A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New representation theory for closed geodesic subflows.
Collar lemma proven for certain surface group representations.
Groups with hyperbolic properties don't have strong Property (T).
Special orthogonal representations from octonions have geometric properties linked to binary cubics.
We study the strong predictable representation property in filtrations initially enlarged with a random variable L. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the ex…
New compactification for character varieties with good topological properties.
Develops theory of Anosov representations for Fuchsian groups, showing stability and analytical properties.
New infinite-dimensional representations with bounded multiplicity found for Lie groups.
Several classes of irreducible orthogonal representations of compact Lie groups that are of importance in Differential Geometry have the property that the second osculating spaces of all of their nontrivial orbits coincide with the representation space. We say that representations with this property are of class O^2. O…
We develop the theory of maximal representations of the fundamental group of a compact connected oriented surface with boundary, into a group of Hermitian type. For any such representation we define the Toledo invariant, for which we establish properties such as uniform boundedness on the representation variety, additi…
Slot Attention extracts object-centric representations from images.
Study compares atom representations in graph neural networks for molecular properties.
ExpCLR uses expert features to improve time-series representation learning.
Dual representations for robust risk measures and uncertainty sets.
Study geometric properties of surfaces with specific formulae.
Study Anosov representations of reducible suspensions of hyperbolic groups.
Anosov representations give a higher-rank analogue of convex cocompactness in a rank-one Lie group which shares many of its good geometric and dynamical properties; geometric finiteness in rank one may be seen as a controlled weakening of convex cocompactness to allow for isolated failures of hyperbolicity. We introduc…
When two boundary-parabolic representations of knot groups are given, we introduce the connected sum of these representations and show several natural properties including the unique factorization property. Furthermore, the complex volume of the connected sum is the sum of each complex volumes modulo and the twi…
We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory a…
GNNs learn graph representations, with new theory on their power and limitations.
Deep Learning has been shown to learn efficient representations for structured data such as image, text or audio. In this chapter, we present neural network architectures that are able to learn efficient representations of molecules and materials. In particular, the continuous-filter convolutional network SchNet accura…
New approach identifies latent properties from mechanisms, not just data.
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants of different types. We also study properties of the augmentation representation…
In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and establish a convergence property for them, analogue to a differentiability property. As an application of this convergence, we prove that t…
Variational autoencoders (VAEs) defined over SMILES string and graph-based representations of molecules promise to improve the optimization of molecular properties, thereby revolutionizing the pharmaceuticals and materials industries. However, these VAEs are hindered by the non-unique nature of SMILES strings and the c…
Minimalistic model captures head direction system properties.
Improved molecular property prediction using WL embedding in GNNs.
Enhances knot Floer homology with algebraic representation theory.
We identify a large class of Orlicz spaces for which the topology fails the C-property introduced in [7]. We also establish a variant of the C-property and use it to prove a -representation theorem for proper convex increasing functionals on dual Banach lattices that satisfy a suitable version …
Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of these representations in terms of classical transformation theory of -surfaces.
We establish various results on the large level limit of projective quantum representations of surface mapping class groups obtained by quantizing moduli spaces of flat SU(n)-bundle. Working with the metaplectic correction, we proved that these projective representations lift to asymptotic representations. We show that…
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…
Characterizes Anosov representations and strongly convex cocompact groups with eigenvalue gaps.
Improved VAE representations lead to better image classification.
To evaluate disentangled representations several metrics have been proposed. However, theoretical guarantees for conventional metrics of disentanglement are missing. Moreover, conventional metrics do not have a consistent correlation with the outcomes of qualitative studies. In this paper we analyze metrics of disentan…
INNs can approximate diverse functions despite layer restrictions.
ASGN uses active semi-supervised learning to predict molecular properties efficiently.
In this paper we study weakly irreducible holonomy representations of the normal connection of a spacelike submanifold in a pseudo-Riemannian space from. We associate screen representations to weakly irreducible normal holonomy groups and classify the screen representations having the Borel-Lichnérowicz property. In pa…
Investigates statistical properties of perturb-softmax and perturb-argmax distributions.
New subgroups found in CAT(0) groups with exotic finiteness properties.
We provide a variety of results for (quasi)convex, law-invariant functionals defined on a general Orlicz space, which extend well-known results in the setting of bounded random variables. First, we show that Delbaen's representation of convex functionals with the Fatou property, which fails in a general Orlicz space, c…
The paper studies SDP feasibility and sos ranks for specific polynomials.
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation of resulting risk measures from the properti…
We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and investigate properties of the corresponding representations. We obtain some structural …
In this paper, we propose a property which is a natural generalization of Kazhdan's property and prove that many, but not all, groups with property also have this property. Let $\G$ be a finitely generated group. One definition of $\G$ having property is that $H^1(\G,π,\fh)=0$ where the coefficient mo…
Direct proof of Alexander polynomial scaling for L-shaped representations.
How can intelligent agents solve a diverse set of tasks in a data-efficient manner? The disentangled representation learning approach posits that such an agent would benefit from separating out (disentangling) the underlying structure of the world into disjoint parts of its representation. However, there is no generall…
We prove that a free group F_2 admits a faithful discrete representation into Diff_{+}(I). We also prove that F_2 admits a faithful discrete representation into Homeo_{+}(I). Some properties of these representations have been studied. In the last section we raise several questions.