4-manifolds from hyperbolic knots have curious metrics.
problem Understanding metrics on 4-manifolds from hyperbolic knot complements.
method Constructing 4-manifolds using hyperbolic knot complements.
result Curious metric properties of 4-manifolds constructed from hyperbolic knots.
Curious Replay improves model-based reinforcement learning agents' adaptability.
problem Existing model-based reinforcement learning agents struggle to adapt quickly to changing environments.
method Curious Replay uses a curiosity-based priority signal for prioritized experience replay tailored to model-based agents.
result Agents using Curious Replay achieve improved performance in exploration and on benchmarks.
Standard S4 proved to be diffeomorphic to a curious homotopy sphere.
problem Determining the diffeomorphism of a curious homotopy sphere to the standard S4. method Proof based on properties of homotopy spheres and loose corks.
result The curious homotopy sphere is diffeomorphic to the standard S4. The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at such points that leads to a curious phenomenon: geodesics cannot pass through s…
Recently Guillemin gave an explicit combinatorial way of constructing "toric" Kahler metrics on (symplectic) toric varieties, using only data on the moment polytope. In this paper, differential geometric properties of these metrics are investigated using Guillemin's construction. In particular, a nice combinatorial for…
Curious Meta-Controller alternates between model-based and model-free control to improve sample efficiency.
problem Combining the benefits of model-based and model-free control to enhance sample efficiency.
method Adaptive alternation between model-based and model-free control using curiosity feedback.
result Significantly improved sample efficiency and near-optimal performance on robotic tasks.
Curious structure of special orthogonal, unitary, and symplectic groups as products of Grassmannians discovered.
problem Understanding the structure of special orthogonal, unitary, and symplectic groups.
method Expressing these groups as products of Grassmannians realized as involution matrices.
result Special orthogonal, special unitary, and symplectic groups can be expressed as products of their corresponding Grassmannians.
Curious examples of lifting spaces not as inverse limits of covering spaces.
problem Understanding inverse limits of covering spaces and their properties.
method Analyzing inverse limits of sequences of covering spaces over a given space.
result Presented examples of lifting spaces that cannot be obtained as inverse limits of covering spaces.
Decor protects decentralized learning models from curious users.
problem Privacy violation in decentralized learning.
method Decor uses correlated Gaussian noises to protect local models in decentralized SGD with differential privacy guarantees.
result Decor matches central DP optimal privacy-utility trade-off for arbitrary connected graphs.
Study classifies gravitational instantons based on their asymptotic geometry.
problem Classifying gravitational instantons based on their asymptotic properties.
method Investigation of asymptotic geometry of Hermitian non-Kähler Ricci-flat metrics.
result All Hermitian non-Kähler gravitational instantons can be compactified to log del Pezzo surfaces.
We formulate a class of minimal tori in S^3 in terms of classical mechanics, reveal a curious property of the Clifford torus, and note that the question of periodicity can be made more explicit in a simple way.
Curious hierarchical reinforcement learning improves learning performance.
problem Combining hierarchical abstraction and curiosity-driven exploration in reinforcement learning.
method Developed a method that combines hierarchical reinforcement learning with curiosity.
result Curiosity can more than double learning performance and success rates.
Curious connection found between dynamical systems and 3D manifold fibrations.
problem Existence of fibrations in 3D manifolds and their relation to dynamical systems.
method Established a one-to-one correspondence between fibrations of the Whitehead link complement and `simple orbit pairs` on the torus.
result Found a correspondence between the order of rational numbers and the order of orbits in fibrations.
HHVG algorithm reconciles boredom and curiosity for better exploration and learning.
problem Effective exploration and superior forward model learning.
method Homeo-Heterostatic Value Gradients (HHVG) algorithm.
result Boredom-enabled agents consistently outperform curious or explorative agents in model building benchmarks.
A numerical expression in the form of an integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a curious sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. A few graphs are drawn.
Study on Calabi-Yau threefolds' diffeomorphism classes.
problem Investigating Calabi-Yau threefolds' classification.
method Focus on embedded Calabi-Yau threefolds in toric Fano manifolds.
result Curious remark on mirror symmetry.
In this paper we study the price dynamics in a simple model of financial markets with heterogeneous agents. We concentrate on how increases in the total number of active traders influences fluctuations of asset prices. We find that a curious route to chaos is observed when the total number of [active traders] increases…
Study connects curvature to graph theory and reveals differences.
problem Exploring differences between Quadratic Orthogonal Bisectional Curvature and Real Bisectional Curvature.
method Real (1,1)--forms and Weitzenböck curvature operator used to represent graph Dirichlet energy.
result Curvature differences illuminated between Quadratic Orthogonal Bisectional Curvature and Real Bisectional Curvature.
We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on mapping class groups of once-punctured surfaces and have quite curious behaviour…
It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones fun…
Two knots with unique surgery properties.
problem Characterizing strongly invertible L-space knots.
method Examined surgeries and knot properties.
result Found knots whose surgeries are never Khovanov thin.
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chruściel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; bu…
Fixing a closed hyperbolic surface S, we define a moduli space AI(S) of unmarked hyperbolic 3-manifolds homotopy equivalent to S. This 3-dimensional analogue of the moduli space M(S) of unmarked hyperbolic surfaces homeomorphic to S has bizarre local topology, possessing many points that are not closed. There is, howev…
Paper shows attackers can steal model weights with just noise inputs.
problem Model weight theft with minimal inputs.
method Used i.i.d. Bernoulli noise inputs to achieve high accuracy.
result Achieved high accuracy (96% for MNIST, 82% for KMNIST) with minimal inputs.
The purpose of the present paper is to introduce and explore two surprises that arise when we apply a standard procedure to study the number of finite type invariants of 3-manifolds introduced independently by M. Goussarov and K. Habiro based on surgery on claspers, Y-graphs or clovers, \cite{Gu,Ha,GGP}. One surprise i…
The study explores how brain development can inspire efficient deep learning models.
problem Efficient and robust optimization procedures for deep learning.
method Inspiration from biological neural development to improve deep learning models.
result Biological neural development can inspire efficient and robust optimization procedures.
New protocol makes federated learning more scalable and private.
problem Securely aggregate data from distributed, private datasets.
method Proposes a new protocol for aggregation in the shuffled model that is more efficient in terms of communication and error.
result Achieves differential privacy guarantees with polylogarithmic scaling in the number of users.
Report on formalizing differential geometry in Lean.
problem Formalizing differential geometry in a proof assistant.
method Lean's type theory approach to formalization.
result Surprising differences between formal and informal proofs.
New formula and properties of inverted Habiro series derived from GM series.
problem Understanding and manipulating knot invariants using series expansions.
method Developed a new formula for the inverted Habiro series (IHS) in terms of GM series and theta functions. Proved a multiplication formula for IHS.
result Established a natural ring structure for IHS and studied its residues, applying them to Dehn surgery formulas.
Single parameter fits any dataset, simplifying complex data science.
problem Approximating any dataset with a single parameter.
method Adopting chaos theory concepts, adjusting a single real-valued parameter.
result Arbitrary precision fit to all data samples.
The study examines when MAML's objective has a benign landscape.
problem Understanding when MAML's objective landscape is benign.
method Analyzing the landscape of MAML objective on LQR tasks.
result The benign landscape of the MAML objective depends on task similarities.
We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict local martingales are i…
Study improves bounds on non-orientable slice genus using knot signatures and concordance invariants.
problem Improving bounds on the non-orientable slice genus of knots.
method Negative surgeries on knots, lower bound derivation using signature and concordance invariants.
result Superadditivity of bounds on stable non-orientable genus, sometimes better than bounds on γ4(K). We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In particular, they may be used to give an explicit check that spherical braid grou…
This work explores limits of machine learning robustness against adversarial attacks.
problem Fundamental limits of adversarial learning without specific attack methods.
method Information-theoretic analysis of learning from noisy data.
result General bounds on adversarial learning without assuming specific attack methods.
The JLS model explains market crashes as critical phenomena.
problem Understanding market crashes as critical points.
method Study of Johansen-Ledoit-Sornette model.
result The JLS model provides a causal explanation of market crashes.
We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain provable guarantees, previous work requires randomized sampling of the columns wi…
Research connects geometric structures to knot theory and algebraic combinatorics.
problem Understanding the mixed Hodge structure on cohomology of open positroid varieties.
method Relates mixed Hodge structure to Khovanov-Rozansky homology of associated links.
result Rational q,t-Catalan numbers are derived from mixed Hodge polynomials of open positroid varieties. Generative models predict page quality without training, useful for low-resource settings.
problem Detecting low-quality content in web articles.
method Human evaluation and analysis of 500 million web articles.
result Generative models can predict page quality without training, useful for low-resource settings.
Study on information evolution in interactive decision making using multi-armed bandits.
problem Understanding information dynamics in interactive decision making.
method Stochastic multi-armed bandit problem, focusing on optimal arm with a fixed margin.
result Distinct growth phases in mutual information, showing decoupling between success probability and information gain.
Research suggests using deep learning for better recommendation systems.
problem Recommender systems rely on proxies for A/B testing, leading to random success.
method Advocates for using deep learning to improve recommendation performance.
result Deep learning can potentially optimize reward in recommendation systems.
Novelty search learns attentional layers to quickly explore and guess numbers.
problem Exploring and guessing numbers quickly in structured spaces.
method Attentional neural network layers trained on supervised learning of local sensory-motor contingencies.
result Greedy local policies can quickly explore structured spaces and guess numbers.
Study on price-volume correlation fractal features and market type effects.
problem Understanding the fractal features and market type effects of price-volume correlation.
method Applied MF-DXA method to analyze price, trading volume, and their coupling.
result Price, trading volume, and price-volume coupling exhibit power law and multifractal properties.
Researchers compute K-theory for cohomogeneity-one actions.
problem Computing equivariant K-theory for cohomogeneity-one actions.
method Equivariant homotopy theory, representation theory, Lie theory.
result Derived generators and relations for K-theory ring.
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein module is a deformation of a 2-move, i.e. a crossing change). Our main …
Single neuron sensitivity reveals model weaknesses.
problem Understanding model susceptibility to adversarial attacks.
method Analyzing sensitivity of individual neurons to perturbations.
result Single neuron attacks are as effective as full model attacks.
Compact parameterization improves Bayesian neural network performance.
problem Improving performance of Bayesian neural networks using variational methods.
method Restricting variational distribution to a k-tied Normal distribution with low-rank factorization.
result Compact parameterization improves signal-to-noise ratio and convergence speed.
New analysis shows entropy term cancels out in likelihood-based OOD detection.
problem Curious likelihood values for out-of-distribution data.
method Decomposed average likelihood into KL divergence and entropy terms.
result Entropy term explains OOD behaviour and cancels out in expectation.