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 neural network architectures use signed permutation representations for finite groups, improving performance.
Signed-permutation coordinate transport improves model alignment across checkpoints.
We demonstrate how a 3-manifold, a Heegaard diagram, and a group presentation can each be interpreted as a pair of signed permutations in the symmetric group We demonstrate the power of permutation data in programming and discuss an algorithm we have developed that takes the permutation data as input and determi…
Link Floer homology is an invariant for links which has recently been described entirely in a combinatorial way. Originally constructed with mod 2 coefficients, it was generalized to integer coefficients thanks to a sign refinement. In this paper, thanks to the spin extension of the permutation group we give an alterna…
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoid…
P. Berglund, T. Hübsch, and M. Henningson proposed a method to construct mirror symmetric Calabi-Yau manifolds. They considered a pair consisting of an invertible polynomial and of a finite (abelian) group of its diagonal symmetries together with a dual pair. A. Takahashi suggested a method to generalize this construct…
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of threads. In this way, subgroups and quotients are easily visualized. The general i…
Drinfel'd used associators to construct families of universal representations of braid groups. We consider semi-associators (i.e., we drop the pentagonal axiom and impose a normalization in degree one). We show that the process may be reversed, to obtain semi-associators from universal representations of 3-braids. We v…
Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community detection. Such network embedding methods are largely focused on finding distribute…
Many problems at the intersection of combinatorics and computer science require solving for a permutation that optimally matches, ranks, or sorts some data. These problems usually have a task-specific, often non-differentiable objective function that data-driven algorithms can use as a learning signal. In this paper, w…
The paper introduces DP algorithms using random projections and sign random projections for improved privacy in machine learning.
π-GNN learns soft permutations for graph representations, improving graph classification and regression.
A new protocol evaluates small machine learning improvements conservatively.
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This …
New method estimates tensors from noisy data with missing entries.
Quandles with involutions that satisfy certain conditions, called good involutions, can be used to color non-orientable surface-knots. We use subgroups of signed permutation matrices to construct non-trivial good involutions on extensions of odd order dihedral quandles. For the smallest example of order 6 that is an ex…
The article extends Thurston's Grafting Theorem to signed spaces and defines a framed monodromy map.
We use the equivariant Yang-Mills moduli space to investigate the relation between the singular set, isotropy representations at fixed points, and permutation modules realized by the induced action on homology for smooth group actions on certain 4-manifolds.
Signed Evidence Flow (SEF) combines fitted prediction with signed feature attributions to measure evidence conflict and stability.
The paper studies algebraic structures related to quantum groups.
A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum …
Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of considered entities (). It makes the direct definition of a multinomial dist…
Sample efficiency and scalability to a large number of agents are two important goals for multi-agent reinforcement learning systems. Recent works got us closer to those goals, addressing non-stationarity of the environment from a single agent's perspective by utilizing a deep net critic which depends on all observatio…
New basis for permutation equivariant layers reduces computation costs.
Paper presents a method to summarize HMC samples for neural networks, providing meaningful uncertainty estimates.
Shephard groups are unitary reflection groups arising as the symmetries of regular complex polytopes. For a Shephard group, we identify the representation carried by the principal ideal in the coinvariant algebra generated by the image of the product of all linear forms defining reflecting hyperplanes. This representat…
We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph representation for graphs of varying dimensions through a differentiable node attention po…
SMP model preserves proximity and permutation in graph neural networks.
Graphs benefit from unique node identifiers but lose permutation-equivariance. We propose a method to maintain this property.
The group of a nontrivial knot admits a finite permutation representation such that the corresponding twisted Alexander polynomial is not a unit.
Novel neural GP kernels learn stable, flexible covariance structures.
SLIM model predicts social network polarization using signed links.
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
Transformers tend to learn more symmetric functions in sequence data.
Two autoencoding models learn latent traffic scene representations.
Geometric framework for signed multivariate tail-dependence compatibility at various thresholds.
New method improves transfer and robustness of supervised contrastive learning.
We decompose the exchange rates returns of 41 currencies (incl. gold) into their sign and amplitude components. Then we group together all exchange rates with a common base currency, construct Minimal Spanning Trees for each group independently, and analyze properties of these trees. We show that both the sign and the …
We consider the question of existence of ramified covers over P_1 matching certain prescribed ramification conditions. This problem has already been faced in a number of papers, but we discuss alternative approaches for an existence proof, involving elliptic curves and universal ramified covers with signature. We also …
New Poisson bracket connects to logarithmic manifolds.
A new bootstrapping method reduces key sizes and runtime in FHE.
The study examines how permutation-based optimization performance varies across different function representations.
Wavesplit separates speech from mixtures using clustering.
Enhances graph neural networks with structural message-passing for better generalization.
InSphereNet uses infilling spheres for 3D object classification, improving accuracy with fewer parameters.
Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the whole manifold M. These are applied to representations of fundamental groups of…