DNF-Net tackles tabular data challenges with neural architecture.
problem Handling tabular data efficiently using neural networks.
method DNF-Net uses a neural architecture with inductive bias corresponding to logical Boolean formulas in disjunctive normal form over affine soft-threshold decision terms.
result DNF-Net significantly outperforms fully connected networks on tabular data.
Paper proves hardness of learning various complex models under local pseudorandom generators.
problem Hardness of learning various complex models.
method Existence of local pseudorandom generators.
result Proves hardness of learning shallow ReLU neural networks and other models.
Improved algorithm for conditional linear regression with heterogeneous covariances.
problem Identifying a linear predictor for a fraction of data with varying covariances.
method Polynomial time algorithm using Disjunctive Normal Form (DNF) to identify a condition and linear predictor.
result Removed requirement for similar covariances in each condition term, improving algorithm applicability.
Reinterprets DNF as a deep generative LDA model for complex data.
problem Limited applicability of LDA in complex data scenarios.
method Proposes a discriminative normalization flow (DNF) model and interprets it as a deep generative LDA.
result DNF and its subspace version outperform conventional LDA in modeling complex data.
DNFS trains efficient samplers for discrete distributions using locally equivariant Transformers.
problem Sampling from unnormalised discrete distributions.
method DNFS learns a rate matrix to satisfy the Kolmogorov equation, using control variates and locally equivariant Transformers.
result DNFS achieves efficient and effective sampling across various applications.
We consider the following conditional linear regression problem: the task is to identify both (i) a k-DNF condition c and (ii) a linear rule f such that the probability of c is (approximately) at least some given bound μ, and f minimizes the ℓp loss of predicting the target z in the distribution of …
The paper proposes deep normalization to improve speaker recognition performance.
problem Non-Gaussian and non-homogeneous distributions of deep speaker vectors negatively impact speaker recognition.
method Proposes a deep normalization approach based on a novel discriminative normalization flow (DNF) model.
result DNF-based normalization delivers substantial performance gains and strong generalization capability.
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
problem Understanding how neural networks learn and generalize on Boolean data.
method End-to-end analysis of depth-2 discrete fully connected networks and DNF formulas, using Monte Carlo learning.
result Predictable training dynamics and interpretable features emerge, linking inductive bias and generalization.
This work connects hardness of approximation and learning.
problem Hardness of approximation and learnability in machine learning.
method Shows a single hardness property implying both approximation and learning hardness.
result Obtains new results on hardness of approximation and learnability of specific functions.
Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there does not often exist a good model on the whole dataset, so we seek to find a small subset where there exists a useful model. We ar…
Since its inception in the 1980s, ID3 has become one of the most successful and widely used algorithms for learning decision trees. However, its theoretical properties remain poorly understood. In this work, we introduce a novel metric of a decision tree algorithm's performance, called mean iteration statistical consis…
Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly identifying a significant (but perhaps small) segment of a population in which there is a…
Efficient algorithms for online learning with changing action sets, achieving no-approximate-regret guarantees.
problem Online learning with sleeping experts/bandits, where only a subset of actions are available each time.
method Developed computationally efficient algorithms providing no-approximate-regret guarantees for the general problem and better approximation ratios for special cases.
result Achieved no-approximate-regret guarantees for the general sleeping expert/bandit problems and better approximation ratios for specific cases.
A new method learns interpretable decision rules using submodular optimization.
problem Learning interpretable decision rules from data.
method Submodular optimization approach for selecting rules from a large set.
result The method effectively learns interpretable rule sets from real datasets.
Bayesian PINNs solve noisy PDE problems with physics constraints.
problem Uncertainty quantification in noisy PDE problems.
method Bayesian framework combining PINNs and HMC/VI for posterior estimation.
result HMC outperforms VI for noisy data.
Proves a general connected sum formula for families Seiberg-Witten invariants.
problem Limited connected sum formulae for families Seiberg-Witten theory.
method Develops a general connected sum formula incorporating previous results.
result Proves a new connected sum formula for Seiberg-Witten families.
Derives an integral formula for G2-structures.
problem Calculating properties of G2-structures.
method Applies an integral formula for G-structures to G2.
result Derives an integral formula relating curvatures and quadratic invariants.
Derives integral formulae on weighted manifolds.
problem No specific problem stated; focuses on mathematical derivations.
method Introduces weighted mean sigma-r curvature and uses weighted Newton transformations.
result Derives integral formulae generalizing previous work.
Paper derives trace formula for magnetic Laplacian at zero energy.
problem Trace formula for magnetic Laplacian at zero energy.
method Generalizes Gutzwiller trace formula, focuses on zero energy level.
result Derives trace formula at zero energy level.
The Gauss formula is extended to various Laplacians on submanifolds.
problem Deriving formulas for Laplacians on submanifolds.
method Extending the Gauss formula to different types of Laplacians.
result Formulas for various Laplacians on submanifolds.
The paper is devoted to the problem of finding explicit combinatorial formulae for the Pontryagin classes. We discuss two formulae, the classical Gabrielov-Gelfand-Losik formula based on investigation of configuration spaces and the local combinatorial formula obtained by the author in 2004. The latter formula is based…
We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the symplectic-sum formula for Gromov-Witten invariants. The second formula is stronger, …
Note on new cancellation formulas for manifolds.
problem Generalizing anomaly cancellation formulas to manifolds.
method Proving new (a, b) type cancellation formulas and using transgression.
result Obtained characteristic forms with modularity properties.
The main result of the present paper is a coincidence formula for foliated manifolds. To prove this we establish Kuenneth formula, Poincare duality and intersection product in the context of tangential de Rham cohomology and homology of tangential currents. We apply the formula to get a dynamical Lefschetz formula for …
Formula calculates volume of two-bridge knots.
problem Calculating the volume of two-bridge knots.
method Derived from Hopf formula and Fox derivatives.
result Closed formula for the volume of two-bridge knots.
Introduces a universal Bochner formula for scalar curvature.
problem None explicitly stated; focuses on a new formula.
method Introduces a universal Bochner formula.
result Contains special cases like stability inequality and Schrödinger-Lichnerowicz-type formula.
Formula connects surgeries to Seiberg-Witten invariants.
problem Understanding how surgeries affect Seiberg-Witten invariants.
method Proves surgery formulas for Seiberg-Witten invariants and families.
result Expresses new invariants in terms of original ones.
It has been shown that the Alvarez-Gaumeˊ-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula i…
Proves a formula for a special invariant of 4-manifolds.
problem Calculating the Bauer-Furuta invariant for connected sums of 4-manifolds.
method Uses a finite dimensional approximation of the Seiberg-Witten monopole map to derive a formula for the families Bauer-Furuta invariant of a fibrewise connected sum.
result Derives a general connected sum formula for the families Bauer-Furuta invariant.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
problem Proving a special case of the Gaussian kinematic formula.
method Viewing the GKF as the limit of spherical kinematic formulas for large dimension spheres.
result Proves a special case of the Gaussian kinematic formula.
New Crofton formulae derived from existing ones.
problem Generalizing Crofton formulae for products.
method Calculations in the ring of normal densities.
result Generalizations of Crofton formulae in terms of mixed Riemannian volume.
Formulae for non-symmetric connections derived from covariant derivatives.
problem Deriving commutation formulae for non-symmetric affine connections.
method Covariant derivatives of tensors with respect to symmetric and non-symmetric affine connections.
result Formulae for non-symmetric connections derived from covariant derivatives.
Formula connects curvature to volume in special geometric spaces.
problem Deriving formulas for curvature in specific geometric spaces.
method Used strong locality of Laplacian and eigenfunction approximation.
result Proved integral type Gauss-Green formula linking curvature to volume.
Kenmotsu's formula describes surfaces in Euclidean 3-space by their mean curvature functions and Gauss maps. In Lorentzian 3-space, Akutagawa-Nishikawa's formula and Magid's formula are Kenmotsu-type formulas for spacelike surfaces and for timelike surfaces, respectively. We apply them to a few problems concerning rota…
The paper proves T-duality and Hori formulae for winding loop spaces.
problem Realizing T-duality and Hori formulae for loop spaces.
method Proving T-duality and Hori formulae for winding q-loop spaces.
result T-duality and Hori formulae for winding q-loop spaces are proven.
New formulas for measuring geometric properties of definable sets.
problem Measuring geometric properties of definable sets in a non-standard setting.
method Proved two kinematic formulas integrating on SO(n)imesSn−1. result Generalized Cauchy-Crofton and infinitesimal linear kinematic formulas.
Guillemin trace formula adapted for group actions.
problem Distributional trace for proper, cocompact group actions.
method Developing an equivariant version of the distributional trace.
result Equivariant Guillemin trace formula for group actions.
Unified entropy formula for real, complex, and quaternionic DLNs.
problem Deriving a formula for DLNs over different fields.
method Extending Menon and Yu's formula to complex and quaternionic DLNs.
result Unified entropy formula for DLNs over R, C, and H. Proves an Euler-type formula for Möbius strip partitions.
problem No specific problem stated; focuses on a mathematical formula.
method Analyzes partitions of the Möbius strip.
result Proves an Euler-type formula for Möbius strip partitions.
We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson cross-sections.
Paper derives matrix formulae and proves skein relations for non-orientable surfaces in quasi-cluster algebras.
problem Understanding quasi-cluster algebras on non-orientable surfaces.
method Developed matrix formulae and proved skein relations for quasi-cluster variables.
result Laurent expansion and skein relations for quasi-cluster variables on non-orientable surfaces.
New formulas for coassociative submanifolds' volume variation.
problem Understanding volume changes in coassociative submanifolds.
method Proved new variation formulae using G2 data. result Highlight the role of ambient torsion and Ricci curvature in volume changes.
New methods derive a generalized Frenkel trace formula for Lie groups.
problem Deriving a generalized Frenkel trace formula for Lie groups.
method Applying supersymmetric localization to quantum mechanical and gauged sigma models.
result Presented two complementary approaches for the derivation of the trace formula.
Alternative closed-form formula for spread call option prices under log-normal models.
problem Valuation of spread call options under log-normal models.
method Developed an alternative closed-form formula for spread call option prices.
result Our formula performs better for certain range of model parameters than existing closed-form formula.
The paper derives new Gauss-Bonnet formulas for frontal bundles over surfaces with boundary.
problem Deriving new formulas for coherent tangent bundles over surfaces with boundary.
method Defining frontal bundles and applying Gauss-Bonnet theorems to derive formulas.
result Four new Gauss-Bonnet type formulas for frontal bundles are derived.
In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails o…
Proves a formula in Heegaard Floer homology using combinatorial methods.
problem Proving Lipshitz's Maslov index formula in Heegaard Floer homology.
method Combinatorial proof via Heegaard diagrams.
result Validated Lipshitz's Maslov index formula in Heegaard Floer homology.
We give a formula of the colored Alexander invariant in terms of the homological representation of the braid groups which we call truncated Lawrence's representation. This formula generalizes the famous Burau representation formula of the Alexander polynomial.