New complexity measure helps in agnostic reinforcement learning with or without access to MDP dynamics.
problem Understanding the number of rounds needed to learn an ε-suboptimal policy in unknown MDPs.
method Introducing spanning capacity as a new complexity measure and developing POPLER algorithm.
result There is a separation between generative and online access models for agnostic learnability.
We experimentally achieve a 19% capacity gain per Watt of electrical supply power in a 12-span link by eliminating gain flattening filters and optimizing launch powers using machine learning by deep neural networks in a massively parallel fiber context.
Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.
problem Temperature transferability of MLCG models for proteins.
method Explicit decomposition of CG potential into energetic and entropic components.
result Reproduces temperature-dependent quantities like heat capacity.
Matryoshka hides secret models in a carrier model, achieving high capacity and robustness.
problem Stealing functionality of private ML data by hiding models in a carrier model.
method Parameter sharing approach exploiting the learning capacity of the carrier model.
result Hides a 26x larger secret model or 8 secret models in the carrier model.
This paper shows neural networks can solve complex graph problems efficiently.
problem Solving exact maximum flow computation and minimum spanning tree problems.
method Introduces Max-Affine Arithmetic Programs and shows equivalence to neural networks.
result Two combinatorial optimization problems can be solved with polynomial-size neural networks.
Survey of large language models in financial prediction and trading.
problem Improving predictability and robustness of financial predictions and trading decisions.
method Task-centered taxonomy, review of empirical evidence, design patterns, benchmarks, and challenges analysis.
result Improved predictability and robustness of financial predictions and trading decisions through large language models.
Study builds dataset and benchmarks ML models for accurate solar and wind power forecasting in France.
problem Accurate prediction of non-dispatchable renewable energy sources for grid stability and price prediction.
method Comprehensive methodology using machine learning models trained with spatially explicit weather data and production site capacity.
result Neural networks outperform traditional models in forecasting solar and wind power production in France.
We consider the task of building compact deep learning pipelines suitable for deployment on storage and power constrained mobile devices. We propose a unified framework to learn a broad family of structured parameter matrices that are characterized by the notion of low displacement rank. Our structured transforms admit…
Weighted SVM (or fuzzy SVM) is the most widely used SVM variant owning its effectiveness to the use of instance weights. Proper selection of the instance weights can lead to increased generalization performance. In this work, we extend the span error bound theory to weighted SVM and we introduce effective hyperparamete…
Improved NODEs for long-term time series forecasting.
problem Dealing with complex, multi-frequency data.
method Progressive learning paradigm with curriculum learning.
result Performance improved by over 64%.
New spanning 3-disks found for unlink in 4-sphere.
problem 2-component unlink in 4-sphere.
method Found infinitely many isotopy classes of Brunnian spanning 3-disks.
result Infinitely many Brunnian spanning 3-disks for 2-unlink in 4-sphere.
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.
Machine learning enhances ocean studies by analyzing sparse, multi-scale data.
problem Sparse, multi-scale ocean data limits traditional methods.
method Machine learning techniques applied to ocean observations, theory, and numerical simulations.
result ML can advance theoretical oceanographic exploration and numerical simulations.
Sharp bounds for spanning tree entropy in planar lattices.
problem Estimating spanning tree entropy in planar lattice graphs.
method Using hyperbolic geometry and polyhedra volumes.
result Proved bounds are easy to compute and provide excellent estimates.
Totally geodesic surfaces found in knots and links.
problem Finding totally geodesic surfaces in knots and links.
method Constructing infinite families of knots and links with totally geodesic spanning surfaces in various 3-manifolds.
result Infinite families of knots and links with totally geodesic spanning surfaces in multiple 3-manifolds.
Solves a discrete logarithmic Minkowski problem for electrostatic p-capacity.
problem Characterize measures generated by electrostatic p-capacity.
method Solves the discrete logarithmic Minkowski problem for 1 < p < n.
result Solves the discrete logarithmic Minkowski problem for measures in general position.
CapOptix uses options theory to price capacity in electricity markets.
problem Traditional capacity market designs fail to account for risk and price shocks.
method Interprets capacity commitments as reliability options and uses Markov Regime Switching Process.
result CapOptix provides more accurate pricing of capacity premia compared to existing mechanisms.
The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning trees provide a filtration on the reduced Khovanov complex and a …
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…
A new classification method based on Minimum Spanning Trees
problem Improving classification in supervised learning
method Proposing a classification algorithm based on Minimum Spanning Trees
result The proposed method is effective and computationally efficient
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…
The paper explores neural networks for improving delta hedging in financial markets.
problem Real-world financial markets do not perfectly match the assumptions of the Black-Scholes model.
method The authors test various neural architectures (RNN, TCN, Attention, MLP) for delta hedging and combine them with traditional models.
result NNHedge framework provides a pipeline for model development and assessment.
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 rigidity by logarithmic capacity and related functions.
problem Rigidity phenomena in kernel functions and capacities.
method Exploration of Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance/volume.
result Established rigidity theorems by logarithmic capacity.
Ancient curves span halfplanes via flow.
problem Ancient solutions to Curve Shortening Flow.
method Constructing infinite family of solutions.
result Spanning halfplane with ancient curves.
Study binary perceptrons' capacity using random duality theory.
problem Characterize the capacity of binary perceptrons with general thresholds.
method Utilized fully lifted random duality theory (fl RDT) to characterize the capacity.
result Characterizations match replica symmetry breaking predictions and uncover the capacity for zero-threshold scenario.
Refines knot defect measurement in 3D and 4D.
problem Measuring how far knots are from being alternating.
method Extends spanning surface defect to 4-ball, making comparisons and proving formulas.
result Connected sum formula proven.
Spanning attack improves black-box attacks with unlabeled data.
problem Query inefficiency in black-box attacks due to high input space dimensionality.
method Proposes spanning attack by constraining adversarial perturbations in a low-dimensional subspace via an auxiliary unlabeled dataset.
result Significantly improves query efficiency of black-box attacks.
Proves bounds on spanning two-forests and random cut sizes.
problem Counting spanning two-forests and estimating random cut sizes.
method Uses pairwise effective resistances and potential theory.
result Establishes bounds on the number of spanning two-forests and average cut size.
Alexander polynomial equals spanning tree count at t=1.
problem Alexander polynomial for spatial graphs.
method Combinatorial constructions generalized to weighted graphs.
result Value of Alexander polynomial at t=1 equals weighted spanning tree count.
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.
Framework improves marine mammal monitoring in noisy underwater environments.
problem Underwater bioacoustic monitoring challenges due to overlapping calls and variable noise.
method Multi-step attention-guided framework with segmentation and mid-level fusion.
result Improved signal discrimination, reduced false positives, reliable representations.
New complete panel dataset for LMICs helps analyze innovation and development.
problem Lack of complete data for empirical analyses in LMICs.
method Predictive Mean Matching multiple imputation technique.
result Created a large dataset of 47 variables for 82 LMICs from 2005-2019.
Upper bounds for Lagrangian capacities of Liouville domains
problem Lagrangian capacity of Liouville domains
method Using S1-equivariant techniques result Extremal Lagrangian torus on the boundary of ellipsoid
We introduce the warping polynomial of an oriented knot diagram. In this paper, we characterize the warping polynomial, and define the span of a knot to be the minimal span of the warping polynomial for all diagrams of the knot. We show that the span of a knot is one if and only if it is non-trivial and alternating, an…
Memory capacity of DAM scales exponentially with feature separation, unaffected by correlations.
problem Understanding how feature correlations impact DAM's capacity.
method Developed an empirical framework to analyze DAM's capacity under varying feature correlations and pattern separations.
result Memory capacity scales exponentially with feature separation, unaffected by correlations.
Proves local maximizers for higher Ekeland-Hofer capacities in 4D star-shaped domains.
problem Finding local maximizers for higher Ekeland-Hofer capacities in specific domains.
method Analogous to 4D local Viterbo conjecture, proving maximizers for rational ellipsoids.
result Local maximizers of the k-th Ekeland-Hofer capacities are symplectomorphic to rational ellipsoids.
Develops a theory for mth order p-affine capacity for convex bodies containing the origin.
problem Defines and studies the mth order p-affine capacity for convex bodies containing the origin.
method Provides equivalent definitions, proves properties, and establishes inequalities.
result Establishes inequalities comparing to other geometric measures.
Derives an empirical capacity model for self-attention neural networks.
problem Theoretical capacity of large transformer models is not fully utilized by current optimization algorithms.
method Analyzes memory capacity of transformers using synthetic training data and common training algorithms.
result Derives an empirical capacity model (ECM) for a generic transformer.
New spanning tree model connects knot homology, s-invariant, and exotic discs.
problem Understanding exotic discs in the 4-ball for knots.
method Explicitly defined differential in spanning tree complex, described Rasmussen's s-invariant.
result Identified new infinite family of knots bounding exotic discs.
We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning given some stochastic dominance relation. We define the concept of Markowitz stochas…
New algorithms find optimal policies without knowing MDP span.
problem Finding optimal policies in MDPs without knowing span.
method Horizon calibration and span penalization techniques.
result First algorithms achieving optimal span-based complexity without prior knowledge.
Improves online learning algorithms for functional models with capacity assumptions.
problem Convergence rates of online stochastic gradient descent algorithms for functional linear models.
method Characterizations of slope function regularity, kernel space capacity, and sampling process covariance operator.
result Capacity assumptions can alleviate saturation of convergence rates as function regularity increases.
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…
Non-spanning identification of scheduled event risk in option pricing.
problem Separating continuous surface from scheduled jump in option pricing.
method Modeling FOMC decisions, CPI releases, and NFP reports as deterministic-time jumps in risk-neutral option pricing.
result Improves held-out event-spanning pricing with Gaussian and two-component mixture jumps.
Study relates symplectic homology capacity to periodic orbits in Liouville domains.
problem Relating symplectic homology capacity to periodic orbits in Liouville domains.
method Uses positive symplectic homology and Hofer-Zehnder capacity to establish bounds and existence of periodic points.
result Non-zero positive symplectic homology implies finite upper bound for Hofer-Zehnder capacity relative to skeleton and Hamiltonian diffeomorphisms.
Learning capacity measures model complexity, correlating with test loss and sample size.
problem Understanding model complexity and its relation to test performance.
method Formal correspondence between thermodynamics and inference; learning capacity as a measure of effective dimensionality.
result Learning capacity correlates with test loss and is a small fraction of model parameters.
New invariants measure how far spanning surfaces are from being compressible.
problem Understanding how essential spanning surfaces are in 3-manifolds.
method Introducing algebraic and geometric essence invariants, proving plumbing respects algebraic essence, and extending results to arbitrary 3-manifolds.
result Plumbing respects the algebraic essence of spanning surfaces, extending Ozawa's theorem.