相关论文: The Latent Structure of Dictionaries
How many words are needed to define all the words in a dictionary? Graph-theoretic analysis reveals that about 10% of a dictionary is a unique Kernel of words that define one another and all the rest, but this is not the smallest such…
A dictionary defines words in terms of other words. Definitions can tell you the meanings of words you don't know, but only if you know the meanings of the defining words. How many words do you need to know (and which ones) in order to be…
Meaning cannot be based on dictionary definitions all the way down: at some point the circularity of definitions must be broken in some way, by grounding the meanings of certain words in sensorimotor categories learned from experience or…
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…
Language models often generate long chain-of-thought traces, but it remains unclear how much of this reasoning is necessary for preserving the final prediction. We study this through the lens of overcomplete reasoning traces: generated…
A coreset (or core-set) of a dataset is its semantic compression with respect to a set of queries, such that querying the (small) coreset provably yields an approximate answer to querying the original (full) dataset. In the last decade,…
Most language modeling methods rely on large-scale data to statistically learn the sequential patterns of words. In this paper, we argue that words are atomic language units but not necessarily atomic semantic units. Inspired by HowNet, we…
The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a…
We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of…
A total dominating set of a graph $G=(V,E)$ is a subset $D \subseteq V$ such that every vertex in $V$ is adjacent to some vertex in $D$. Finding a total dominating set of minimum size is NP-hard on planar graphs and W[2]-complete on general…
In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…
The cognitive constraints that humans exhibit in their social interactions have been extensively studied by anthropologists, who have highlighted their regularities across different types of social networks. We postulate that similar…
Dense word embeddings, which encode semantic meanings of words to low dimensional vector spaces have become very popular in natural language processing (NLP) research due to their state-of-the-art performances in many NLP tasks. Word…
Deep networks are frequently tuned to novel tasks and continue learning from ongoing data streams. Such sequential training requires consolidation of new and past information, a challenge predominantly addressed by retaining the most…
Sentences are important semantic units of natural language. A generic, distributional representation of sentences that can capture the latent semantics is beneficial to multiple downstream applications. We observe a simple geometry of…
Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets construction…
Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We…
We construct non-power words which have small image in SL(2; 22n) for each n. In particular, the corresponding word maps are non-surjective. We also use this to construct word maps whose values are precisely the identity and a single…
A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…
Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily…