Deep neural networks and glassy systems share dynamics but differ in landscape properties.
problem Comparing training dynamics of DNNs and glassy systems.
method Statistical physics methods applied to DNN training.
result DNN dynamics slow down due to many flat directions, diffusing at the loss minimum.
Review of gradient-based algorithms in statistical inference problems.
problem Understanding the dynamics of gradient-based algorithms in statistical inference.
method Insights from physics of glassy systems.
result Quantitative and qualitative understanding of algorithm performance.
Combining ML and physics for understanding glassy systems.
problem Understanding supercooled liquids and glasses due to disorder and non-equilibrium effects.
method Data-driven approach using machine learning with physical intuition.
result Building a phenomenological theory of disordered materials.
Study dynamics of alternating minimization for bilinear regression under large system limits.
problem Understanding the time evolution of alternating minimization for bilinear regression.
method Replica method applied to a multi-temperature glassy system.
result Dynamics of alternating minimization can be described by a two-dimensional discrete stochastic process.
Hard phase in inference problems is glassy and hard to reconstruct.
problem Hard phase in inference problems that are hard to solve algorithmically.
method Study of metastable states and their entropy in low-rank matrix factorization.
result AMP algorithm performance is not improved by considering glassy states.
Experimental fractal landscape dynamics observed in emulsions.
problem Understanding anomalous motions in soft glassy materials.
method Quantitative analysis of oil droplet trajectories in dense emulsions.
result Experimental fractal geometry matches computational model of soft glassy dynamics.
Study of Langevin algorithm in noisy high-dimensional inference.
problem Analyzing the Langevin algorithm's performance in noisy high-dimensional inference.
method Analytic study of Langevin algorithm's performances using the spiked matrix-tensor model.
result The algorithmic threshold of the Langevin algorithm is sub-optimal compared to AMP.
The dynamical behavior of the currency exchange rate after its large-scale catastrophe is discussed through a case study of the rate of Russian rubles to US dollars after its crash in 2014. It is shown that, similarly to the case of the stock market crash, the relaxation is characterized by a power law, which is in ana…
Paper introduces supervised and unsupervised TAM models for binary neurons.
problem Learning and retrieval of structured triplets of patterns in neural networks.
method Extends Hebbian paradigm to supervised and unsupervised protocols, using glassy statistical mechanical techniques.
result Obtained self-consistency equations for critical dataset sizes and retrieval performance.
In our model, n traders interact with each other and with a central bank; they are taxed on the money they make, some of which is dissipated away by corruption. A generic feature of our model is that the richest trader always wins by 'consuming' all the others: another is the existence of a threshold wealth, below wh…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The…
Paper introduces ASP, a variant of AMP for low-rank matrix estimation, showing improved performance under model mismatch.
problem Statistical inference for low-rank matrix estimation problems.
method Introduces approximate survey propagation (ASP) algorithm for low-rank matrix estimation problems.
result ASP converges in a larger regime and can reach lower errors compared to AMP when there is a model mismatch.
Model explains asset price fluctuations using interacting neurons.
problem Understanding volatility and price dynamics in financial markets.
method Structural model based on interacting neurons, generating functional analysis, simulations.
result Model predicts fat-tailed and broader distributions of asset returns.
Deep neural networks undergo hierarchical free-energy landscape transitions with increasing data size.
problem Understanding the design space and dynamics of deep neural networks.
method Statistical mechanical approach based on replica method.
result Hierarchical free-energy landscape transitions with ultrametricity, leading to simpler configurations in deeper layers.
Study energy landscapes in glass models, focusing on Gaussian and spiked-tensor functions.
problem Characterize statistical properties and phase transitions of high-dimensional energy landscapes.
method Developed a Kac-Rice method framework to compute landscape complexity and analyze phase transitions rigorously.
result Characterized the ruggedness and arrangements of local minima in energy landscapes.
Empirical data of supermarket sales show stylised facts that are similar to stock markets, with a broad (truncated) Levy distribution of weekly sales differences in the baseline sales [R.D. Groot, Physica A 353 (2005) 501]. To investigate the cause of this, the influence of social interactions and advertisements are st…
Overview of integrable systems with symmetries, focusing on toric and semitoric systems.
problem Classifying and understanding integrable systems with symmetries.
method Using decorated polygons and controlled bifurcations in one-parameter families of systems.
result Construction of explicit semitoric systems with prescribed invariants.
New method to derive integrable systems from existing Lax systems.
problem Deriving new integrable systems from existing ones.
method Systematic method of deriving new integrable systems from a given one.
result Examples of new integrable systems derived, including the dispersionless Hirota equation, the general heavenly equation, and the web equations.
Learning to control linear systems is statistically hard, especially for underactuated systems.
problem Statistical difficulty of learning to control linear systems, especially underactuated ones.
method Utilized minimax lower bounds and structural assumptions to prove learning complexity can be exponential.
result Learning complexity can be at most exponential with the controllability index of the system.
Discrete-time systems can be characterized by simple flat coordinates and their shifts.
problem Characterizing flatness of discrete-time systems.
method Developed a map from flat coordinates and their shifts to system state and input, fulfilling system equations identically.
result Derived necessary conditions for a system to be flat, without requiring differential geometry methods.
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.
problem High sample complexity for learning partially observed linear dynamical systems in high dimensions.
method Introduces an ℓ1-regularized estimation method that reduces sample complexity from linear to logarithmic with system dimension. result Markov parameters can be learned with logarithmic number of samples relative to system dimension, improving sample complexity.
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
problem Existence of Riemannian invariants for integrable systems of hydrodynamic type.
method Finding coordinates where the generator and all symmetries are diagonal.
result In integrable hydrodynamic systems, there exist coordinates where the generator and all symmetries are diagonal.
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
problem Analyzing nonholonomic constraints in Hamiltonian systems.
method Deriving distributional RCH systems, geometric constraint conditions, and Hamilton-Jacobi theorems.
result Derives precise geometric constraint conditions and Hamilton-Jacobi theorems for nonholonomic systems.
New method models unknown systems with hidden parameters using neural networks.
problem Modeling unknown dynamical systems with hidden parameters.
method Training a deep neural network (DNN) model using trajectory data of the unknown system.
result DNN model accurately predicts unknown dynamical systems with new initial conditions.
MLSys aims to bridge ML and systems research.
problem Designing ML systems for real-world deployment is challenging.
method Foster a new conference and research community.
result MLSys conference focuses on intersection of systems and ML.
A new financial system with ethics risk modeled using fractional calculus.
problem Modeling financial systems with ethical considerations and market confidence.
method Introduced a five-dimensional conformable derivative financial system and a discretization scheme.
result Numerical solutions of the conformable derivative system were tested for hyperchaos.
Paper analyzes CCT sensitivity in constrained power systems, offering insights into system stability and parameter changes.
problem Identifying preventive control measures to avoid large generation losses during disturbances.
method Derived first-order CCT sensitivity for generic constrained power systems using trajectory sensitivity computation.
result Sensitivity of CCT to system parameters, providing insights into feasibility and stability.
Estimates input from output of nonlinear systems using ANN.
problem Estimating unknown compositional input from system output.
method Artificial Neural Networks (ANNs) for nonlinear system inversion.
result ANNs can compete with optimal bounds for linear systems and demonstrate promising results for nonlinear systems.
Study absolute equivalence for Pfaffian systems, applying to control systems.
problem Absolute equivalence of Pfaffian systems with specific independence conditions.
method Structural results for Pfaffian systems of corank 3, applied to control systems.
result Dynamic feedback linearization of control systems with 2 inputs.
Solves selecting the best optimizing system problems.
problem Selecting the best system among contenders with unknown performance.
method Adaptive algorithms integrating stochastic gradient descent and sequential elimination.
result Exponential rates of convergence to zero for false selection probability.
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…
Two new methods improve efficiency of conformal predictive systems.
problem Efficiency of conformal predictive systems in regression problems.
method Split conformal predictive systems and cross-conformal predictive systems.
result Cross-conformal predictive systems are more efficient but not guaranteed valid.
Solves new quadratic BSDE systems for market performance analysis.
problem Characterizing forward performance processes in regime switching markets.
method Introduces and solves ergodic BSDE systems in infinite time horizon.
result Connection between ergodic BSDE solutions and long-term growth rates of utility maximization.
Superintegrable systems on curved manifolds found to have Hessian structures.
problem Characterizing superintegrable systems on curved manifolds.
method Identifying and computing Hessian coordinates for superintegrable systems.
result Examples of superintegrable systems in 2D and 3D have natural Hessian coordinates.
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…
The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.
problem Finding general solutions for Lie systems.
method Develops mixed superposition rules for Lie systems with imprimitive Lie algebras and semidirect sums.
result Extends coalgebra method to Lie systems of partial differential equations.
Researchers solve boundary and scattering rigidity problems for magnetic systems.
problem Recovering magnetic systems from boundary or scattering data.
method Reduced to magnetic systems and applied results from [DPSU07].
result Recovering MP-system up to a gauge. Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
problem Reduction of controlled Lagrangian systems with symmetry and momentum map.
method Using Legendre transformation and Euler-Lagrange vector field, the paper extends symmetric reduction theory.
result Established regular reduction theory for RCL systems with symmetry and momentum map.
Polynomial-time algorithm learns latent-state systems without spectral radius assumptions.
problem Learning latent-state linear dynamical systems without spectral radius assumptions.
method Spectral filtering technique with a novel convex relaxation.
result Efficient identification of phases for general transition matrices.
This paper proposes a system-agnostic policy for dynamic scheduling.
problem Dynamic scheduling in changing systems is challenging due to system-specific optimal policies.
method Descriptive policy that learns a system-agnostic scheduling principle.
result System-agnostic meta-learning enables adaptation to unseen system characteristics.
The paper studies connections in superintegrable systems, revealing geometric insights.
problem Understanding non- and semi-degenerate superintegrable systems.
method Analyzes two torsion-free connections associated with superintegrable systems.
result Semi-degenerate secondary structure tensor is the Ricci curvature of a natural torsion-free connection.
Learn dynamics of a system using auxiliary data from similar systems.
problem Learning dynamics of a linear system with limited data.
method Weighted least squares approach, incorporating auxiliary data.
result Auxiliary data can help reduce intrinsic error due to noise.
The inability to see and quantify systemic financial risk comes at an immense social cost. Systemic risk in the financial system arises to a large extent as a consequence of the interconnectedness of its institutions, which are linked through networks of different types of financial contracts, such as credit, derivativ…
New adaptive conformal predictive systems developed.
problem Severe restrictions on adapting predictive distributions to test objects.
method Calibrating existing predictive systems to ensure full adaptability and validity.
result Developed fully adaptive split-conformal and cross-conformal predictive systems.
Abstract reviews geometric theories of smooth and F-smooth systems.
problem Geometric theories of smooth and F-smooth systems.
method Reviews geometric theories of smooth and F-smooth systems.
result Discusses geometric theories of smooth and F-smooth systems.
The paper defines Haar system preserving morphisms and applies them to groupoid C∗-algebras.
problem Understanding and constructing inverse systems of groupoids.
method Defining Haar system preserving morphisms and using them to induce *-morphisms between convolution algebras.
result Inverse systems of groupoids with Haar system preserving bonding maps have limits, and corresponding direct systems of groupoid C∗-algebras. Elliptic systems are characterized by Darboux integrability.
problem Characterizing elliptic differential systems with holomorphic solutions.
method Using a complex manifold and associated holomorphic Pfaffian system.
result Elliptic systems are Darboux integrable under generic conditions.