The paper explores reflection principles for lightlike line segments on maximal surfaces.
problem Reflection property does not hold for lightlike line segments on maximal surfaces.
method Analyzes reflection properties for lightlike line segments connecting shrinking singularities.
result Shows a kind of reflection principle for lightlike line segments on maximal surfaces.
Study maximal hypersurfaces in open spacetimes using a maximum principle.
problem Characterize maximal hypersurfaces in open spacetimes.
method Use a generalized maximum principle to analyze hypersurfaces in spatially open Generalized Robertson-Walker spacetimes.
result Provide new uniqueness and non-existence results for complete maximal hypersurfaces in open Robertson-Walker spacetimes.
The paper extends physics-based information maximization to complex bandit problems.
problem Designing efficient decision-making policies for complex bandit problems.
method Information and free-energy maximization principles adapted to three distinct bandit types.
result Information maximization leads to strong performance in complex bandit problems.
Classifies maximal symmetry models of CR dimension 1.
problem Classifying maximal symmetry models of CR manifolds.
method Classification based on Bloom-Graham and Tanaka types, coordinate realization, and extension principle.
result Classification and coordinate realization of maximal symmetry models.
Optimal insurance strategy for maximizing RDEU under various premium principles.
problem Maximizing a risk-averse individual's RDEU with insurance priced by a distortion-deviation principle.
method Proved necessary and sufficient conditions for the optimal solution, considered ambiguity orders, and analyzed specific examples.
result Conditions for no insurance or deductible insurance to be optimal.
Study h-principles for non-integrable distributions on manifolds.
problem Existence and classification of maximally non-integrable distributions of derived length one.
method Introduced formal structures and used h-principles to discuss existence and classification.
result Discussed existence and classification of maximally non-integrable distributions of derived length one.
New bandit algorithm maximizes information gain.
problem Optimizing decision-making in uncertain environments.
method Approximates information maximization using entropy and free energy principles.
result Asymptotic optimality proven for two-armed bandit problem.
Study harmonic surfaces in 3D space, proving superposition principle.
problem Understanding harmonic surfaces in R3. method Using harmonic Enneper immersions and superposition principle.
result Minimal and maximal surfaces can be decomposed into harmonic components.
The paper explores variational principles for equations of maximal symmetry, providing new insights and results.
problem Exploring variational principles for equations of maximal symmetry.
method Study of variational and divergence symmetries for linear and nonlinear equations of maximal symmetry, providing first integrals in explicit form.
result Significantly different results and more general variational symmetry algebra for linear and nonlinear equations compared to previous studies.
Paper investigates reflection principles for zero mean curvature surfaces in isotropic 3-space.
problem Investigating reflection principles for zero mean curvature surfaces in isotropic 3-space.
method Analyzes reflection principles for zero mean curvature surfaces in I3. result Shows a reflection principle for isotropic line segments on zero mean curvature surfaces in I3. Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.
problem Maximally non-integrable almost complex structures and their cohomological properties.
method h-principle and topological invariants characterization.
result Existence of almost complex structures with maximal Nijenhuis tensor rank on parallelizable and certain manifolds.
Maximizes coding rate difference for robust, discriminative features.
problem Learning robust, discriminative features from high-dimensional data.
method Maximal Coding Rate Reduction (MCR^2) principle.
result Significantly more robust to label corruptions in classification.
Unified approach combines reward maximization and empowerment for RL.
problem Combining reward maximization and empowerment for reinforcement learning.
method Unified Bellman optimality principle for empowered reward maximization.
result Unified approach leads to improved initial and competitive final performance.
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …
The paper solves a 25-year-old problem about maximal growth distributions on manifolds.
problem Existence and classification of maximal growth distributions on smooth manifolds.
method Higher order convex integration and new criteria for ampleness of differential relations.
result Positive answer to the open question about parallelizable manifolds admitting maximal growth distributions.
Recently, crowdsourcing has emerged as an effective paradigm for human-powered large scale problem solving in various domains. However, task requester usually has a limited amount of budget, thus it is desirable to have a policy to wisely allocate the budget to achieve better quality. In this paper, we study the princi…
This work introduces uncertainty principles to mitigate Maximal Extractable Value in blockchain systems.
problem Maximal Extractable Value (MEV) in decentralized systems due to transaction submission privacy and monopolist power.
method Unified approaches via uncertainty principles, akin to harmonic analysis and physics, to quantify trade-offs between transaction flexibility and user economic payoff.
result Demonstrates a quantitative trade-off between transaction flexibility and user economic payoff, analogous to the Nyquist-Shannon sampling theorem.
New algorithm estimates semi-continuous data density using entropy maximization.
problem Estimating density functions for semi-continuous data.
method Maximum entropy principle, requiring only constraint function samples.
result Estimate has significantly less bias compared to existing methods.
We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit for…
A new method to break down insurance costs into risk and uncertainty.
problem Understanding and quantifying insurance costs in uncertain environments.
method An axiomatic approach to decompose premium principles into risk and deviation measures.
result Maximal risk and minimal deviation measures can be uniquely identified in decompositions.
We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic progr…
Active inference minimizes expected free energy for optimal behavior.
problem Understanding and optimizing behavior in complex systems.
method Combines Bayesian decision theory, optimal Bayesian design, and the free energy principle.
result Active inference emerges as a unified framework for information-seeking, utility maximization, and goal-directed behavior.
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic backward stochastic differential equation (BSDE in short). We characterize the op…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from…
Paper refutes EM convergence theory and introduces a new EM algorithm.
problem The convergence theory of the EM algorithm is incorrect and affects its performance.
method Proposes a new EM algorithm called the Channel Matching (CM) EM algorithm and provides an initialization map.
result The locally maximal Q can affect the convergent speed but not the global convergence.
Though the deep learning is pushing the machine learning to a new stage, basic theories of machine learning are still limited. The principle of learning, the role of the a prior knowledge, the role of neuron bias, and the basis for choosing neural transfer function and cost function, etc., are still far from clear. In …
In this paper, we provide an information-theoretic interpretation of the Vector Quantized-Variational Autoencoder (VQ-VAE). We show that the loss function of the original VQ-VAE can be derived from the variational deterministic information bottleneck (VDIB) principle. On the other hand, the VQ-VAE trained by the Expect…
Study extremals on Lie groups with asymmetric polyhedral Finsler structures using Pontryagin's Maximal Principle.
problem Finding extremals on Lie groups with asymmetric polyhedral Finsler structures.
method Using Pontryagin's Maximal Principle and control systems of Euler-Arnold type to find extremals on the cotangent bundle of the group.
result Uniqueness of the control u(t) can be studied through the asymptotic curvature of the vertical part of the Pontryagin extremal. In the present paper, we revisit the rigidity of hypersurfaces in Euclidean space. We highlight Darboux equation and give new proof of rigidity of hypersurfaces by energy method and maximal principle.
Maximizing margins leads to lossless compression of training data.
problem Generalization in supervised learning.
method Information-theoretic interpretation of margin maximization.
result Margin maximization is a form of lossless maximal compression.
Work maximization guides machine learning models in adaptive systems.
problem How machine learning models can be optimized for thermodynamic efficiency.
method Introducing thermodynamic principle to compare with maximum-likelihood principle.
result Maximum-work models are equivalent to maximum-likelihood models in adaptive systems.
New scaling framework for MoE architectures ensures stability and optimal performance at scale.
problem Lack of principled understanding of how hyperparameters should scale in MoE architectures.
method Developed a novel Dynamical Mean Field Theory (DMFT) for three scaling regimes of MoE architectures.
result Derived Maximally Scale-Stable Parameterization (MSSP) for SGD and Adam, providing robust learning rate transfer and monotonic improvement with scale.
Locally maximizing orbits studied in twist maps and billiards.
problem Characterize orbits in locally maximizing class for twist maps.
method Geometric and variational analysis of orbits in the cotangent bundle of a torus or ball bundle over a sphere.
result Two generating functions for the Birkhoff billiard map have the same class of locally maximizing orbits.
We prove the hyperbolization theorem for punctured torus bundles and two-bridge link complements by decomposing them into ideal tetrahedra which are then given hyperbolic structures, following Rivin's volume maximization principle.
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options. We show …
Two derivations of PCA for distributional data.
problem PCA for datasets of distributions.
method Two derivations: variance maximization and reconstruction error minimization.
result Closed-form solution for distributional PCA.
Bayesian scores improve structure learning in probabilistic circuits.
problem Improper structure learning in probabilistic circuits based on heuristics.
method Developed Bayesian structure scores for deterministic PCs, using them in a greedy cutset algorithm.
result Effective protection against overfitting and fast, almost hyper-parameter-free structure learner.
Semi-supervised clustering aims to introduce prior knowledge in the decision process of a clustering algorithm. In this paper, we propose a novel semi-supervised clustering algorithm based on the information-maximization principle. The proposed method is an extension of a previous unsupervised information-maximization …
YOPO reduces adversarial training time by one forward/backward pass per group of updates.
problem Adversarial training's high computational cost limits deep learning's robustness.
method YOPO uses the Pontryagin's Maximal Principle to limit propagation to the first layer.
result YOPO achieves comparable defense accuracy with significantly less computational time.
Paper develops MRCs for supervised classification using generalized maximum entropy.
problem Developing robust classifiers for decision problems.
method Generalized maximum entropy principle applied to minimax risk classifiers.
result Learning techniques for determining MRCs with performance guarantees.
The paper solves an insurance problem using mean-variance and rank-dependent utility theory.
problem Formulating and solving an insurance problem with rank-dependent utility and mean-variance premium principle.
method Formulated as a non-concave maximization problem, then turned into a concave quantile optimization problem, solved using calculus of variations.
result An optimal insurance contract is derived and numerically computed.
We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the L2 Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.
Typical dimensionality reduction methods focus on directly reducing the number of random variables while retaining maximal variations in the data. In this paper, we consider the dimensionality reduction in parameter spaces of binary multivariate distributions. We propose a general Confident-Information-First (CIF) prin…
The h-principle fails for prelegendrians in fat distributions of corank 2.
problem Investigating the h-principle for fat distributions of corank 2.
method Developed the theory of prelegendrians, including front projection and pseudoholomorphic curve invariants.
result Found an infinite family of non-prelegendrian isotopic tori in the standard fat distribution.
We present a two-stage approach for learning dictionaries for object classification tasks based on the principle of information maximization. The proposed method seeks a dictionary that is compact, discriminative, and generative. In the first stage, dictionary atoms are selected from an initial dictionary by maximizing…
This paper looks at the splitting problem for globally hyperbolic spacetimes with timelike Ricci curvature bounded below containing a (spacelike, acausal, future causally complete) hypersurface with mean curvature bounded from above. For such spacetimes we show a splitting theorem under the assumption of either the exi…
New causal versions of MaxEnt and PIR avoid paradoxical probability updates.
problem Paradoxical probability updates in causal MaxEnt and PIR.
method Separate constraints into cause-specific and mechanism-specific restrictions.
result Causal MaxEnt avoids paradoxical updates and aligns with Information Geometric Causal Inference.
Batch Reinforcement Learning (RL) algorithms attempt to choose a policy from a designer-provided class of policies given a fixed set of training data. Choosing the policy which maximizes an estimate of return often leads to over-fitting when only limited data is available, due to the size of the policy class in relatio…