Algorithm for stable allocation in heterogeneous ad-hoc networks.
problem Decentralized spectrum allocation in dynamic, heterogeneous networks.
method Multi-armed bandit based distributed algorithm for static and dynamic networks.
result Achieves stable orthogonal allocation in finite time with low complexity.
The Shapley value theory is used for risk allocation in non-orthogonal risk factors.
problem Risk allocation among non-orthogonal risk factors in financial portfolios.
method Using Shapley value from cooperative game theory to allocate risk contributions.
result Explicit formulas and numerical algorithms for calculating risk allocations are derived.
Facing the FRTB, banks need to allocate their capital to each business units or risk positions to evaluate the capital efficiency of their strategies. This paper proposes two computationally efficient allocation methods which are weighted according to liquidity horizon. Both methods provide more stable and less negativ…
Meta-learning performance is affected by how task diversity is allocated, not just overall variability.
problem Meta-learning performance degrades when task diversity is unevenly distributed.
method Decomposed task-specific regression effects into structurally informative and orthogonal components.
result Meta-learning prediction degrades when a larger fraction of task variability is orthogonal and non-informative.
Paper proves every stable 4-sphere has a unique diffeomorphism class.
problem Identifying stable 4-spheres and their diffeomorphisms.
method Using Wall's result and properties of surface-knot spaces.
result Every stable 4-sphere has a unique orientation-preserving diffeomorphism class.
Gradient descent biases towards stable rank networks for nearly-orthogonal data.
problem Understanding implicit bias in non-smooth neural networks trained by gradient descent.
method Analysis of two-layer ReLU and leaky ReLU networks trained by gradient descent on nearly-orthogonal data.
result Gradient descent biases towards networks with stable rank and uniform margin for nearly-orthogonal data.
Proposes a new RNN structure to improve expressivity without sacrificing stability.
problem Exploding and vanishing gradient problems in RNNs and reduced expressivity.
method Introduces a non-normal RNN structure using Schur decomposition and splitting.
result Enhances expressivity while maintaining stability and training speed.
OOMP selects features online for sparse linear regression.
problem Feature selection in high-dimensional sparse linear models.
method Online algorithm that alternates between feature selection and coefficient estimation.
result Theoretical guarantees and computational complexity analysis of OOMP.
New mathematical foundations for stable RKHSs improve system identification.
problem Improving stability tests and modeling of impulse responses.
method Providing new structural properties and stability conditions for stable RKHSs.
result Any stable kernel admits feature maps induced by orthogonal eigenvectors in l2.
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. S…
Develops deformation theory for mapping spaces related to Morse theory and Bott-Thom isomorphism.
problem Studying weak homotopy equivalences and decompositions of vector bundles.
method Morse theory on path spaces, deformation theory, Clifford representations, Bott-Thom isomorphism.
result Stable decompositions of vector bundles over sphere bundles derived from Clifford representations.
Proposes a new risk model using stable laws to manage company-wide losses.
problem Managing aggregate risks and pricing policies in the presence of systematic risk.
method Develops a modified risk model using multivariate stable distributions to account for various risk phenomena.
result Computes the Tail Conditional Expectation of aggregate risks and corresponding allocations.
Pion optimizes LLMs by preserving weight matrix singular values.
problem Training large language models (LLMs) with standard optimizers leads to unstable weight matrices.
method Pion uses orthogonal transformations to update weight matrices, preserving their singular values.
result Pion offers a stable alternative to standard optimizers for LLM pretraining and finetuning.
When looking at Bott's original proof of his periodicity theorem for the stable homotopy groups of the orthogonal and unitary groups, one sees in the background a differential geometric periodicity phenomenon. We show that this geometric phenomenon extends to the standard inclusion of the orthogonal group into the unit…
A new method for optimizing neural networks with orthogonal constraints.
problem Optimizing neural networks with orthogonal constraints.
method Parametrization using the exponential map to transform constrained optimization into unconstrained.
result Faster, more accurate, and stable convergence in RNNs with orthogonal recurrent weights.
Paper compares RL models for finance, finding Reward Clipping best.
problem Optimizing asset allocation in finance.
method Actor-only, actor-critic, and PPO models compared; Reward Clipping introduced.
result Reward Clipping model outperforms others in bull and bear markets.
MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.
problem Training matrix-valued parameters with orthogonalized-update optimizers like Muon.
method MuonEq introduces three lightweight pre-orthogonalization equilibration schemes: two-sided row/column normalization (RC), row normalization (R), and column normalization (C).
result Row/column normalization acts as a zeroth-order surrogate for whitening and improves the geometry seen by orthogonalization.
Stability inequalities for specific solutions in high dimensions.
problem Stability of solutions to the one-phase Bernoulli problem.
method Proving strict stability inequalities for cohomogeneity one solutions with bi-orthogonal symmetry.
result Strict stability for cohomogeneity one solutions in dimensions 7 and above.
The paper proposes a new portfolio allocation method combining RMT and machine learning.
problem Optimal allocation instability in high-dimensional portfolios.
method Combines Random Matrix Theory covariance estimators with Nested Clustered Optimization.
result The modified NCO algorithm achieves stable allocations without risky short positions.
Orthogonium offers unified, efficient layers for robust deep learning.
problem Fragmented and computationally demanding implementations of orthogonal and 1-Lipschitz layers.
method Unified, efficient PyTorch library providing orthogonal and 1-Lipschitz layers.
result Reduced overhead and standardized tools for robust experimentation.
Optimizes asset allocation for risk measures in a Lévy market.
problem Maximizing time-consistent mean-risk reward with general risk measures.
method Uses a generalized Lévy market model and Hamilton-Jacobi-Bellman equation.
result Deterministic optimal solution under certain conditions.
Comonotonic allocations are restored under certain constraints, improving risk-sharing.
problem Feasibility constraints can distort optimal risk-sharing allocations.
method Identified componentwise convex-order solidity as a sufficient condition to restore comonotonic allocations.
result Componentwise convex-order solidity ensures comonotonic improvements under feasible constraints.
New optimization algorithms on orthogonal group for machine learning.
problem Efficient optimization on the orthogonal group for machine learning tasks.
method Stochastic geometric algorithms on Lie groups.
result Strong performance on diverse machine learning tasks.
This paper proposes a decentralized reinforcement learning method for multi-agent resource allocation.
problem Allocating heterogeneous resources among multiple agents in a decentralized manner.
method Liquid-Graph-Time Clustering-IPPO, integrating dynamic cluster consensus.
result LGTC-IPPO achieves more stable rewards, better coordination, and robust performance.
Scheduling and power allocation improve federated learning efficiency in NOMA networks.
problem Efficiently scheduling and allocating power for federated learning in bandwidth-limited wireless networks.
method Proposed a scheduling policy and power allocation scheme using NOMA to maximize data rate and convergence speed.
result Simulation results show improved federated learning accuracy in NOMA networks.
This study uses HMM and RL to dynamically allocate equities, Treasuries, and gold based on market regimes.
problem Developing a dynamic portfolio allocation strategy for different market conditions.
method Characterizes market regimes using Markov switching models and HMM, then applies RL for allocation decisions.
result RL-based allocation outperforms passive strategies, providing lower drawdowns and higher Sharpe ratios.
Dynamic risk factor model improves portfolio performance in high dimensions.
problem Dynamic portfolio allocation in high-dimensional financial markets.
method Time-varying sparsity on factor loadings, sequential learning of parameters and volatilities.
result Significant portfolio performance improvements and higher utility gains.
This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop novel orthogonality regularizations on training deep CNNs, utilizing various adva…
Researchers prove a method to upgrade Morse-Bott homology to stable homotopy invariants.
problem Proving a method to upgrade Morse-Bott homology to stable homotopy invariants rigorously.
method Rigorous construction of stable normal framings and proof of stable homotopy type recovery.
result The stable homotopy type recovers Σ∞+M and Thom spectra for all reduced KO-theory classes.
Spectral method for joint community detection and group synchronization.
problem Jointly detecting communities and synchronizing orthogonal groups in graphs.
method Spectral decomposition followed by CPQR factorization.
result Near-optimal guarantees for exact and stable recovery of cluster memberships and orthogonal transforms.
ABO extends RLS for online learning in non-stationary time-series, improving accuracy and speed.
problem Online learning in non-stationary time-series with overparameterized models.
method QR-based exponentially weighted RLS algorithm with orthogonal-triangular updates.
result ABO maintains bounded residuals and stable condition numbers while achieving speed improvements.
Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to a cohomology class of a homotopy colimit BSO of classifying spaces BSO_n. Simil…
We consider moment matching techniques for estimation in Latent Dirichlet Allocation (LDA). By drawing explicit links between LDA and discrete versions of independent component analysis (ICA), we first derive a new set of cumulant-based tensors, with an improved sample complexity. Moreover, we reuse standard ICA techni…
Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space problem and …
New method offsets DML's error-compounding issue and provides more stable causal parameter estimates.
problem Estimating ATE from observational data with robustness and stability.
method Robust Causal Learning (RCL) method to offset DML's deficiencies.
result RCL estimators are more stable and perform better than DML and traditional estimators.
Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.
problem Fluctuations in deep networks with Gaussian weights can impair training, especially in networks with depth comparable to width.
method Analytical and numerical studies of fully-connected networks with orthogonal weight initialization and tanh activations.
result Rectangular networks with orthogonal weights have stable fluctuations independent of network depth, leading to better generalization and training speed.
Adversaries manipulate wireless power allocation to reduce user rates.
problem Adversaries exploit deep learning for power control to decrease communication rates.
method Adversaries craft perturbations to inputs of a DNN to minimize power allocation.
result Adversarial attacks are highly effective and robust to uncertainties.
Investigates harmonic self-maps' stability on cohomogeneity one manifolds.
problem Stability of harmonic self-maps on cohomogeneity one manifolds.
method Systematic study of Jacobi equation for harmonic self-maps.
result Explicit solutions for specific cases show identity map's stability.
New pension product combines lifetime income and estate value.
problem Optimal allocation of pension savings between income and estate.
method Power utility function analysis of tontine and bequest accounts.
result Risk aversion affects optimal allocation, with least risk averse allocating most to tontine.
The paper extends a theorem about stable minimal surfaces to higher codimensions.
problem Stability and holomorphicity of parabolic stable minimal surfaces in higher-dimensional spaces.
method Generalization of a classical theorem to higher codimensions, with additional assumptions on the normal bundle.
result Holomorphicity of stable minimal surfaces in higher-dimensional spaces.
Ancient curve shortening flow in a disc with mixed boundary conditions is solved.
problem Ancient curve shortening flow in a disc with mixed boundary conditions.
method Constructing convex eternal solutions and proving uniqueness.
result The only non-flat convex ancient solutions to the curve shortening flow satisfying the specified boundary conditions.
The study examines stable minimal surfaces in higher dimensions and provides bounds on their properties.
problem Properties of stable minimal surfaces in higher codimension.
method Structural analysis of holomorphic vector bundles and geometric inequalities.
result Explicit bounds on the systole for stable minimal tori and surfaces.
We investigate a class of feature allocation models that generalize the Indian buffet process and are parameterized by Gibbs-type random measures. Two existing classes are contained as special cases: the original two-parameter Indian buffet process, corresponding to the Dirichlet process, and the stable (or three-param…
This work analyzes how users and services adapt to reduce risk, leading to specialization.
problem Adaptation of users and services to reduce risk affects learning and performance.
method Analyzed a class of dynamics where users allocate participation and services update parameters.
result Repeated myopic updates with multiple learners lead to better outcomes than repeated risk minimization.
The paper proves conditions for minimal surfaces to be holomorphic and stable.
problem Conditions for stable minimal surfaces to be holomorphic.
method Developed a method of constructing variations to prove the equivalence.
result Holomorphicity and stability conditions for minimal surfaces.
New method prevents gradient attenuation in Lipschitz constrained convolutional networks.
problem Gradient norm attenuation in Lipschitz constrained convolutional networks.
method Block Convolution Orthogonal Parameterization (BCOP) to train scalable, expressive, provably Lipschitz convolutional networks.
result Empirically, BCOP parameterization is competitive with existing approaches to provable adversarial robustness and Wasserstein distance estimation.
String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend the description of String structures from connected covers of the definite-signat…
The paper identifies a mesoscopic market structure and uses it to improve portfolio optimization.
problem The optimal mean-variance allocation differs from the heuristic equally-weighted portfolio.
method Clustering techniques from Random Matrix Theory (RMT) to study mesoscopic market structure.
result A new wealth allocation scheme that attaches equal importance to stocks in the same community improves portfolio reliability.