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.
The paper introduces closed-form expressions for interpreting Tsetlin Machines.
New interpretation of complex hyperbolic form as Weil-Petersson form.
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive normal form (OR-of-ANDs). A principled objective function is proposed to trade …
S2KAN integrates symbolic primitives into neural network activations for improved interpretability.
We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern-Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets …
In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by …
We provide local expressions for Chern-Weil type forms built from superconnections associated with families of Dirac operators previously investigated in work by S. Scott and later work by S. Scott and the second author. When the underlying fibration of manifolds is trivial, the even degree forms can be interpreted as …
FP uses random projections to train networks without feedback, achieving comparable performance to backpropagation.
Closed-form polynomial approximations replace MLPs in transformers, enabling new interpretability methods.
causalKANs provides interpretable treatment effect estimates using neural networks.
The paper proposes an interpretable off-policy learning algorithm for medical treatments.
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps determining projections of the tangent bundle onto the partial connection; this approach e…
New algorithms for interpreting complex multivariate functions.
SDE automatically recovers interpretable discrete distributions.
The paper provides a differential form interpretation of a theorem about the dimensions of rational homotopy groups of Diff(D^4).
More and more AI services are provided through APIs on cloud where predictive models are hidden behind APIs. To build trust with users and reduce potential application risk, it is important to interpret how such predictive models hidden behind APIs make their decisions. The biggest challenge of interpreting such predic…
A method interprets black-box models using an ensemble of gradient boosting machines.
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed context and, in particular, enriches it with new natural operations. Applications wi…
Kontsevich's formula for a deformation quantization of Poisson structures involves a Feynman series of graphs, with the weights given by some complicated integrals (using certain pullbacks of the standard angle form on a circe). We explain the geometric meaning of this series as degrees of maps of some grand configurat…
Proposes a supervised VAE to reveal model invariances for interpretability.
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can be used to create more interpretable machine learning models. By proposing a nove…
The problem of explaining deep learning models, and model predictions generally, has attracted intensive interest recently. Many successful approaches forgo global approximations in order to provide more faithful local interpretations of the model's behavior. LIME develops multiple interpretable models, each approximat…
A new method learns interpretable decision rules using submodular optimization.
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-Kähler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces of harmonic forms and cohomologies with the classical de Rham, Dolbeault, Bott-Che…
Machine learning is used more and more often for sensitive applications, sometimes replacing humans in critical decision-making processes. As such, interpretability of these algorithms is a pressing need. One popular algorithm to provide interpretability is LIME (Local Interpretable Model-Agnostic Explanation). In this…
Curvature interpretation for WDVV equation in Frobenius manifolds.
V-HMN integrates memory mechanisms for improved image recognition.
Integrating causal machine learning with inherently interpretable models for decision support.
New models predict mobility flows as well as complex machine learning but are simpler and interpretable.
Despite outstanding contribution to the significant progress of Artificial Intelligence (AI), deep learning models remain mostly black boxes, which are extremely weak in explainability of the reasoning process and prediction results. Explainability is not only a gateway between AI and society but also a powerful tool t…
The present paper contains an interpretation and generalization of Novikov's theory of Morse type inequalities for 1-forms in terms of Conley's theory for dynamical systems.
The latent spaces of GAN models often have semantically meaningful directions. Moving in these directions corresponds to human-interpretable image transformations, such as zooming or recoloring, enabling a more controllable generation process. However, the discovery of such directions is currently performed in a superv…
Curvature penalties improve interpretability of KANs without sacrificing accuracy.
Introducing Nijenhuis forms on Lie-infinity algebras gives a general frame to understand deformations of the latter. We give here a Nijenhuis interpretation of a deformation of an arbitrary Lie algebroid into a Lie-infinity algebra. Then we show that Nijenhuis forms on Lie-infinity algebras also give a short and effici…
Flexible VAEs using FIFs improve model likelihood on image datasets.
Interpretable neural networks improve economic research by balancing accuracy and transparency.
We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1) the web germ admits at least one infinitesimal symmetry, 2) the Chern connection f…
Motivated by the relationship between symplectic fibrations and classical Yang-Mills theories, we study the closeness of a -form (n=2,3) defined on the total space of a fibration as a simple model for an abstract field theory. We introduce 2-plectic fibrations and interpret geometrically the corresponding equations …
We detail the construction of a weak Poisson bracket over a submanifold of a smooth manifold M with respect to a local foliation of this submanifold. Such a bracket satisfies a weak type Jacobi identity but may be viewed as a usual Poisson bracket on the space of leaves of the foliation. We then lift this weak Poisson …
The purpose of this article is to give a geometric interpretation to the so-called "twelve surfaces of Darboux", or "Darboux wreath", which appear by applying repeatedly certain simple transformations to a given infinitesimal isometric deformation of a surface in euclidean three space. This interpretation is a differen…
Model interpretability is an increasingly important component of practical machine learning. Some of the most common forms of interpretability systems are example-based, local, and global explanations. One of the main challenges in interpretability is designing explanation systems that can capture aspects of each of th…
We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Mueller theorem on Ray-Singer torsion and Reidemeister torsion, to the case where the flat vector bundle over a closed manifold carries a nondegenerate symmetric bilinear form. As a consequence, we prove the Burghelea-Haller conjecture which gives an an…
We give a topological interpretation of the space of L2-harmonic forms on finite-volume manifolds with sufficiently pinched negative curvature. We give examples showing that this interpretation fails if the curvature is not sufficiently pinched and that our result is sharp with respect to the pinching constants. The me…
New framework aims to make neural network explanations more reliable.
We give a topological interpretation of the space of harmonis forms of some QALE manifolds introduced by D. Joyce. We introduce a analytical criterium which make possible the used of Mayer-Vietoris sequence.
We study the noncommutative differential geometry of the algebra of endomorphisms of any SU(n)-vector bundle. We show that ordinary connections on such SU(n)-vector bundle can be interpreted in a natural way as a noncommutative 1-form on this algebra for the differential calculus based on derivations. We interpret the …
Study special complexified Kähler forms in mirror symmetry.
Let be an elliptic, product-type suspended (which is to say parameter-dependant in a symbolic way) family of pseudodifferential operators on the fibres of a fibration with base The standard example is where is a family, in the usual sense, of first order, self-adjoint and elliptic pseudodiffe…