by the RKHS norm of the target function.
Gradient Descent Fails to Learn High-frequency Functions and Modular Arithmetic
In the novel framework, the hardness of a class is usually quantified by the variance of the gradient with respect to a random choice of a target function.
Intractability of Learning the Discrete Logarithm with Gradient-Based Methods
The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols.
Autoencoders for a manifold learning problem with a Jacobian rank constraint
This constraint is included in the objective function as a new term, namely a squared Ky-Fan $k$-antinorm of the Jacobian function.
Computing a partition function of a generalized pattern-based energy over a semiring
For a general language $\Gamma$ and non-positive weights, the minimization task can be carried out in ${\mathcal O}(|V|\cdot |\overline{\Gamma^{\cap}}|^2)$ time.
On the speed of uniform convergence in Mercer's theorem
The classical Mercer's theorem claims that a continuous positive definite kernel $K({\mathbf x}, {\mathbf y})$ on a compact set can be represented as $\sum_{i=1}^\infty \lambda_i\phi_i({\mathbf x})\phi_i({\mathbf y})$ where $\{(\lambda_i,\phi_i)\}$ are eigenvalue-eigenvector pairs of the corresponding integral operator.
Spectral bounds of the $\varepsilon$-entropy of kernel classes
Further, we develop a series of lower bounds on the $\varepsilon$-entropy that can be established from a connection between covering numbers of a ball in RKHS and a quantization of a Gaussian Random Field that corresponds to the kernel $K$ by the Kosambi-Karhunen-Lo\`eve transform.
How many moments does MMD compare?
If ordered singular values of the integral operator associated with $p({\mathbf x}, {\mathbf y})$ die down rapidly, the MMD distance defined by the new symbol $p_r$ differs from the initial one only slightly.
Semantics- and Syntax-related Subvectors in the Skip-gram Embeddings
We show that the skip-gram embedding of any word can be decomposed into two subvectors which roughly correspond to semantic and syntactic roles of the word.
Reducing the dimensionality of data using tempered distributions
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i. e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a $k$-dimensional subspace.
Context Vectors are Reflections of Word Vectors in Half the Dimensions
This paper takes a step towards theoretical analysis of the relationship between word embeddings and context embeddings in models such as word2vec.
Fourier Neural Networks: A Comparative Study
We review neural network architectures which were motivated by Fourier series and integrals and which are referred to as Fourier neural networks.
Fourier analysis perspective for sufficient dimension reduction problem
It turns out that the latter problem allows a reformulation in the dual space, i. e. instead of searching for ${\mathbf g}(P{\mathbf x})$ we suggest searching for its Fourier transform.
Reproducing and Regularizing the SCRN Model
We reproduce the Structurally Constrained Recurrent Network (SCRN) model, and then regularize it using the existing widespread techniques, such as naive dropout, variational dropout, and weight tying.
Reusing Weights in Subword-aware Neural Language Models
We propose several ways of reusing subword embeddings and other weights in subword-aware neural language models.
Patterns versus Characters in Subword-aware Neural Language Modeling
Further, for every word we construct a new sequence over an alphabet of patterns.
Syllable-aware Neural Language Models: A Failure to Beat Character-aware Ones
Syllabification does not seem to improve word-level RNN language modeling quality when compared to character-based segmentation.
Combining pattern-based CRFs and weighted context-free grammars
We propose a {\em Grammatical Pattern-Based CRF model }(\GPB) that combines the two in a natural way.
Proceedings of The 38th Annual Workshop of the Austrian Association for Pattern Recognition (ÖAGM), 2014
The 38th Annual Workshop of the Austrian Association for Pattern Recognition (\"OAGM) will be held at IST Austria, on May 22-23, 2014.
Inference algorithms for pattern-based CRFs on sequence data
(Komodakis & Paragios, 2009) gave an $O(n L)$ algorithm for computing the MAP.
