Estimator Vectors learns OOV word embeddings using subword and context clues.
problem Lack of OOV word representations in neural network models.
method Jointly learns word, subword, and context clue representations.
result Strong estimates for OOV words via combined subword and context clue embeddings.
Byte-level machine translation outperforms embedding-based methods.
problem Improving machine translation without embedding layers.
method Replacing embedding layers with one-hot representations of bytes, and using decoder-input dropout.
result Byte-to-byte machine translation achieves BLEU scores comparable to character-level and subword-level models.
Study on representations of four-punctured sphere group in hyperbolic spaces.
problem Understanding representations of the four-punctured sphere group.
method Investigation into simple-stable and Bowditch representations in Gromov-hyperbolic spaces.
result Simple-stable representations and Bowditch representations are equivalent.
New combinatorial framework for geometric realizations of subword complexes.
problem Proving or disproving geometric realizations of subword complexes of Coxeter groups.
method Algebraic combinatorics and discrete geometry framework, parameter matrices.
result Existence of parameter matrices equivalent to realizability of subword complexes as chirotopes.
The study proves a theorem about subword complexity for free group automorphisms.
problem Analyzing subword complexity for attracting fixed points of automorphisms of free groups.
method Combinatorial arguments and train tracks.
result Subword complexity of attracting fixed points is equivalent to n, n log log n, n log n, or n^2.
We propose several ways of reusing subword embeddings and other weights in subword-aware neural language models. The proposed techniques do not benefit a competitive character-aware model, but some of them improve the performance of syllable- and morpheme-aware models while showing significant reductions in model sizes…
AV-ASR system improves speech recognition with visual context.
problem Improving speech recognition accuracy with visual information.
method Transformer-based architecture with multiresolution and multimodal training.
result Multiresolution training speeds up convergence and improves WER by 18%.
A model corrects Lithuanian grammatical errors.
problem Lack of language skills and typing errors in Lithuanian.
method Transformer architectures for subword and byte-level approaches.
result F0.5=0.92 for Lithuanian grammatical error correction. Universal Language Model for Fine-tuning [arXiv:1801.06146] (ULMFiT) is one of the first NLP methods for efficient inductive transfer learning. Unsupervised pretraining results in improvements on many NLP tasks for English. In this paper, we describe a new method that uses subword tokenization to adapt ULMFiT to langua…
This paper undertakes a study of the structure of the fibers of the Chevalley exponentiation maps f(i1,…,id). The fibers of these maps f(i1,…,id) encode the nonnegative real relations amongst exponentiated Chevalley generators. Our main theorems show that the fibers admit cell stratifications, t…
We introduce Probabilistic FastText, a new model for word embeddings that can capture multiple word senses, sub-word structure, and uncertainty information. In particular, we represent each word with a Gaussian mixture density, where the mean of a mixture component is given by the sum of n-grams. This representation al…
Sequence-to-sequence attention-based models on subword units allow simple open-vocabulary end-to-end speech recognition. In this work, we show that such models can achieve competitive results on the Switchboard 300h and LibriSpeech 1000h tasks. In particular, we report the state-of-the-art word error rates (WER) of 3.5…
Traditionally, many text-mining tasks treat individual word-tokens as the finest meaningful semantic granularity. However, in many languages and specialized corpora, words are composed by concatenating semantically meaningful subword structures. Word-level analysis cannot leverage the semantic information present in su…
We investigate intersections of geodesic lines in H2 and in an associated tree T, proving the following result. Let M be a punctured hyperbolic torus and let γ be a closed geodesic in M. Any edge of any triangle formed by distinct geodesic lines in the preimage of γ in H2 is shorter then γ. However, a simil…
Acoustic Neighbor Embeddings map speech and text to fixed dimensions for phonetic confusability.
problem Mapping speech and text to fixed dimensions for phonetic confusability.
method Adapting SNE to sequential inputs, training two encoder neural networks.
result More accurate results with low-dimensional embeddings in word recognition tasks.
We consider the problem of making machine translation more robust to character-level variation at the source side, such as typos. Existing methods achieve greater coverage by applying subword models such as byte-pair encoding (BPE) and character-level encoders, but these methods are highly sensitive to spelling mistake…
Text normalization is an important enabling technology for several NLP tasks. Recently, neural-network-based approaches have outperformed well-established models in this task. However, in languages other than English, there has been little exploration in this direction. Both the scarcity of annotated data and the compl…
Paper reduces vocabulary losslessly for language model cooperation.
problem Language models struggle to cooperate with different tokenizations.
method Established a theoretical framework for lossless vocabulary reduction.
result Efficiently converts models with different tokenizations to cooperate with maximal common vocabulary.
SAFER method certifies robustness to word substitutions without model structure.
problem Certified robustness against synonymous word substitutions in NLP models.
method Randomized smoothing with stochastic ensemble of randomized inputs.
result Significantly outperforms state-of-the-art methods for certified robustness.
New representation theory for closed geodesic subflows.
problem Classifying representations with good geometric properties.
method Restricting to invariant closed geodesic subflows.
result Equivalent characterizations and properties of new representations.
Proves EGF representations in specific geometric contexts.
problem Understanding representations of groups with hyperbolic properties.
method Analyzes projectively convex cocompact manifolds and convex projective manifolds with generalized cusps.
result Holonomy representations of specific geometric manifolds are EGF representations.
The paper establishes isomorphisms and constructs colored versions of Lawrence representations.
problem Understanding isomorphisms and colored versions of Lawrence representations.
method Explicit isomorphisms and construction of colored versions.
result Matrices for colored versions of BKL and Lawrence representations provided.
Study k-positive surface group representations and their degenerations.
problem Understanding the behavior of surface group representations under degenerations.
method Introduced k-positive representations and studied their degenerations using a limit theorem for positively ratioed representations.
result Degenerations of k-positive representations can lead to limits that are at least (k-3)-positive and irreducible limits are (k-1)-positive.
Develops theory of Anosov representations for Fuchsian groups, showing stability and analytical properties.
problem Understanding geometrically finite Fuchsian groups and their representations.
method Theory of Anosov representations, type-preserving deformations, limit maps, relative Anosov and dominated representations.
result Cusped Hitchin representations are Borel Anosov, stable under deformations, and limit maps vary analytically.
This article reviews statistical methods for learning data representations.
problem Learning meaningful representations of data.
method Statistical perspective on unsupervised and supervised representation learning.
result Recent advances in representation learning from a statistical viewpoint.
New representations defined for groups and graphs, with applications to stable representations.
problem Defining and constructing new types of representations for groups and graphs.
method Introducing (R,Λ)-directed Anosov representations and using Fock-Goncharov positivity to construct them. result Constructs large families of primitive stable representations from F2 to PGL(V), including non-discrete and non-faithful examples. Collar lemma proven for certain surface group representations.
problem Proving a collar lemma for specific surface group representations.
method Using partial hyperconvexity properties and Anosov representations.
result 'Positivity properties' hold for partially hyperconvex representations.
Study subgroup actions on mapping class groups using Heisenberg representations.
problem Untwisting representations of mapping class groups on Heisenberg subgroups.
method Restrict and analyze twisted representations of mapping class groups to Heisenberg subgroups.
result Untwisting representations on Torelli group for any Heisenberg representation.
Researchers describe unitary representations of mixed braid groups.
problem Understanding unitary representations of mixed braid groups.
method Explicitly describe unitary representations on cohomology of Abelian branched covers.
result Image of the representation is generated by complex reflections and related to the multivariate Burau representation.
This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka r…
A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this pape…
Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed representations. These are Anosov representations with the additional condition that certain …
Polynomial representations found in surface braid and mapping class groups.
problem Homological representations of surface braid and mapping class groups.
method Study of homological representation functors and short exact sequences.
result Many homological representation functors are polynomial.
In this paper, we introduce a study of prolongations of representations of Lie groups. We obtain a faithful (one-to-one) representation of TG where G is a finite-dimensional Lie group and TG is the tangent bundle of G, by using (not necessarily faithful) representations of G. We show that tangent functions of Lie group…
Paper addresses the disparity between sampled and mean representations in disentangled learning.
problem Disparity between sampled and mean representations in disentangled learning.
method Proposes a method to eliminate the disparity by proving and utilizing the relationship between total correlation of sampled and mean representations for multivariate normal distributions.
result Demonstrates that a factorized mean representation can have lower total correlation than the sampled representation.
New Θ-positive representations of surface groups discovered.
problem Generalizing Lusztig's total positivity to surface groups.
method Introducing Θ-positivity and proving properties of Θ-positive representations. result Discrete and faithful Θ-positive representations exist and form open sets in representation varieties. New representations for surface groups expand known Anosov classes.
problem Understanding new types of representations for surface groups.
method Introducing and studying simple Anosov representations of closed hyperbolic surface groups.
result Simple Anosov representations strictly contain Anosov representations.
New findings on cusped Borel Anosov representations and their properties.
problem Characterizing and understanding cusped Borel Anosov representations.
method Analyzing representations of lattices in PGL2(R) to PGLd(R). result Cusped Borel Anosov representations with specific properties are Hitchin representations.
The paper formalizes criteria for non-spurious and disentangled representations using causal methods.
problem Formalizing criteria for non-spurious and disentangled representations in representation learning.
method Causal perspective, counterfactual quantities, observable consequences of causal assertions.
result Computable metrics for assessing representation learning based on observed data.
Characterizes Anosov reducible representations in terms of eigenvalues.
problem Understanding Anosov representations in reducible settings.
method Characterizes Anosov representations using eigenvalue magnitudes of irreducible block factors.
result Connected components of character varieties do not contain reducible representations for many non-elementary hyperbolic groups.
This study compares global vs local observation and action representations for DRL in RTS games.
problem Improving Deep Reinforcement Learning performance in RTS games.
method Comparing two observation and action representations in μRTS.
result Local representation outperforms global representation in resource harvesting tasks.
Convex-cocompact groups in infinite hyperbolic space are deformable.
problem Understanding deformability of convex-cocompact groups in infinite hyperbolic spaces.
method Proving convex-cocompact representations form an open set and using bending to deform them.
result Deformable convex-cocompact representations of surface groups not conjugate to exotic PSL(2,R) representations.
In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in arXiv:1305.2620, we show that order preserving representations into Lie groups of Hermit…
Study local structure of knot group representations into SL(n,C).
problem Understanding the local structure of knot group representations.
method Analysis of tangent cone and use of Luna's slice theorem.
result Local structure of representation variety at diagonal representations.
We propose a family of new representations of the braid groups on surfaces that extend linear representations of the braid groups on a disc such as the Burau representation and the Lawrence-Krammer-Bigelow representation.
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe the structure of the Zariski closure of their image. Furthermore we prove that t…
New method finds Fuchsian representations dominating others in surface group representations.
problem Finding Fuchsian representations that dominate others in surface group representations.
method Straightening the pleated plane and applying strip deformations.
result There exists a Fuchsian representation that strictly dominates a given non-Fuchsian representation.
We characterize groups admitting Anosov representations into SL(3,R), projective Anosov representations into SL(4,R), and Borel Anosov representations into SL(4,R). More generally, we obtain bounds on the cohomological dimension of groups admitting Pk-Anosov r…