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.
Word2vec (Mikolov et al., 2013) has proven to be successful in natural language processing by capturing the semantic relationships between different words. Built on top of single-word embeddings, paragraph vectors (Le and Mikolov, 2014) find fixed-length representations for pieces of text with arbitrary lengths, such a…
A classical link in 3-space can be represented by a Gauss paragraph encoding a link diagram in a combinatorial way. A Gauss paragraph may code not a classical link diagram, but a diagram with virtual crossings. We present a criterion and a linear algorithm detecting whether a Gauss paragraph encodes a classical link. W…
A Gauss paragraph is a combinatorial formulation of a generic closed curve with multiple components on some surface. A virtual string is a collection of circles with arrows that represent the crossings of such a curve. Every closed curve has an underlying virtual string and every virtual string has an underlying Gauss …
Classic Topic Models are built under the Bag Of Words assumption, in which word position is ignored for simplicity. Besides, symmetric priors are typically used in most applications. In order to easily learn topics with different properties among the same corpus, we propose a new line of work in which the paragraph str…
In this paper we use theory of embedded graphs on oriented and compact PL-surfaces to construct minimal realizations of signed Gauss paragraphs. We prove that the genus of the ambient surface of these minimal realizations can be seen as a function of the maximum number of Carter's circles. For the case of signed Gaus…
Feature extraction has gained increasing attention in the field of machine learning, as in order to detect patterns, extract information, or predict future observations from big data, the urge of informative features is crucial. The process of extracting features is highly linked to dimensionality reduction as it impli…
We study finite sample expressivity, i.e., memorization power of ReLU networks. Recent results require N hidden nodes to memorize/interpolate arbitrary N data points. In contrast, by exploiting depth, we show that 3-layer ReLU networks with Ω(N) hidden nodes can perfectly memorize most datasets with N po…
Learning latent representations from long text sequences is an important first step in many natural language processing applications. Recurrent Neural Networks (RNNs) have become a cornerstone for this challenging task. However, the quality of sentences during RNN-based decoding (reconstruction) decreases with the leng…
Generative diffusion models gradually memorize training data, losing independent dimensions.
problem Understanding how generative diffusion models memorize training data, especially on low-dimensional manifolds.
method Measuring latent dimensionality via the learned score field, proposing a geometric memorization theory.
result Generative diffusion models experience a smooth collapse of their capacity to vary across independent directions as data become scarce, leading to near point-wise replication of salient features.
This paper explores memorization in adversarial training and proposes a mitigation algorithm.
problem Understanding and mitigating robust overfitting in adversarial training.
method Demonstrated the capacity of deep networks to memorize adversarial examples, analyzed convergence and generalization issues, and proposed a new mitigation algorithm.
result Identified robust overfitting as a significant drawback of adversarial training and proposed a mitigation algorithm.
We present an attention-based ranking framework for learning to order sentences given a paragraph. Our framework is built on a bidirectional sentence encoder and a self-attention based transformer network to obtain an input order invariant representation of paragraphs. Moreover, it allows seamless training using a vari…
We present a new local entity disambiguation system. The key to our system is a novel approach for learning entity representations. In our approach we learn an entity aware extension of Embedding for Language Model (ELMo) which we call Entity-ELMo (E-ELMo). Given a paragraph containing one or more named entity mentions…
Learning to solve sequential tasks with recurrent models requires the ability to memorize long sequences and to extract task-relevant features from them. In this paper, we study the memorization subtask from the point of view of the design and training of recurrent neural networks. We propose a new model, the Linear Me…
State-of-the-art results on image recognition tasks are achieved using over-parameterized learning algorithms that (nearly) perfectly fit the training set and are known to fit well even random labels. This tendency to memorize the labels of the training data is not explained by existing theoretical analyses. Memorizati…
Deep models memorize training data in geophysical inversion, leading to biased posterior distributions.
problem Memorization of training data biases learned priors in geophysical inverse problems.
method Casting generative models' training as maximum likelihood, we show memorization results in a reweighted empirical distribution for diffusion models, leading to Gaussian mixture priors and posteriors.
result Memorization leads to posterior distributions that are likelihood-weighted lookup among stored training examples, affecting full waveform inversion outcomes.
We consider the large-scale query-document retrieval problem: given a query (e.g., a question), return the set of relevant documents (e.g., paragraphs containing the answer) from a large document corpus. This problem is often solved in two steps. The retrieval phase first reduces the solution space, returning a subset …
The roles played by learning and memorization represent an important topic in deep learning research. Recent work on this subject has shown that the optimization behavior of DNNs trained on shuffled labels is qualitatively different from DNNs trained with real labels. Here, we propose a novel permutation approach that …