arXiv research

The paper proves conditions for compact complex manifolds to be Kahler outside analytic subsets.

We find the minimum dilatation of pseudo-Anosov braids with many strands.

We note an intimate connection between the Lefschetz Theorem for c-arrangements, and a theorem of Hironaka relating the complement of an arrangement to its boundary manifold. This results in a generalization of Hironaka's result.

Building upon ideas of Hironaka, Bierstone-Milman, Malgrange and others we generalize the inverse and implicit function theorem (in differential, analytic and algebraic setting) to sets of functions of larger multiplicities (or ideals). This allows one to describe singularities given by a finite set of generators or by…

Minimal stretch factors for certain pseudo-Anosov maps are bounded.

Invariant polynomials improve machine learning performance.

New proof of Grauert's theorem using differential geometry.

Given $φ$ a pseudo-Anosov map, let $\ell_\mathcal{T}(φ)$ denote the translation length of $φ$ in the Teichmüller space, and let $\ell_\mathcal{C}(φ)$ denote the stable translation length of $φ$ in the curve graph. Gadre--Hironaka--Kent--Leininger showed that, as a function of Euler characteristic $χ(S)$, the minimal po…

From a simple observation about a construction of Thurston, we derive several interesting facts about subgroups of the mapping class group generated by two positive multi-twists. In particular, we identify all configurations of curves for which the corresponding groups fail to be free, and show that a subset of these d…

The study improves bounds on pseudo-Anosov maps and certifies minimum and accumulation points of normalized dilatations.

New combinatorial type helps distinguish plane curve topologies.

We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq 2$. For a sequence $(Σ_n, ψ_n)$ of fibers and monodromies in the fibered cone, we show that the asymptotic translation len…

Grothendieck's Esquisse d'un programme is often referred to for the ideas it contains on dessins d'enfants, the Teichm{ü}ller tower, and the actions of the absolute Galois group on these objects or their etale fundamental groups. But this program contains several other important ideas. In particular, motivated by surfa…

This work computes integral variation and monodromy maps for plane curve singularities.

This paper concerns the set $\hat{\mathcal{M}}$ of pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the magic 3-manifold $N$ by Dehn filling three cusps with a mild restriction. We prove that for each $g$ (resp. $g \not\equiv 0 \pmod{6}$), the minimum among dilatations of elements (res…

Let $δ_g$ be the minimal dilatation for pseudo-Anosovs on a closed surface $Σ_g$ of genus $g$ and let $δ_g^+$ be the minimal dilatation for pseudo-Anosovs on $Σ_g$ with orientable invariant foliations. This paper concerns the pseudo-Anosovs which occur as the monodromies on closed fibers for Dehn fillings of $N(r)$ for…

A new geometric concept, the dead direction, bridges singular learning theory and information geometry.

Deep neural networks (DNNs) have been widely used in the fields such as natural language processing, computer vision and image recognition. But several studies have been shown that deep neural networks can be easily fooled by artificial examples with some perturbations, which are widely known as adversarial examples. A…

Generates positive examples from noisy data streams.

We construct new examples of self-similar solutions and translating solitons for Lagrangian mean curvature flow by extending the method of Joyce, Lee and Tsui. Those examples include examples in which the Lagrangian angle is arbitrarily small as the examples of Joyce, Lee and Tsui.

With rapid progress and significant successes in a wide spectrum of applications, deep learning is being applied in many safety-critical environments. However, deep neural networks have been recently found vulnerable to well-designed input samples, called adversarial examples. Adversarial examples are imperceptible to …

Model forgets examples; this research predicts which ones to replay.

Cincer cleans both new and past data by identifying and relabeling suspicious and counter-examples.

Gödel's sentence is an adversarial example but unsolvable.

Deep learning frameworks leverage GPUs to perform massively-parallel computations over batches of many training examples efficiently. However, for certain tasks, one may be interested in performing per-example computations, for instance using per-example gradients to evaluate a quantity of interest unique to each examp…

It has been shown that adversaries can craft example inputs to neural networks which are similar to legitimate inputs but have been created to purposely cause the neural network to misclassify the input. These adversarial examples are crafted, for example, by calculating gradients of a carefully defined loss function w…

Proposes BATer for improved adversarial example detection.

We consider learning problems where the training set consists of two types of examples: private and public. The goal is to design a learning algorithm that satisfies differential privacy only with respect to the private examples. This setting interpolates between private learning (where all examples are private) and cl…

Detecting adversarial examples currently stands as one of the biggest challenges in the field of deep learning. Adversarial attacks, which produce adversarial examples, increase the prediction likelihood of a target class for a particular data point. During this process, the adversarial example can be further optimized…

Catastrophic forgetting of connectionist neural networks is caused by the global sharing of parameters among all training examples. In this study, we analyze parameter sharing under the conditional computation framework where the parameters of a neural network are conditioned on each input example. At one extreme, if e…

Deep neural networks (DNNs) have transformed several artificial intelligence research areas including computer vision, speech recognition, and natural language processing. However, recent studies demonstrated that DNNs are vulnerable to adversarial manipulations at testing time. Specifically, suppose we have a testing …

RelatIF selects more intuitive training examples for explaining model predictions.

New examples of variational bivectors found that are not Poissonian.

We give examples of certain kind of minimal orbits of Hermann actions and discuss whether each of the examples is austere.

Recent studies show that widely used deep neural networks (DNNs) are vulnerable to carefully crafted adversarial examples. Many advanced algorithms have been proposed to generate adversarial examples by leveraging the $\mathcal{L}_p$ distance for penalizing perturbations. Researchers have explored different defense met…

Algorithm learns from both labeled and arbitrary test examples, giving guarantees for bounded VC dimension classes.

When learning a new concept, not all training examples may prove equally useful for training: some may have higher or lower training value than others. The goal of this paper is to bring to the attention of the vision community the following considerations: (1) some examples are better than others for training detector…

StrokeCoder uses Transformers to generate images from single examples.

The paper analyzes how forgetting in LLMs is linked to simple task-upstream example associations.

Despite the great success achieved in machine learning (ML), adversarial examples have caused concerns with regards to its trustworthiness: A small perturbation of an input results in an arbitrary failure of an otherwise seemingly well-trained ML model. While studies are being conducted to discover the intrinsic proper…

New examples of manifolds with positive scalar curvature and infinitely many poles.

Paper generates natural adversarial examples for hyperspectral data.

This study explores how examples influence ICL in LLMs.

In many classification problems unlabelled data is abundant and a subset can be chosen for labelling. This defines the context of active learning (AL), where methods systematically select that subset, to improve a classifier by retraining. Given a classification problem, and a classifier trained on a small number of la…

ManiGen generates adversarial examples without classifier knowledge.

Deep networks prioritize easier examples over harder ones, leading to faster training.

Detects adversarial examples using autoencoders at hidden layers.

Algorithm predicts with optimal loss by abstaining from uncertain test examples.