arXiv research

New seq2seq model can copy entire spans, outperforming simpler models in editing tasks.

The Riemannian hemisphere has a lower bound for its mass.

Study the boundary of a space related to Outer space.

We study model-agnostic copies of machine learning classifiers. We develop the theory behind the problem of copying, highlighting its differences with that of learning, and propose a framework to copy the functionality of any classifier using no prior knowledge of its parameters or training data distribution. We identi…

We consider the polynomial representation S(V*) of the rational Cherednik algebra H_c(W) associated to a finite Coxeter group W at constant parameter c. We show that for any degree d of W and nonnegative integer m the space S(V*) contains a single copy of the reflection representation V of W spanned by the homogeneous …

This paper introduces DPI, a new metric to assess data-copying risk in tabular data.

Paper analyzes gradient descent with noisy data copies for linear regression, showing regularization and acceleration effects.

In many real-world systems, information can be transmitted in two qualitatively different ways: by copying or by transformation. Copying occurs when messages are transmitted without modification, e.g., when an offspring receives an unaltered copy of a gene from its parent. Transformation occurs when messages are modifi…

New test detects when generative models memorize training data.

Shapes can roll downhill following any curve, but often return to initial orientation after crossing multiple copies.

Every lens space has a locally flat embedding in a connected sum of 8 copies of the complex projective plane and a smooth embedding in n copies of the complex projective plane for some positive integer n. We show that there is no n such that every lens space smoothly embeds in n copies of the complex projective plane.

New system resists meme coin copy trading bots.

GMC benchmark isolates retrieval in Transformers, revealing max-margin alignment.

Bayesian theory explains abrupt emergence of copy subcircuit in attention.

A condition for the existence of false gauge field copies in terms of the Lefschetz number of a certain differential operator is presented.

CN-SBM clusters cancer samples and regions based on copy number variants.

Under-parameterized networks can either copy or average teacher weights, leading to universal optimal solutions.

Automatic question generation is an important problem in natural language processing. In this paper we propose a novel adaptive copying recurrent neural network model to tackle the problem of question generation from sentences and paragraphs. The proposed model adds a copying mechanism component onto a bidirectional LS…

The paper introduces a new method to improve model generalization by routing model copies through permutations.

Copies have been proposed as a viable alternative to endow machine learning models with properties and features that adapt them to changing needs. A fundamental step of the copying process is generating an unlabelled set of points to explore the decision behavior of the targeted classifier throughout the input space. I…

We prove that an odd pretzel knot is doubly slice if it has $2n+1$ twist parameters consisting of $n+1$ copies of $a$ and $n$ copies of $-a$ for some odd integer $a$. Combined with the work of Issa and McCoy, it follows that these are the only doubly slice odd pretzel knots.

Is it possible to generally construct a dynamical system to simulate a black system without recovering the equations of motion of the latter? Here we show that this goal can be approached by a learning machine. Trained by a set of input-output responses or a segment of time series of a black system, a learning machine …

We show that the maximal orbit dimension of a simultaneous Lie group action on n copies of a manifold does not pseudo-stabilize when n increases. We also show that if a Lie group action is (locally) effective on subsets of a manifold, then the induced Cartesian action is locally free on an open subset of a sufficiently…

A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a counterexample to a conjecture of Lewis made in 1968.

For a closed 4-manifold X and closed 3-manifold M we investigate the smallest integer n (perhaps infinity) such that M embeds in the connected sum of n copies of X. It is proven that any lens space (or homology lens space) embeds topologically locally flatly in a connected sum of 8 copies of the complex projective plan…

A fibration of ${\mathbb R}^n$ by oriented copies of ${\mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and Tabachnikov. A classification of smooth fibrations of ${\mathbb R}^3$ by skew oriente…

New unoriented algebraic concordance group defined using mock Seifert matrices.

We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loeh up to dimension five. More precisely, we show that: (1) every simply connected, closed four-manifold admits a bran…

New algorithms for fair item allocation with limited copies.

Weighted SVM (or fuzzy SVM) is the most widely used SVM variant owning its effectiveness to the use of instance weights. Proper selection of the instance weights can lead to increased generalization performance. In this work, we extend the span error bound theory to weighted SVM and we introduce effective hyperparamete…

Proves stability of cone-volume measure with nearly constant density.

We discuss the relationship between the m-th homotopy group of the one-point union of r copies of the two-dimensional sphere and the m-th homotopy group of the one-point union of r+1 copies of the Thom space of the oriented two-dimensional universal vector bundle. Using a suitably choosen isomorphism between them a for…

Characterizes a specific type of Courant algebroid with a Calabi-Yau structure.

Special shadow-complexity equals k+1 for k copies of S1×S3.

New spanning 3-disks found for unlink in 4-sphere.

Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually preserves information from the natural language side in the form of similar token…

A new model for graph sampling that preserves structure without explicit targeting.

Sharp bounds for spanning tree entropy in planar lattices.

Totally geodesic surfaces found in knots and links.

In the past few years, Convolutional Neural Networks (CNNs) have been achieving state-of-the-art performance on a variety of problems. Many companies employ resources and money to generate these models and provide them as an API, therefore it is in their best interest to protect them, i.e., to avoid that someone else c…

The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning trees provide a filtration on the reduced Khovanov complex and a …

A new classification method based on Minimum Spanning Trees

CACTI improves tabular data imputation by leveraging missingness patterns and contextual information.

Ancient curves span halfplanes via flow.

Refines knot defect measurement in 3D and 4D.

Spanning attack improves black-box attacks with unlabeled data.

Proves bounds on spanning two-forests and random cut sizes.

Alexander polynomial equals spanning tree count at t=1.