Semantic Tagging with Deep Residual Networks

We propose a novel semantic tagging task, sem-tagging, tailored for the purpose of multilingual semantic parsing, and present the first tagger using deep residual networks (ResNets). Our tagger uses both word and character representations and includes a novel residual bypass architecture. We evaluate the tagset both intrinsically on the new task of semantic tagging, as well as on Part-of-Speech (POS) tagging. Our system, consisting of a ResNet and an auxiliary loss function predicting our semantic tags, significantly outperforms prior results on English Universal Dependencies POS tagging (95.71% accuracy on UD v1.2 and 95.67% accuracy on UD v1.3).Comment: COLING 2016, camera ready versio

Expressive Power of Abstract Meaning Representations

The syntax of abstract meaning representations (AMRs) can be defined recursively, and a systematic translation to first-order logic (FOL) can be specified, including a proper treatment of negation. AMRs without recurrent variables are in the decidable two-variable fragment of FOL. The current definition of AMRs has limited expressive power for universal quantification (up to one universal quantifier per sentence). A simple extension of the AMR syntax and translation to FOL provides the means to represent projection and scope phenomena. </jats:p

Convergence guarantees for forward gradient descent in the linear regression model

Renewed interest in the relationship between artificial and biological neural networks motivates the study of gradient-free methods. Considering the linear regression model with random design, we theoretically analyze in this work the biologically motivated (weight-perturbed) forward gradient scheme that is based on random linear combination of the gradient. If d denotes the number of parameters and k the number of samples, we prove that the mean squared error of this method converges for k≳d2log(d) with rate d2log(d)/k. Compared to the dimension dependence d for stochastic gradient descent, an additional factor dlog(d) occurs.</p

Convergence guarantees for forward gradient descent in the linear regression model

Renewed interest in the relationship between artificial and biological neural networks motivates the study of gradient-free methods. Considering the linear regression model with random design, we theoretically analyze in this work the biologically motivated (weight-perturbed) forward gradient scheme that is based on random linear combination of the gradient. If d denotes the number of parameters and k the number of samples, we prove that the mean squared error of this method converges for $k\gtrsim d^2\log(d)$ with rate $d^2\log(d)/k.$ Compared to the dimension dependence d for stochastic gradient descent, an additional factor $d\log(d)$ occurs.Comment: 15 page