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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,341 papers · 148 categories

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24487195 · Oct 201919922001200920182026
48 results for word norm

Paper refines cross-lingual word embeddings using Manhattan norm.

problem Sensitivity of 2\ell_{2} norm loss function to outliers in CLWEs.
method Post-processing step using 1\ell_{1} norm to improve CLWEs.
result The 1\ell_{1} refinement substantially outperforms state-of-the-art baselines.

The paper proves norms on braid group commutator subgroup are unbounded.

problem Understanding norms on the commutator subgroup of infinite braid groups.
method Constructed stably unbounded norms and showed equivalence to biinvariant word norms.
result Found norms on commutator subgroup are equivalent to biinvariant word norms and are stably unbounded.

We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isometric embedding of a locally compact tree into the biinvariant Cayley graph of a nonabelian free group. We investigate the geometry of cyclic …

2013-10-10abs ↗pdf ↗

Sparse activations in neural models correlate with frequent words, suggesting sparsity is natural.

problem Interpretability and resource efficiency in neural language models.
method Used the Taxi-Euclidean norm to measure sparsity and analyzed gradients and activations of frequent words.
result Frequent input words are associated with sparse activations, while frequent target words are associated with dispersed activations.

Let G be a word-hyperbolic group, obtained as a graph of free groups amalgamated along cyclic subgroups. If H_2(G;Q) is nonzero, then G contains a closed hyperbolic surface subgroup. Moreover, the unit ball of the Gromov-Thurston norm on H_2(G;R) is a finite-sided rational polyhedron.

2008-03-28abs ↗pdf ↗

New ONMF model minimizes KL divergence for better sparse data modeling.

problem Clustering and data modeling with sparse vectors.
method Developed KL-ONMF algorithm based on alternating optimization.
result KL-ONMF outperforms Frobenius-norm ONMF for document classification and hyperspectral image unmixing.

We prove a rigidity theorem for the geometry of the unit ball in random subspaces of the scl norm in B_1^H of a free group. In a free group F of rank k, a random word w of length n (conditioned to lie in [F,F]) has scl(w)=log(2k-1)n/6log(n) + o(n/log(n)) with high probability, and the unit ball in a subspace spanned by…

2011-04-10abs ↗pdf ↗

The paper offers generalization bounds for Transformers that ignore sequence length.

problem Developing generalization bounds for Transformers that are independent of sequence length.
method Covering number approach to upper bound Rademacher complexity of bounded linear transformations.
result Theoretical bounds for Transformer generalization are independent of sequence length.

Unified scalable equivalent formulations for Schatten quasi-norms improve efficiency.

problem Efficiently solving Schatten quasi-norm minimization problems for large-scale matrices.
method Proved equivalence between Schatten-p quasi-norm and product/sum of Schatten-p1 and p2 norms of factor matrices.
result Transformed SQNM problems into simpler, more efficient algorithms for p>1/2.

Study on quantitative aspects of trace polynomials in free groups.

problem Understanding the exact formula and bounds for trace polynomials in free groups.
method Proved exact formula for leading homogeneous part, obtained sharp bounds, studied random words, and provided deterministic algorithm.
result Sharp bounds on the degree of trace polynomials and growth rates of polynomial sizes.

Transformers trained with three normalization changes outperform state-of-the-art on low-resource translation tasks.

problem Improving the training of Transformers, especially on low-resource datasets.
method Three normalization changes: PreNorm, ScaleNorm, and FixNorm.
result Significant improvements in BLEU scores on low-resource translation tasks.

A new method selects anchor words for better topic discovery in text corpora.

problem Selecting anchor words for improved topic modeling in text corpora.
method Proposes a new greedy method to find a minimum edge-weight anchor clique in a word similarity graph.
result The proposed method outperforms existing methods on topic quality and is faster.

There are certain families of words and word sequences (words in the generators of a two-generator group) that arise frequently in the Teichm{ü}ller theory of hyperbolic three-manifolds and Kleinian and Fuchsian groups and in the discreteness problem for two generator matrix groups. We survey some of the families of su…

2007-01-20abs ↗pdf ↗

Probabilistic FastText captures multiple word senses and sub-word structures.

problem Capturing multiple word senses and sub-word structures in word embeddings.
method Probabilistic FastText uses Gaussian mixture densities to represent words, sharing statistical strength across sub-word structures and capturing different word senses.
result Probabilistic FastText outperforms existing models on word-similarity benchmarks and discerning different meanings.

We obtain sharp estimates on the growth rate of stable commutator length on random (geodesic) words, and on random walks, in hyperbolic groups and groups acting nondegenerately on hyperbolic spaces. In either case, we show that with high probability stable commutator length of an element of length nn is of order $n/\l…

2010-08-29abs ↗pdf ↗

We discuss a topological approach to words introduced by the author. Words on an arbitrary alphabet are approximated by Gauss words and then studied up to natural modifications inspired by the Reidemeister moves on knot diagrams. This leads us to a notion of homotopy for words. We introduce several homotopy invariants …

2006-09-19abs ↗pdf ↗

The abstract explains how word and relation representations capture semantic meaning.

problem Understanding how word and relation representations capture semantic meaning.
method Theoretical justification and extension of geometric relationships between word embeddings and knowledge graph representations.
result The geometric relationships between word embeddings correspond to semantic relations between words and entities in knowledge graphs.

This paper improves monaural source enhancement using SDR as an objective function.

problem Maximizing signal-to-distortion ratio (SDR) for better monaural source enhancement.
method Uses signal-to-distortion ratio (SDR) as an objective function to improve monaural source enhancement.
result The proposed method achieved better performance than conventional methods.

Approaches KL divergence for learning multi-sense word distributions.

problem Capturing the polysemy and uncertainty of words in word embeddings.
method Modeling words as multi-sense Gaussian mixtures and using KL divergence for learning.
result The proposed approach effectively captures word entailment and distribution similarity.

Word2vec improved but lacks multi-meaning words; ConEc creates new embeddings.

problem Lack of meaningful embeddings for words with multiple meanings and OOV words.
method Context encoders (ConEc) extend word2vec by multiplying embeddings with context vectors.
result ConEc creates embeddings for OOV words and words with multiple meanings based on local contexts.

Proposes MorphMine for unsupervised morpheme segmentation to improve word embeddings.

problem Lack of semantic information in word-level analysis for infrequent and out-of-vocabulary words.
method MorphMine applies a parsimony criterion to hierarchically segment words into the fewest number of morphemes.
result MorphMine segments words into human-verified morphemes and improves word embedding quality.

End-to-end ASR model combines word and character representation for improved performance.

problem Difficulty in training with word-level supervision due to sparsity of examples.
method Multi-task learning framework combining word and character representations.
result Improved word-error rate (WER) by interpolating between word-level and character-level models.

Paper analyzes word embedding composition using tensor decomposition.

problem Given vector representations of two words, compute a vector for the entire phrase.
method Generative model with low rank Tucker decomposition of word embedding correlations.
result Word embeddings and a core tensor can be derived from the Tucker decomposition.

The study examines how character and word-level representations improve sentence-level tasks.

problem Improving the quality of word and sentence representations using character-level information.
method Feature-wise sigmoid gating mechanism for combining character and word-level representations.
result Modeling characters improves final word and sentence representations, especially for less frequent words.

By defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to show that there exist Gauss words that are not homotopically equivalent to the empty Gauss word, disproving a conjecture by Turaev. In fact, …

2009-01-31abs ↗pdf ↗

We introduce a topological approach to words. Words are approximated by Gauss words and then studied up to natural modifications inspired by homotopy transformations of curves on the plane.

2005-03-29abs ↗pdf ↗

A longstanding question of Gromov asks whether every one-ended word-hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed hyperbolic surface. An infinite family of word-hyperbolic groups can be obtained by taking doubles of free groups amalgamated along words that are not proper powers. W…

2009-10-25abs ↗pdf ↗