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.
We improve deep threshold networks' memorization capacity exponentially.
problem Memorizing datasets with randomized labels using deep neural networks.
method Using Gaussian random weights in the first layer and binary or integer weights in subsequent layers, we prove a new dependence on minimum distance.
result We show that O(δ1+n) neurons and O(δd+n) weights are sufficient.
We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Temp…
External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size o…
Overwhelming theoretical and empirical evidence shows that mildly overparametrized neural networks -- those with more connections than the size of the training data -- are often able to memorize the training data with 100% accuracy. This was rigorously proved for networks with sigmoid activation functions and, very …
Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut stochastic gradient descent (SGD) learning in networks composed of multiple lay…
A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary logarithm of the number of functions it can compute, as the synaptic weights are vari…
The paper proves a geometric capacitary inequality for sub-static manifolds with harmonic potentials.
problem Proving a geometric capacitary inequality for sub-static manifolds with harmonic potentials.
method Introducing a one-parameter family of functions that are monotone along the level-set flow of the potential, up to the optimal threshold.
result Proves a geometric capacitary inequality where the capacity of the horizon plays the same role as the ADM mass in the celebrated Riemannian Penrose Inequality.
Paper uses Sugeno integral for binary classification with ordinal data.
problem Learning from ordinal data in machine learning.
method Proposes a method using the Sugeno integral for binary classification, transforming feature values into local evaluations and tuning a threshold.
result Generalizes approach to k-maxitive capacities to control classifier flexibility and prevent overfitting.
One unexamined assumption in foreign ownership regulation is the notion that majority voting rights translate to 'effective control'. This assumption is so deeply entrenched in foreign investments law that possession of majority voting rights can determine the nationality of a corporation and its capacity to engage in …
Sharp limits found for storing and retrieving input-output associations in linear associative memories.
problem Understanding the fundamental limits of storing and retrieving input-output associations in neural networks.
method Study of a minimal linear associative memory model, introducing a decoupled model and using statistical physics to characterize storage capacity.
result Linear associative memory can store up to 1/2 log(p) associations, providing a sharp statistical-physics characterization.
Optimal control of reserve assets for stablecoins to maintain peg stability.
problem Balancing immediate liquidity and yield on reserve assets for stablecoin peg maintenance.
method Developed a stochastic model predictive control framework with moment closure for event intensities, incorporating a soft-thresholding structure for rebalancing.
result Optimal policy shifts predictably toward cash as expected outflows intensify or windows lengthen, preserving most bill carry in calm markets and quickly building cash during stress.
New findings challenge the importance of forecast accuracy in battery storage optimization, highlighting the role of rank correlation instead.
problem The challenge of optimizing battery storage dispatch decisions in multi-market electricity trading using forecast accuracy metrics.
method A hierarchical three-layer optimization system trading in multiple markets (FCR, aFRR, day-ahead, intraday) with real market data.
result Rank correlation (Kendall tau) is a better predictor of intraday dispatch value than forecast accuracy (MAE), with a threshold of tau around 0.85-0.95 capturing up to 97-100% of perfect-foresight revenue.
Autonomous construction of deep neural network (DNNs) is desired for data streams because it potentially offers two advantages: proper model's capacity and quick reaction to drift and shift. While the self-organizing mechanism of DNNs remains an open issue, this task is even more challenging to be developed for standar…
This paper studies a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching that is motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a natural resource from a reserve with finite capacity, and sells it in the market at a …
The Denoising Autoencoder (DAE) enhances the flexibility of the data stream method in exploiting unlabeled samples. Nonetheless, the feasibility of DAE for data stream analytic deserves an in-depth study because it characterizes a fixed network capacity that cannot adapt to rapidly changing environments. Deep evolving …
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.
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.