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.
Paper proves PI consensus algorithm converges exponentially under restricted secant inequality.
We show that the triangle with angles Pi/12, Pi/3 and 7*Pi/12 has the lattice property and compute this triangle's Veech group.
By seeking the narrowest prediction intervals (PIs) that satisfy the specified coverage probability requirements, the recently proposed quality-based PI learning principle can extract high-quality PIs that better summarize the predictive certainty in regression tasks, and has been widely applied to solve many practical…
SBI provides more accurate pole positions than chi-squared minimization in model misspecification.
New research suggests privileged information doesn't improve model performance.
The neural network (NN)-based direct uncertainty quantification (UQ) methods have achieved the state of the art performance since the first inauguration, known as the lower-upper-bound estimation (LUBE) method. However, currently-available cost functions for uncertainty guided NN training are not always converging and …
Every torus knot can be represented as a Fourier-(1,1,2) knot which is the simplest possible Fourier representation for such a knot. This answers a question of Kauffman and confirms the conjecture made by Boocher, Daigle, Hoste and Zheng. In particular, the torus knot T(p,q) can be parameterized as x(t)=cos(pt), y(t)=c…
This study evaluates methods for constructing prediction intervals with neural networks.
This paper improves SVM prediction uncertainty quantification methods.
Let K be a knot of genus g. If K is fibered, then it is well known that the knot group pi(K) splits only over a free group of rank 2g. We show that if K is not fibered, then pi(K) splits over non-free groups of arbitrarily large rank. Furthermore, if K is not fibered, then pi(K) splits over every free group of rank at …
CryptoNAS improves PI accuracy by 3.4% with 2.4x less latency.
Lower bounds for PI on multi-action MDPs are established, showing complexity grows with action count.
A K(pi,1)-foliation is one for which the universal covers of all leaves are contractible (thus all leaves are K(pi,1)'s for some pi). In the first part of the paper we show that the tangential Lusternik--Schnirelmann category cat F of a K(pi,1)-foliation F on a manifold M is bounded from below by t-codim F for any t wi…
New Ricci curvature means derived from plane curvatures.
This paper presents a method to automatically generate high-quality prediction intervals for neural networks.
Gromov and Lawson conjectured that a closed spin manifold M of dimension n with fundamental group pi admits a metric with positive scalar curvature if and only if an associated element in KO_n(B pi) vanishes. In this note we present counter examples to the `if' part of this conjecture for groups pi which are torsion fr…
Proposes a method to generate prediction intervals using weighted asymmetric loss functions.
Sigma-Pi-Sigma neural networks (SPSNNs) as a kind of high-order neural networks can provide more powerful mapping capability than the traditional feedforward neural networks (Sigma-Sigma neural networks). In the existing literature, in order to reduce the number of the Pi nodes in the Pi layer, a special multinomial P_…
PI-SAC agents learn predictive information to improve RL efficiency.
In this article we construct a minimal symplectic 4-manifold R that has small Euler characteristic (e(R)=8) and two essential Lagrangian tori with nice properties. These properties make R particularly suitable for constructing interesting examples of symplectic manifolds with small Euler characteristic. In particular, …
pi-VAE models neural activity with interpretable latent variables.
Given a closed manifold N and a self-indexing Morse function f: N --> R with up to four distinct Morse indices, we construct a symplectic Lefschetz fibration pi: E --> C which models the complexification of f on the disk cotangent bundle, f_C : D(T*N) --> C, when f is real analytic. By construction, pi: E --> C comes w…
WISCA generates consensus explanations from conflicting model-agnostic interpretability methods.
Adaptive PI by reweighting nonconformity scores improves model uncertainty reflection.
Let pi be a free group of rank 2. Its outer automorphism group Out(pi) acts on the space of equivalence classes of representations in Hom(pi, SL(2,C)). Let SLm(2,R) denote ths subset of GL(2,R) consisting of matrices of determinant -1 and let ISL(2,R) denote the subgroup (SL(2,R) union i SLm(2,R)) of SL(2,C). The repre…
Proposes PI-VAE for solving SDEs with limited measurements.
New algorithms explain Naive Bayes classifiers in polynomial time and delay.
A framework to explain decoder-only sequence classification models using intermediate predictions.
Infinite rank groups found in 3-manifolds with infinite fundamental groups.
Bayesian consensus improves accuracy of forecasts from miscalibrated sources.
This paper considers the generation of prediction intervals (PIs) by neural networks for quantifying uncertainty in regression tasks. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified portion of data. We derive a loss function directly from this axiom that requires no d…
Given k>=2, we construct a (2k-2)-parameter family of properly embedded minimal surfaces in H^2 x R invariant by a vertical translation T, called Saddle Towers, which have total intrinsic curvature 4 pi(1-k), genus zero and 2k vertical Scherk-type ends in the quotient by T. As limits of those Saddle Towers, we obtain J…
We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed pi_1-injective surface of negative Euler characteristic. We also determine …
Bayesian framework for online consensus prediction from expert feedback.
In distributed machine learning, where agents collaboratively learn from diverse private data sets, there is a fundamental tension between consensus and optimality. In this paper, we build on recent algorithmic progresses in distributed deep learning to explore various consensus-optimality trade-offs over a fixed commu…
Let S be a closed, oriented surface of genus at least 2, and consider the extension 1 -> pi_1 S -> MCG(S,p) -> MCG(S) -> 1, where MCG(S) is the mapping class group of S, and MCG(S,p) is the mapping class group of S punctured at p. We prove that any quasi-isometry of MCG(S,p) which coarsely respects the cosets of the no…
Let Pi: M -> B be an onto maximal rank map or a Riemannian submersion between Riemannian manifolds M and B. Initially, we prove necessary and sufficient conditions for any fiber F to be roughly isometric to M. Then, we prove necessary and sufficient conditions for Pi to be a rough isometry. As a corollary M is roughly …
Paper analyzes convergence of decentralized algorithms with noise and bias.
PIF detects anomalies in structured patterns using preference embedding.
CB-APM uses analyst consensus as a bottleneck to interpret stock returns.
Given any knot k, there exists a hyperbolic knot tilde k with arbitrarily large volume such that the knot group pi k is a quotient of pi tilde k by a map that sends meridian to meridian and longitude to longitude. The knot tilde k can be chosen to be ribbon concordant to k and also to have the same Alexander invariant …
In this note we prove that a complex hyperbolic triangle group of type (m,m,infinity), i.e. a group of isometries of the complex hyperbolic plane, generated by complex reflections in three complex geodesics meeting at angles Pi/m, Pi/m and 0, is not discrete if the product of the three generators is regular elliptic.
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph defined by the consensus matrix and the eigenvalues of the associated transition proba…
To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their result is pivotal for deriving interesting properties of consensus clustering beyond…
Given a closed orientable Euclidean cone 3-manifold C with cone angles less than or equal to pi, and which is not almost product, we describe the space of constant curvature cone structures on C with cone angles less than pi. We establish a regeneration result for such Euclidean cone manifolds into spherical or hyperbo…
A new algorithm reduces communication in decentralized optimization.
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its robust and effective performance. Tremendous research efforts have been made to t…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful re…