Related papers: Geometry-Aware Backdoor Attacks: Leveraging Curvat…
Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers…
Deep learning models have achieved unprecedented performance in the domain of object detection, resulting in breakthroughs in areas such as autonomous driving and security. However, deep learning models are vulnerable to backdoor attacks.…
Interior-point methods (IPMs) are a cornerstone of Euclidean convex optimization, due to their strong theoretical guarantees and practical performance. Motivated by scaling problems, recent work by Hirai and the last two authors (FOCS'23)…
Recent knowledge graph embedding (KGE) models based on hyperbolic geometry have shown great potential in a low-dimensional embedding space. However, the necessity of hyperbolic space in KGE is still questionable, because the calculation…
Non-adiabatic and non-closed evolutionary paths play a significant role in the fidelity of quantum gates. We propose a high-fidelity quantum control framework based on the quasi-topological number ($\nu_{\text{qua}}$), which extends the…
Adversarial machine learning has exposed several security hazards of neural models and has become an important research topic in recent times. Thus far, the concept of an "adversarial perturbation" has exclusively been used with reference…
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…
Backdoor attacks represent a serious threat to neural network models. A backdoored model will misclassify the trigger-embedded inputs into an attacker-chosen target label while performing normally on other benign inputs. There are already…
Understanding body part geometry is crucial for precise medical diagnostics. Curves effectively describe anatomical structures and are widely used in medical imaging applications related to cardiovascular, respiratory, and skeletal…
New quadrotor UAV control algorithms are developed, based on nonlinear surfaces composed of tracking errors that evolve directly on the nonlinear configuration manifold, thus inherently including in the control design the nonlinear…
Let $(M, \partial M)$ be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric $g$ on $M$ such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$…
Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
Recent advancements in deep learning-based compression techniques have surpassed traditional methods. However, deep neural networks remain vulnerable to backdoor attacks, where pre-defined triggers induce malicious behaviors. This paper…
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…
Protein-ligand binding prediction is central to virtual screening and affinity ranking, two fundamental tasks in drug discovery. While recent retrieval-based methods embed ligands and protein pockets into Euclidean space for…
In autonomous driving, behavior prediction is fundamental for safe motion planning, hence the security and robustness of prediction models against adversarial attacks are of paramount importance. We propose a novel adversarial backdoor…
Large visual language models (LVLMs) have demonstrated excellent instruction-following capabilities, yet remain vulnerable to stealthy backdoor attacks when finetuned using contaminated data. Existing backdoor defense techniques are usually…
We relate three classes of nonpositively curved metric spaces: hierarchically hyperbolic spaces, coarsely injective spaces, and strongly shortcut spaces. We show that every hierarchically hyperbolic space admits a new metric that is…
A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study…