New approach identifies latent properties from mechanisms, not just data.
problem Identifying latent properties from data generating processes.
method Equivariance perspective on identifiable representation learning.
result Identification of latent properties is possible up to shared equivariances in known mechanisms.
Extracts important peaks from XRD spectra using Attention mechanism.
problem Identifying significant peaks in XRD patterns for material properties.
method Convolutional neural network with Attention mechanism to analyze deep features.
result Selected lattice constant predicts cathodic material cell voltage.
New integrators for mechanical systems on Lie groups simplify based on group properties.
problem Designing numerical integrators for mechanical systems on Lie groups.
method Leverage retraction maps and Lie group properties to design structure-preserving integrators.
result Simplified design of integrators for Euler-Poincare and Lie-Poisson equations.
New closed linkage mechanisms with Möbius strip properties.
problem Designing closed linkage mechanisms with arbitrary number of hinges.
method Proposed a new family of closed linkage mechanisms with singular properties.
result These mechanisms can be considered as discrete Möbius strips.
Study reveals Transformer's expressive power and mechanisms.
problem Understanding the approximation properties of Transformer for sequence modeling.
method Systematic study of Transformer's components and their combined effects, establishing approximation rates.
result Reveals roles of critical parameters in Transformer, such as number of layers and attention heads.
Investigates the fundamental components of attention mechanisms.
problem Understanding the building blocks of attention in deep learning.
method Classified and studied three key mechanisms: additive, multiplicative output, and synaptic attention.
result Additive activation attention is central in proofs of lower bounds.
This paper provides a construction of a quantum statistical mechanical system associated to knots in the 3-sphere and cyclic branched coverings of the 3-sphere, which is an analog, in the sense of arithmetic topology, of the Bost-Connes system, with knots replacing primes, and cyclic branched coverings of the 3-sphere …
Developed neural network for predicting mechanical properties of composite materials.
problem Predicting and optimizing mechanical properties of composite materials.
method Convolutional neural network model integrated with a genetic algorithm optimizer.
result Highly accurate predictions and optimal microstructural designs identified.
MAT uses attention mechanism for molecule property prediction.
problem Designing a competitive neural network for molecule property prediction.
method Augmented attention mechanism using inter-atomic distances and molecular graph structure.
result MAT achieves state-of-the-art performance on diverse molecular prediction tasks.
Framework uses diffusion models to infer material properties from noisy mechanical measurements.
problem Inference of spatially varying material properties from noisy mechanical responses.
method Conditional score-based diffusion models approximating the score function of a conditional distribution.
result Framework can efficiently solve large-scale physics-based inverse problems.
We formulate a class of minimal tori in S^3 in terms of classical mechanics, reveal a curious property of the Clifford torus, and note that the question of periodicity can be made more explicit in a simple way.
With the proliferation of mobile devices and the internet of things, developing principled solutions for privacy in time series applications has become increasingly important. While differential privacy is the gold standard for database privacy, many time series applications require a different kind of guarantee, and a…
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…
Extends PoS proof-of-stake transaction fee mechanism with miner utility model.
problem Designing a transaction fee mechanism for PoS protocol that incorporates miner utility.
method Introduced a new mechanism (BSP(θ)) incorporating a parameter θ to ensure user and miner incentives.
result The new mechanism (BSP(θ)) satisfies user and miner incentives and contract proofness.
Studies geometric mechanics for autonomous and nonautonomous systems.
problem Understanding the geometric basis of mechanics.
method Geometric descriptions, Lagrangian, Hamiltonian, unified formalisms, symmetries, variational principles.
result Characterization of dynamical systems' properties and characteristics.
A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. We were al…
The study develops a word mechanism for knot and link diagrams.
problem Determining incompressible and pairwise incompressible surfaces in knot or link complements.
method Word mechanism applied in knot and link diagrams.
result Finiteness theorem and upper bound on Euler characteristic of surfaces.
Study examines quotients of affine connection control systems.
problem Existence of quotients preserving mechanical structures.
method Local and global sufficient and necessary conditions for geodesically accessible systems.
result Quotients can be constructed for geodesically accessible systems.
The geometry of a Lagrangian mechanical system is determined by its associated evolution semispray. We uniquely determine this semispray using the symplectic structure and the energy of the Lagrange space and the external force field. We study the variation of the energy and Lagrangian functions along the evolution and…
Study on protecting sensitive properties of datasets during analysis.
problem Ensuring privacy of sensitive properties in datasets.
method Proposes definitions and mechanisms for attribute privacy using the Pufferfish framework.
result Developed efficient and inefficient mechanisms for attribute privacy.
Study introduces statistical mechanics for min-max problems.
problem Understanding the properties of min-max problems in high dimensions.
method Statistical mechanical formalism for analyzing min-max problems.
result Derives the relationship between training data and generalization error.
Paper tackles dynamic behavior of variable topology mechanisms, presenting new transition conditions.
problem Dynamic behavior of mechanisms with changing kinematic topology.
method Presented new transition conditions for variable topology mechanisms using projected motion equations and Voronets equations.
result Results show the dynamic behavior of joint locking in 3R and 6DOF mechanisms.
We present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime, the existence, the signature and a specific form of a metric on it, and certain na…
Oil markets profoundly influence world economies through determination of prices of energy and transports. Using novel methodology devised in frequency domain, we study the information transmission mechanisms in oil-based commodity markets. Taking crude oil as a supply-side benchmark and heating oil and gasoline as dem…
Elasticity images map biomechanical properties of soft tissues to aid in the detection and diagnosis of pathological states. In particular, quasi-static ultrasonic (US) elastography techniques use force-displacement measurements acquired during an US scan to parameterize the spatio-temporal stress-strain behavior. Curr…
The paper develops a method for inferring second opinions from experts using counterfactual inference.
problem Designing efficient decision support systems for second opinions.
method Set invariant Gumbel-Max structural causal model for multiclass classification.
result The proposed model can infer second opinions more accurately than non-causal models.
The paper analyzes errors in mechanical systems with external forces.
problem Error analysis of mechanical systems with external forces.
method Analysis of variational integrators with contact order r for discrete mechanical systems. result The contact order of the integrator is the same as the contact order of the original systems.
This work improves the Rényi differential privacy of the SGM mechanism.
problem Improving the privacy amplification of the SGM mechanism.
method Unified and precise computation of SGM's Rényi Differential Privacy using a numerically stable procedure.
result A nearly tight closed-form bound on SGM's Rényi Differential Privacy.
The paper analyzes network models with binary values and sub-Gamma noise, deriving asymptotic properties.
problem Analyzing network models with binary values and sub-Gamma noise.
method Derives asymptotic properties of network models with binary values and sub-Gamma noise.
result Established asymptotic consistency and normality of parameter estimators in network models.
Ranked data appear in many different applications, including voting and consumer surveys. There often exhibits a situation in which data are partially ranked. Partially ranked data is thought of as missing data. This paper addresses parameter estimation for partially ranked data under a (possibly) non-ignorable missing…
A new graph model HMG and neural network HMGNN improve molecule property predictions.
problem Predicting quantum mechanical properties of molecules with limited consideration of many-body interactions.
method Introducing heterogeneous molecular graphs (HMG) and building HMGNN on neural message passing scheme.
result HMGNN achieves state-of-the-art performance in 9 out of 12 tasks on the QM9 dataset.
In this work we introduce a category of discrete Lagrange--Poincare systems LP_d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete mechanical systems obtained by the Lagrangian reduction of symmetric discrete mechanical systems are objects in LP_d. We introdu…
Proposes a new method for estimating counterfactual treatment effects.
problem Uncertainty in identifying causal mechanisms from observational data.
method Introduces a parameterized family of causal mechanisms that generalize Gumbel-max, trained to minimize counterfactual effect variance.
result Trained mechanisms yield lower variance estimates of counterfactual treatment effects.
Unified framework supports lifelong learning properties.
problem Capturing desirable properties of human learning in machine learning.
method Unified framework with one central mechanism.
result Supports almost all desirable properties of human learning.
Survey explores cohomology's roles in applied math and sciences.
problem Understanding cohomology's role in solving differential equations.
method Examining differential complexes and structure-preserving discretizations.
result Various fundamental concepts in mechanics are formulated using differential complexes.
Molecular structure-property relationships are key to molecular engineering for materials and drug discovery. The rise of deep learning offers a new viable solution to elucidate the structure-property relationships directly from chemical data. Here we show that the performance of graph convolutional networks (GCNs) for…
First differentially private mechanism for anonymized histograms.
problem Protecting sensitive data in anonymized histograms.
method Proposes a differentially private mechanism for releasing anonymized histograms.
result Achieves near-optimal privacy utility trade-off in terms of number of items and privacy parameter.
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propos…
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
Novel compression method preserves privacy while reducing communication costs.
problem Reducing communication costs in differential privacy mechanisms.
method Poisson private representation (PPR) for compressing and simulating local randomizers.
result Achieves compression within a logarithmic gap from theoretical lower bound.
Differential equations explain neural network dynamics.
problem Understanding neural networks using differential equations.
method Analyzing properties of differential equations as machine learning models.
result Neural networks can be modeled by differential equations.
We describe an approach to understand the peculiar and counterintuitive generalization properties of deep neural networks. The approach involves going beyond worst-case theoretical capacity control frameworks that have been popular in machine learning in recent years to revisit old ideas in the statistical mechanics of…
GraphOpt learns the formation mechanism of graphs from observed structures.
problem Learning formation mechanisms from observed graphs with complex structural properties.
method GraphOpt uses maximum entropy inverse reinforcement learning to solve the link formation problem in a sequential decision-making process.
result GraphOpt discovers a latent objective function that can explain and transfer across different graphs.
Paper applies fluid dynamics to stock market behavior.
problem Understanding stock market dynamics using physical principles.
method Uses Stokes law to model stock market as fluid system.
result Stock market dynamics can be explained by physical properties.
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
This work generalizes Hamiltonian mechanics using closed differential forms.
problem Hidden invariants in classical Hamiltonian mechanics.
method Establishes a novel correspondence between generalized Hamiltonian mechanics and multisymplectic geometry.
result Key theorems linking classical and generalized Hamiltonian systems.
Sturm theory applied to symplectic geometry and mechanics.
problem Detecting geometric properties of solutions in symplectic geometry and mechanics.
method Generalization of symplectic Sturm theory to Hamiltonians and application to semi-Riemannian manifolds and singular Lagrangian systems.
result Detection of conjugate and focal points on semi-Riemannian manifolds and geometrical properties of solutions space.
The paper explores how mixing and diffusion mechanisms can enhance privacy in data processing.
problem Enhancing privacy guarantees of data mechanisms through post-processing.
method The study uses Markov operators and coupling arguments to analyze privacy amplification.
result The introduction of a new family of diffusion-based mechanisms that are closed under post-processing.