Many methods for automated software test generation, including some that explicitly use machine learning (and some that use ML more broadly conceived) derive new tests from existing tests (often referred to as seeds). Often, the seed tests from which new tests are derived are manually constructed, or at least simpler t…
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48 results for “Provenance”
Tribuo integrates ML models with provenance in Java.
problem Tracking and ensuring ML models behave appropriately as they grow in number and complexity.
method Integrates model training, inference, type-safety, runtime checking, and automatic provenance recording into a single Java library.
result Automatic recording of full processing pipeline and training details inside the model object.
It is proven that a local Lie algebra in the sense of A. A. Kirillov determines the base manifold up to a diffeomorphism provided the anchor map is nowhere-vanishing. In particular, the Lie algebras of nowhere-vanishing Poisson or Jacobi brackets determine manifolds. This result has been proven for different types of d…
New homomorphism proven using immersed curves on disks.
problem Existence of homomorphisms and summands in homology groups.
method Approximating involutive Heegaard Floer complexes with immersed curves on the twice punctured disk.
result Existence of a new homomorphism and a summand proven.
The paper aims to improve reproducibility of machine learning experiments.
problem Lack of reproducibility in machine learning experiments.
method Investigates factors affecting reproducibility and proposes FAIR data practices.
result Preliminary results show the role of ProvBook in capturing and comparing provenance.
Kyle's equilibrium model stability proven for 1-2 trading times, but not for 3 or more.
problem Stability of Kyle's equilibrium model in a dynamic trading setting.
method Proof of stability for 1-2 trading times, non-stability for 3 or more trading times, independent of input parameters.
result Kyle's equilibrium model is stable for 1-2 trading times but not for 3 or more trading times.
This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated…
A general Lefschetz formula for the geodesic action on locally symmetric spaces is proven.
In the paper titled "Bockstein basis and resolution theorems in extension theory" (arXiv:0907.0491v2), we stated a theorem that we claimed to be a generalization of the Edwards-Walsh resolution theorem. The goal of this note is to show that the main theorem from (arXiv:0907.0491v2) is in fact equivalent to the Edwards-…
Closed hyperbolic manifolds are proven to minimize volume over all Alexandrov spaces with curvature bounded below by -1 in the same bilipschitz class. As a corollary compact convex cores with totally geodesic boundary are proven to minimize volume over all hyperbolic manifolds in the same bilipschitz class. Also, close…
PrIU optimizes machine learning model updates after data cleaning.
problem Incrementally updating machine learning models after removing problematic training samples.
method Provenance-based approach for efficient model parameter updates.
result PrIU-opt achieves up to two orders of magnitude speed-up compared to retraining from scratch.
There are proven few analogues of the Theorem of Moser using The Approximation Theorem of Artin.
With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature merely focuses on the \textit{worst-case} setting where the input of the neural …
We study a fully nonlinear PDE involving a linear combination of symmetric polynomials of the Kähler form on a Kähler manifold. A \emph{a priori} estimate is proven in general and a gradient estimate is proven in certain cases. Independently, we also provide a method-of-continuity proof via a path of Kähler metri…
Geometric zeta functions of Ihara and Hashimoto are generalized to higher rank. The -adic version of the Patterson conjecture is proven.
It is proven a new analogue of the Theorem of Moser in a generalized context defined by Shilov Boundaries of Bounded and Symmetric Domains.
Equilibrium pricing has been proven to underlie the rational Insured expectancy of premia additivity for composition of policies fully covering independent risks.
Contractibility of tight contact structures on proven.
problem Proving the contractibility of the space of tight contact structures on .
method Using methods from the first author's paper on contact 3-manifolds.
result The space of tight contact structures on is contractible.
Universal Gaussian parity proven for 2D knots.
problem Proving universal Gaussian parity for 2D knots.
method Analyzing Gaussian parity on free 2D knots.
result Gaussian parity is universal for 2D knots.
A surgery classification theory is introduced for manifolds of bounded geometry up to quasi-isometry. The Borel conjecture for this theory is proven for flat Euclidean space.
The volume of an infinitesimally flexible polyhedron is a multiple root of its volume polynomialmath.MG
It is proven that the volume of an infinitesimally flexible polyhedron in is a multiple root of its volume polynomial.
Study reveals heavy-tailed behavior in training ReLU gates.
problem Understanding heavy-tailed distribution in stochastic deep learning.
method Experimental study of heavy-tail index for S.G.D. and a variant.
result Two algorithms exhibit similar heavy-tail behavior on ReLU data.
Researchers solved a model of an exhaustible resource with stochastic discoveries.
problem Optimal exploration of an exhaustible resource with uncertain discoveries.
method Impulse control and Poisson process of new discoveries.
result A frontier of critical levels of proven reserves exists, above which exploration is stopped.
Positive Thompson links are proven for oriented subgroup elements.
problem Proving properties of Thompson links with positive elements.
method Analyzing elements of the oriented subgroup of the Thompson group.
result Positive oriented Thompson links are established.
The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph, they are not in th…
A proof of the monotonicity of an entropy like energy for the heat equation on a quaternionic contact and CR manifolds is proven
The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.
We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.
The author shows that equicontinuous geodesic flows on surfaces are periodic. A similar result for flows on 3-manifolds is also proven. The idea of the proof is to show that the return map is recurrent and therefore periodic.
There has recently been a lot of ongoing research in the areas of fairness, bias and explainability of machine learning (ML) models due to the self-evident or regulatory requirements of various ML applications. We make the following observation: All of these approaches require a robust understanding of the relationship…
Acyclicity proven for curve complex on surfaces.
problem Acyclicity of curve complex on surfaces.
method Analyzing homologous curves on surfaces of genus g.
result Complex is (g-3)--acyclic.
We prove the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds or under special asymptotics.
In this paper it is proven that there is at most one way, up to isotopy, in which a connected, hyperbolic, orientable 3-manifold can fiber over the circle with monodromy in the Torelli group.
In the article a strenthened version of the 'Fundamental Theorem of asset Pricing' for one-period market model is proven. The principal role in this result play total and nonanihilating cones.
In this paper, results of J. Park and of B.D Park and Szabo on simply connected symplectic 4-manifolds are re-proven and extended to non-simply connected manifolds using Luttinger surgeries.
The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a regular, negatively curved, ideal structure.
Some properties of non-orientable 3-manifolds are shown. The semi-group of cobordism of immersions of surfaces in such manifolds is computed and proven actually to be a group. Explicit invariants are provided.
It is proven that the identity component of the group preserving the leaves of a generalized foliation is perfect. This shows that a well-known simplicity theorem on the diffeomorphism group extends to the nontransitive case.
New approach identifies and explains errors in machine learning pipelines.
problem Challenges in identifying and explaining errors in complex machine learning pipelines.
method Uses iteration and provenance to automatically infer root causes of failures.
result Significantly improves precision and recall compared to state-of-the-art methods.
Sequence-to-Sequence (seq2seq) modeling has rapidly become an important general-purpose NLP tool that has proven effective for many text-generation and sequence-labeling tasks. Seq2seq builds on deep neural language modeling and inherits its remarkable accuracy in estimating local, next-word distributions. In this work…
Proves a theorem similar to Moser's using a normalization method.
problem Proving a theorem similar to Moser's in a specific context.
method Iterative normalization procedure based on Generalized Fischer Decompositions.
result An analogue of the Theorem of Moser proven.
It is proven that if a finitely presented group is one ended it has asymptotic dimension bigger than one. It follows that finitely presented groups with asdim 1 are virtually free. A counterexample is given for the finitely generated case.
Critiques incorrect fixed point assertions in digital topology.
problem Incorrect or incorrectly proven fixed point assertions in digital topology.
method Critical review of existing assertions.
result Identifies and critiques incorrect fixed point assertions.
On real hypersurfaces in complex space forms many results are proven. In this paper we generalize some results concerning extrinsic geometry of real hypersurfaces, to CR submanifolds of maximal CR dimension in complex space forms.
Uniqueness of Kähler Ricci shrinkers proven on toric orbifolds.
problem Proving uniqueness of Kähler Ricci shrinkers on toric orbifolds.
method Extending results from toric manifolds to toric orbifolds.
result Uniqueness of Kähler Ricci shrinkers on toric orbifolds established.
Global and local blowups of manifolds are proven equivalent.
problem Equivalence of global and local blowups in differential topology.
method Proof of equivalence between global and local constructions of blowups.
result Global and local constructions of blowups are shown to be equivalent.
Corrects incorrect assertions about fixed points in digital topology.
problem Incorrect or incorrectly proven assertions about fixed points in digital metric spaces.
method Analysis of existing assertions and proofs.
result Identifies and corrects errors in published assertions.
Morse foliations of codimension one on the sphere S^3 are studied and the existence of special components for these foliations is derived. As a corollary the instability of Morse foliations can be proven in almost all cases.