arXiv research

Three hard diagrams of the unknot require extra crossings to simplify.

This paper shows how optimizing with hard negative examples improves image retrieval.

Detecting adversarial examples is as hard as classifying them.

This work connects hardness of approximation and learning.

The Hard Lefschetz Theorem extends to certain Kähler Lie Algebroids with ellipticity.

We describe a method for generating minimal hard prime surface-link diagrams. We extend the known examples of minimal hard prime classical unknot and unlink diagrams up to three components and generate figures of all minimal hard prime surface-unknot and surface-unlink diagrams with prime base surface components up to …

ELF improves long-tailed classification by focusing on hard examples.

Paper shows examples of almost Kähler manifolds satisfying Hard Lefschetz but not Betti-Hodge equality.

Study categorizes knots and links as rigid or shaky based on Reidemeister moves.

Efficient method for generating adversarial examples with limited query budget.

The paper proves a generalized Lefschetz duality for a specific type of manifold.

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the …

In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the p…

New symplectic structures found on complex manifolds without Kähler structures.

Random forest is widely exploited as an ensemble learning method. In many practical applications, however, there is still a significant challenge to learn from imbalanced data. To alleviate this limitation, we propose a deep dynamic boosted forest (DDBF), a novel ensemble algorithm that incorporates the notion of hard …

For a Lie group $G=\R^{n}\ltimes_φ\R^{m}$ with the semi-simple action $φ:\R^{n}\to {\rm Aut}(\R^{m})$, we show that if $Γ$ is a finite extension of a lattice of $G$ then $K(Γ, 1)$ is formal. Moreover we show that a compact symplectic aspherical manifold with the fundamental group $Γ$ satisfies the hard Lefschetz proper…

Hard instances, which require a long time for a specific algorithm to solve, help (1) analyze the algorithm for accelerating it and (2) build a good benchmark for evaluating the performance of algorithms. There exist several efforts for automatic generation of hard instances. For example, evolutionary algorithms have b…

New unsupervised method selects hard negative samples for contrastive learning.

Using the Hard Lefschetz Theorem for Sasakian manifolds, we find two examples of compact K-contact nilmanifolds with no compatible Sasakian metric in dimensions five and seven, respectively

Floer homology is a good example of homological invariants living in the infinite dimension. We suggest a way to construct this kind of invariants using only soft essentially finite-dimensional tools; no hard analysis or PDE is involved. This work is partially inspired by the M. Gromov's survey ``Soft and hard symplect…

In our recent work (Bubeck, Price, Razenshteyn, arXiv:1805.10204) we argued that adversarial examples in machine learning might be due to an inherent computational hardness of the problem. More precisely, we constructed a binary classification task for which (i) a robust classifier exists; yet no non-trivial accuracy c…

Over recent years, devising classification algorithms that are robust to adversarial perturbations has emerged as a challenging problem. In particular, deep neural nets (DNNs) seem to be susceptible to small imperceptible changes over test instances. However, the line of work in provable robustness, so far, has been fo…

The study constructs symplectic solvmanifolds satisfying the hard-Lefschetz condition.

We study the most practical problem setup for evaluating adversarial robustness of a machine learning system with limited access: the hard-label black-box attack setting for generating adversarial examples, where limited model queries are allowed and only the decision is provided to a queried data input. Several algori…

When humans learn a new concept, they might ignore examples that they cannot make sense of at first, and only later focus on such examples, when they are more useful for learning. We propose incorporating this idea of tunable sensitivity for hard examples in neural network learning, using a new generalization of the cr…

We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust classifier exists, in the small-perturbation regime; (b) a non-robust classifier can be l…

PS-KD distills a model's own knowledge to soften hard targets during training.

Extends Hard Lefschetz Property to isometric flows and shows equivalence.

Study defines and proves Hard Lefschetz Property for S^3-actions.

Constructing compact non-Kähler manifolds with and without the Hard Lefschetz Condition

Computer experiments reveal complex knots that don't simplify.

The paper explores when linear system identification is hard or easy, especially for under-actuated systems.

In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Capp…

We prove that the problem of deciding whether a 2- or 3-dimensional simplicial complex embeds into $\mathbb{R}^3$ is NP-hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an $\mathbb{S}^{3}$ filling is NP-hard. The former stands in contrast with the lower dimensional cases wh…

Develops clustering methods based on likelihood and convergence proved.

New proof shows a link problem is hard without complex links.

New findings show some symplectic solvmanifolds fail hard-Lefschetz condition.

Rotation invariant algorithms fail with hard labels sampled from sparse targets.

Adversarial example generation becomes a viable method for evaluating the robustness of a machine learning model. In this paper, we consider hard-label black-box attacks (a.k.a. decision-based attacks), which is a challenging setting that generates adversarial examples based on only a series of black-box hard-label que…

The burgeoning success of deep learning has raised the security and privacy concerns as more and more tasks are accompanied with sensitive data. Adversarial attacks in deep learning have emerged as one of the dominating security threat to a range of mission-critical deep learning systems and applications. This paper ta…

We study the problem of attacking a machine learning model in the hard-label black-box setting, where no model information is revealed except that the attacker can make queries to probe the corresponding hard-label decisions. This is a very challenging problem since the direct extension of state-of-the-art white-box at…

New lower bounds show sparse recovery is hard even with multiple preconditioners.

SapAugment learns adaptive augmentation policies for better model training.

Developed a new thresholding method that connects soft and hard thresholding.

Unified framework for hard affine SDP constraints in vRKHSs.

We find a family of five dimensional completely solvable compact manifolds that constitute the first examples of $K$-contact manifolds which satisfy the Hard Lefschetz Theorem and have a model of Tievsky type just as Sasakian manifolds but do not admit any Sasakian structure.

This article contains detailed proofs and additional examples related to the UAI-2013 submission `Learning Sparse Causal Models is not NP-hard'. It describes the FCI+ algorithm: a method for sound and complete causal model discovery in the presence of latent confounders and/or selection bias, that has worst case polyno…

Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint. This work examines the choice of the thresholding operator, and asks whether it i…