A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on risk measures using distorted Choquet integrals with random distortions.
problem Developing risk measures under random distortions of capacities.
method Introducing and analyzing randomly distorted Choquet integrals with respect to a distorted capacity, establishing properties and providing representations.
result Representation of comonotonic additive conditional risk measures using G-randomly distorted Choquet integrals.
In the paper we give necessary and sufficient conditions for the Jensen inequality to hold for the generalized Choquet integral with respect to a pair of capacities. Next, we apply obtained result to the theory of risk aversion by providing the assumptions on utility function and capacities under which an agent is risk…
We show that the non pluripolar product of positive currents is a bimeromorphic invariant. Under some natural assumptions, we show that the (weighted) energy associated to big cohomology classes are also bimeromorphic invariants. We compare the weighted energy functionals of currents with respect to different cohomolog…
We study finite sample expressivity, i.e., memorization power of ReLU networks. Recent results require N hidden nodes to memorize/interpolate arbitrary N data points. In contrast, by exploiting depth, we show that 3-layer ReLU networks with Ω(N) hidden nodes can perfectly memorize most datasets with N po…
Proves generalization bounds for SGD using Feller processes and Hausdorff dimension.
problem Characterizing generalization properties of SGD in deep learning.
method Proves generalization bounds for SGD under Feller process approximation, linking generalization error to the Hausdorff dimension of trajectories.
result Generalization error controlled by the Hausdorff dimension of trajectories, which is linked to the tail behavior of the driving process.
The paper addresses adversarial robustness in in-context learning models.
problem Adversarial distribution shifts threaten the reliability of in-context learning models.
method A distributionally robust meta-learning framework is introduced to provide worst-case performance guarantees under Wasserstein-based distribution shifts.
result Model robustness scales with the square root of its capacity and is penalized by the square of the perturbation magnitude.
In this paper we show the existence of weak solutions w:M→R of the inverse mean curvature flow starting from a relatively compact set (possibly, a point) on a large class of manifolds satisfying Ricci lower bounds. Under natural assumptions, we obtain sharp estimates for the growth of w and f…
This work addresses causal inference challenges in networked interference and proposes GNN-based estimators for individual treatment effects.
problem Estimating individual treatment effects in randomized experiments with networked interference.
method Uses Graph Neural Networks (GNNs) to capture network dependencies and derive causal effect estimators.
result Provides policy regret bounds and heuristic error bounds for GNN-based causal estimators under network interference and treatment capacity constraints.
The emerging concern about data privacy and security has motivated the proposal of federated learning, which allows nodes to only synchronize the locally-trained models instead their own original data. Conventional federated learning architecture, inherited from the parameter server design, relies on highly centralized…
We study various capacities on compact Kähler manifolds which generalize the Bedford-Taylor Monge-Ampère capacity. We then use these capacities to study the existence and the regularity of solutions of complex Monge-Ampère equations.
In this article, we propose the notion of the general p-affine capacity and prove some basic properties for the general p-affine capacity, such as affine invariance and monotonicity. The newly proposed general p-affine capacity is compared with several classical geometric quantities, e.g., the volume, the p-var…
While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between capacities often lead to surprising relations between different aspects of sympl…
Study excess capacity in neural networks using Rademacher complexity.
problem Understanding how much capacity deep networks have beyond what's needed for classification.
method Unified Rademacher complexity bounds for function composition and convolutional layers, considering Lipschitz constants and initialization norms.
result There is substantial excess capacity per task, and capacity can be kept similar across different tasks.
One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical point of view, the theoretical analysis of generalization performance contribut…
Study capacity constraints in continual learning with a simple model.
problem Understanding optimal resource allocation for agents with limited memory and compute resources.
method Analyzes a capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem and demonstrates optimal capacity allocation strategies.
result Derives a solution to the capacity-constrained LQG sequential prediction problem and shows how to optimally allocate capacity across sub-problems in the steady state.
We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities. As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate it in terms of Gromov-Witten invariants. The (pseudo) symplectic capacitie…