Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
Paper simplifies complex causal identifiability problems with exogenous isomorphism.
problem Achieving consistent answers to causal questions in Structural Causal Models.
method Introducing exogenous isomorphism and proposing ∼EI-identifiability. result Unified and generalized theories for practical applications in counterfactual reasoning.
New theory explains how self-supervised learning converges, advancing AI research.
problem Lack of precise theoretical explanation for self-supervised learning convergence.
method Synthesized Identifiability Theory with empirical evidence to propose Singular Identifiability Theory (SITh).
result SITh provides deeper insights into SSL's implicit data assumptions and advances representation learning.
Identifiability, or recovery of the true latent representations from which the observed data originates, is de facto a fundamental goal of representation learning. Yet, most deep generative models do not address the question of identifiability, and thus fail to deliver on the promise of the recovery of the true latent …
Theory extends optimal learning rates without realizability assumption.
problem Agnostic binary classification without realizability assumption.
method Identifies tetrachotomy of optimal rates and combinatorial structures.
result Optimal universal rates for binary classification in agnostic setting.
Develops identifiability theory for multi-lag regime-switching models.
problem Ensuring interpretability of deep latent variable models with multi-lag dependencies.
method Formulates a general theoretical framework for multi-lag Regime-Switching Models (RSMs), proving identifiability of number of regimes and multi-lag transitions.
result Establishes identifiability conditions for multi-lag regime-switching models, including Markov Switching Models and Switching Dynamical Systems.
New theory for local parameterization of deep ReLU networks.
problem Determining local parameters of deep ReLU neural networks.
method Introducing local lifting operators and charts of a manifold, deriving necessary and sufficient conditions for local identifiability.
result Sharp and testable conditions for local identifiability of deep ReLU networks.
String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use…
Effective action for Kerr-Newman black hole found in twistor theory.
problem Effective action for Kerr-Newman black hole.
method Twistor particle theory to achieve all-orders worldline effective action.
result Exact hidden symmetries identified in self-dual backgrounds.
New theory allows ICA without assuming non-Gaussian sources.
problem Traditional ICA struggles with Gaussian sources.
method Developed identifiability theory based on second-order statistics and sparsity.
result Identifiability theory and estimation methods validated experimentally.
The paper sets sample complexity bounds for identifying LTI systems from a finite set.
problem Identifying an LTI system from a finite set of possible systems using trajectory data.
method Maximum likelihood estimator and information theory tools.
result Upper and lower bounds for sample complexity are derived, independent of stability assumption.
Transformer-based method improves causal discovery from observational data.
problem Causal discovery from observational data requires explicit assumptions.
method CSIvA transformer architecture trained on synthetic data.
result Transformer-based methods adhere to identifiability theory.
This is the first paper in a series which proposes and develops the polyfold Fredholm structure--Kuranishi structure correspondence, identifying these two abstract perturbative structures which are indispensable for constructing and understanding symplectic invariants in the most general settings. In this paper, I pres…
Study homotopy types of free racks and quandles, proving analogs of Milnor's theorem.
problem Understanding the homotopy types of free racks and quandles.
method Proved analogs of Milnor's theorem for racks and quandles and their pointed variants.
result Identified the homotopy types of free racks and quandles on spaces of generators.
We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.
We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example,…
Study uses DNM theory to detect early warning signals of market instability.
problem Detecting early warning signals of financial market instability.
method Applying Dynamical Network Marker (DNM) theory to trading data from the Tokyo Stock Exchange.
result Early warning signals of large price movements can be detected on a daily time scale.
This work closes the gap between theory and practice for nICA identifiability.
problem Identifying latent components in nonlinearly mixed data.
method Finite-sample analysis of GCL-based nICA, combining GCL properties, statistical generalization, and numerical differentiation.
result Establishes a trade-off between function learner complexity and expressiveness.
New framework for identifying spatial data components using TP latent components.
problem Identifying complex dependencies in spatial data.
method Introduces a new nonlinear ICA framework with t-process latent components and develops a learning and inference algorithm. result Identifiability of TP independent components under general conditions and Gaussian Process limit.
Study instantons on asymptotically conical Spin(7)-manifolds, identifying deformation spaces.
problem Deformation theory of instantons on specific Spin(7)-manifolds.
method Relating deformation complex to spinors, identifying kernel of twisted negative Dirac operator.
result Virtual dimension of moduli space calculated using index theorem and Dirac operator spectrum.
In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal surfaces, we seek examples of triply periodic polyhedral surfaces that have an identifia…
New method AnInfoNCE uncovers latent factors in contrastive learning with practical variability.
problem Theoretical assumptions of contrastive learning loss overlook practical variability in positive pairs.
method AnInfoNCE, a generalization of InfoNCE, models anisotropic variability to uncover latent factors.
result AnInfoNCE increases recovery of latent factors in CIFAR10 and ImageNet, albeit at the cost of accuracy.
Unsupervised learning models can be indistinguishable without identifiability, leading to unreliable representations.
problem Unsupervised learning models may be indistinguishable without identifiability, making it impossible to recover a ground truth generative model.
method Construction based on nonlinear independent component analysis theory to illustrate potential failure cases.
result Counterexamples show that identifiability is crucial for reliable unsupervised representation learning.
Modernizes classical theory linking isothermic surfaces to Bonnet pairs.
problem Classical theory of isothermic surfaces and Bonnet pairs.
method Identifies derivatives of Bonnet pairs with retraction form of isothermic surfaces.
result Modern account and identification of retraction form.
New method identifies latent relationships in deep models without additional constraints.
problem Latent representations in deep latent variable models are not statistically identifiable.
method Identifies relationships between latent variables (distances, angles, volumes) under mild model conditions.
result Empirically demonstrates more reliable latent distances without additional labeled data.
Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in na…
This research improves neural network representation identifiability through task structures.
problem Improving neural network representation identifiability in multi-task settings.
method Analyzing the effects of task distributions and causal structures on latent factors, leading to simpler optimization.
result A straightforward optimization procedure enables better representation recovery in both synthetic and real-world data.
The proof of Theorem 7.12 of "Uniqueness of smooth cohomology theories" by the authors of this note is not correct. The said theorem identifies the flat part of a differential extension of a generalized cohomology theory E with ER/Z (there called "smooth extension"). In this note, we give a correct proof. Moreover, we …
Quantum oracles help identify counterfactuals better than classical ones.
problem Identifying unknown causal parameters in causal models.
method Using quantum oracles to query and identify all causal parameters and counterfactuals.
result Quantum oracles enable identification of all two-way joint counterfactuals and tighter bounds on higher-order counterfactuals.
New method identifies key genes affecting phenotypes in biological systems.
problem Identifying genes that drive specific phenotypes in complex biological systems.
method Data-driven observability decomposition using Koopman operators.
result Koopman operator representation identifies genes that drive phenotypes.
This paper uses MIS to identify key financial institutions with minimal risk contagion.
problem Mitigating systemic risk during extreme financial events.
method Applying extreme value theory and MIS from graph theory to identify diversified portfolios.
result Identified a subset of institutions with minimal extremal dependence for diversified portfolios.
Neural interaction discoveries can be real or artifacts of model flexibility.
problem Identifying real neural interactions from data.
method Using a multiplicative-gating extension of neural additive vector autoregression.
result Effective rank of the joint lag-block covariance predicts interaction recoverability.
Tab-Shapley identifies top-k anomalies in tabular data quality insights.
problem Challenges in identifying anomalies in unlabeled tabular datasets.
method Cooperative game theory using Shapley values to quantify attribute contributions.
result Efficiently identifies top-k tabular data quality insights using closed-form Shapley values.
We relate decategorifications of Ozsváth-Szabó's new bordered theory for knot Floer homology to representations of Uq(gl(1∣1)). Specifically, we consider two subalgebras Cr(n,S) and Cl(n,S) of Ozsváth- Szabó's algebra B(n,S), an…
Theory explains how deep nets learn features from data.
problem Understanding how deep neural networks learn features from data.
method Developed a noise-nonlinearity phase diagram and a mechanical theory.
result Links feature learning across layers to generalization.
New method identifies latent variables with sparse perturbations.
problem Identifying latent variables with minimal supervision.
method Weakly supervised representation learning with sparse perturbations.
result Identification of latent variables up to specified blocks.
This paper provides a full controlled version of algebraic K-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior of the inverse limit as the control parameter goes to 0. There…
LeJEPA learns latent variables from nonlinear observations.
problem Learning latent variables from nonlinear observations.
method Proves linear identifiability of Gaussian latent distributions.
result Gaussian distribution uniquely guarantees linear identifiability.
The paper characterizes boundaries in Turaev-Viro TQFTs and Dijkgraaf-Witten theories.
problem Characterizing boundaries in Turaev-Viro TQFTs and Dijkgraaf-Witten theories.
method Identifying explicit boundary locality conditions and proving consistency with state sum models.
result Turaev-Viro and Dijkgraaf-Witten theories with boundary defects admit a state sum description.
Study ALE spaces via nodal curves and compactifications.
problem Understanding ALE spaces through nodal curves and compactifications.
method Circle action on 4-manifold, C^* action on compactification, identification of nodal curves.
result Identified nodal rational curve in a projective rational surface.
Automatically identifies geometric flat outputs for robotic systems.
problem Lack of systematic and practical means to identify flat outputs for arbitrary robotic systems.
method Casts the search for a globally valid, equivariant flat output as an optimization problem using Riemannian geometry, Lie group theory, and differential forms.
result Approximate transcription of continuum formulation to a quadratic program achieves precise agreement with known closed-form flat outputs.
Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply the theory to the ZS-AKNS nxn heirarchy (which includes the non-linear Schrödinger …
We show that the unnormalised Khovanov homology of an oriented link can be identified with the derived functors of the inverse limit. This leads to a homotopy theoretic interpretation of Khovanov homology.
Paper establishes identifiability conditions for a model with two latent vectors and auxiliary data.
problem Identifying conditions for a statistical model with two latent vectors and auxiliary data.
method Proposes a statistical model with two latent vectors and auxiliary data, establishing various identifiability conditions.
result Identifiability conditions reveal a dimensionality relation and link model indeterminacies to maximum link weights.
Hypothesis testing in singular models is fundamentally about identifiable vs. non-identifiable parameters.
problem Testing in singular models is inherently problematic due to non-identifiability and degeneracy of Fisher information.
method Formalized the overlap obstruction and showed that hypotheses over non-identifiable parameters are untestable, while those over identifiable parameters reduce to classical testing.
result Hypotheses over non-identifiable parameters are untestable, while those over identifiable parameters reduce to classical testing.
The paper analyzes frameworks for integrating sustainability into investment decisions.
problem Understanding how ESG factors influence investment choices.
method Examined and analyzed various theoretical frameworks including Behavioral Finance, Modern Portfolio, and Risk Management.
result Investors increasingly integrate ESG factors to optimize financial outcomes and societal goals.
New framework for disentangling features from noisy data.
problem Disentangling identifiable features from noisy data.
method Structured Nonlinear Independent Component Analysis (SNICA).
result Identifiability holds even in the presence of noise of unknown distribution.