Lean 2-layer RBMs achieve similar representational power as single-layer RBMs with fewer parameters.
problem Understanding and quantifying the representational power of multi-layer RBMs.
method Inherent Structure Capacity (ISC) and Lean RBMs.
result 2-layer RBMs can achieve the same representational power as single-layer RBMs with fewer parameters.
Residual networks' depth is mathematically equivalent to expanding an implicit ensemble size.
problem Understanding why deep residual networks are effective.
method Formal analysis of residual networks as ensembles of shallow models.
result Increasing network depth is equivalent to expanding the size of an implicit ensemble, revealing a hierarchical structure.
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.
Novel framework learns efficient student models from teacher networks.
problem Model capacity gap between teacher and student networks.
method Neural architecture search and oracle knowledge distillation.
result Searched student models often outperform teacher models.
MiME learns EHR data structure for predictive healthcare tasks.
problem Data insufficiency in EHR for predictive healthcare tasks.
method Leverages multilevel structure of EHR data and learns multilevel embedding.
result MiME outperforms baseline methods in diverse evaluation settings.
Free Random Projection enhances reinforcement learning by naturally incorporating hierarchical structure.
problem Improving reinforcement learning algorithms for better generalization and adaptability.
method Introduces Free Random Projection, a method that uses free probability theory to create random orthogonal matrices encoding hierarchical structure.
result Empirically shows consistent improvement in generalization over standard methods on multi-environment benchmarks.
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.
New method optimizes resource allocation for uncertain tasks.
problem Optimal resource allocation for uncertain tasks with limited capacity.
method Formulated as an assignment problem, optimized using learning to rank with net discounted cumulative gain.
result Achieves higher expected profit and precision compared to classification methods.
Paper optimizes graph neural networks for better structural graph classification.
problem Improving graph neural networks for structural graph classification.
method Focus on aggregation functions, specifically sum and histogram-based functions, to enhance discrimination.
result Design of a graph neural network that learns discriminative graph representations.
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.
Holographic Neural Architectures learn representations from data.
problem Representation learning in deep learning.
method Holographic Neural Architectures (HNAs) derive Holographic Representations from training data.
result HNAs are effective for generative networks, regression, and noise resistance.
Finite resources limit false discovery rate control in structured hypothesis spaces.
problem Controlling false discovery rate in hypothesis testing with finite data and structured hypothesis spaces.
method Framework for exact FDR control and adaptive power maximization.
result Exact FDR control and adaptive power maximization.
Study on neural networks' storage capacity and solution space structure.
problem Understanding the storage capacity and solution space structure of neural networks.
method Replica method from statistical physics.
result Storage capacity per parameter remains finite even with infinite width and weights exhibit negative correlations.
HyperBERT enhances BERT for node classification on text-attributed hypergraphs.
problem Challenges in capturing hypergraph structure and text attributes in node classification.
method Mixing hypergraph-aware layers with BERT for improved node classification.
result HyperBERT achieves state-of-the-art results on text-attributed hypergraph benchmarks.
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.
Estimates and compares the capabilities of neural network architectures.
problem Developing quantitative methods to estimate and compare neural network architectures.
method Defining capacity as the logarithm of the number of functions an architecture can compute, and proving a cubic polynomial formula for layered architectures.
result The capacity of a neural network is given by a cubic polynomial in the layer sizes, with bottlenecks affecting the capacity.
Framework uses RL and simulation for optimal microgrid energy storage planning.
problem Optimal investment in diverse energy storage technologies for microgrids.
method Combines reinforcement learning with simulation-based optimization for long-term planning.
result Derives better engineering solutions for future microgrid applications.
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.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
In this paper we address the following question, given a face representation, how many identities can it resolve? In other words, what is the capacity of the face representation? A scientific basis for estimating the capacity of a given face representation will not only benefit the evaluation and comparison of differen…
gLSTM improves graph neural networks by increasing storage capacity to prevent over-squashing.
problem Over-squashing in GNNs collapses information from a large receptive field into a single vector, creating an information bottleneck.
method Introduced a new synthetic task to measure over-squashing and adapted ideas from sequence modeling to develop gLSTM, a novel GNN architecture with improved capacity.
result gLSTM architecture demonstrates strong performance on synthetic and real-world graph benchmarks, mitigating over-squashing.
Study improves generalization bounds for equivariant networks on Markov data.
problem Challenges in integrating equivariance with Markov dependencies in neural networks.
method Applied McDiarmid's inequality and computed covering number using group theory.
result Derived upper bound on Rademacher complexity for equivariant neural networks on Markov datasets.
RAF model explains neural networks' dual rule learning and fact memorization.
problem Understanding how neural networks learn rules and memorize facts simultaneously.
method Introduces the Rules-and-Facts (RAF) model to bridge generalization and memorization.
result Characterizes conditions for simultaneous rule learning and fact memorization in neural networks.
MolHF generates complex molecules with hierarchical flow-based model.
problem Designing novel molecular structures with desired properties.
method MolHF is a hierarchical normalizing flow model that generates molecular graphs in a coarse-to-fine manner.
result MolHF achieves state-of-the-art performance in random generation and property optimization.
The study improves the perceptron's storage capacity by optimizing variable selection.
problem Distinguishing genuine structure from random correlations in high-dimensional data.
method Replica method from statistical mechanics for optimal variable selection.
result Optimal variable selection can surpass the Cover--Gardner bound for pattern classification.
The memory capacity of linear echo state networks is accurately calculated using new numerical methods.
problem Numerical evaluations of memory capacity in recurrent neural networks often contradict theoretical bounds.
method Developed robust numerical approaches exploiting MC neutrality with respect to the input mask matrix.
result Memory curves fully agree with theory when using the proposed methods.
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.
Powerpropagation makes neural networks inherently sparse.
problem Training sparse neural networks to reduce computational footprint and model size.
method Introduces a new weight-parameterisation technique exploiting gradient descent dynamics.
result Models trained with Powerpropagation have a higher density of zero weights, allowing for more efficient pruning.
Paper develops framework for valuing and assessing credit risk in renewable PPAs.
problem Renewable PPAs expose both parties to counterparty credit risk.
method Modelled joint dynamics of electricity prices and renewable output, incorporated default probabilities.
result Provides transparent metric for PPA valuation under counterparty risk.
New method reduces overfitting in deep neural networks by measuring and regulating hidden unit diversity.
problem Overfitting in deep neural networks.
method Introduces a new redundancy measure based on mutual information to improve generalization.
result Reduction of redundancy improves generalization capacity, reducing overfitting.
Investigates how neural network capacity impacts the learning of compositional languages.
problem The importance of communicative bandwidth in emergent language learning.
method Exploration of how neural network capacity affects the learning of compositional languages.
result There is a specific range of model capacity and channel bandwidth that induces compositional structure.
We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity --- the Fisher-Rao norm --- that possesses desirable invariance properties and is motivated by Information Geometry. We discover an analytical characterization of…
This research proves guarantees on sequence models' generalization to longer and novel sequences.
problem Generalization to longer sequences and novel token combinations in sequence models.
method Provable guarantees on length and compositional generalization for various sequence models.
result Limited capacity models achieve both length and compositional generalization with diverse training distributions.
Researchers analyze neural process architectures and their representational capacities.
problem Understanding what functions can be represented by different neural process architectures.
method Analyzing four types of neural process architectures: CNPs, ANPs, TNPs, and their latent variants.
result Prove these architectures form a strict hierarchy and characterize their representational capabilities.
Deep learning predicts bridge load capacity from images.
problem Lack of data on aging bridges in post-disaster zones.
method Crowd-sourced images trained on a new CNN for multiclass classification.
result Improved prediction accuracy and practical optimisation.
The study calculates the injectivity capacity of ReLU networks using a novel mathematical approach.
problem Determining the injectivity capacity of ReLU networks layers.
method Employing fully lifted random duality theory (fl RDT) to handle the ℓ0 spherical perceptron and implicitly the ReLU layers injectivity. result The lifting mechanism converges remarkably fast with relative corrections not exceeding 0.1%.
A new prior for VAEs improves model capacity by allowing a more flexible latent space.
problem Standard Gaussian priors in VAEs limit model capacity and performance.
method Proposed a Riemannian Brownian motion prior over a Riemannian structure of the latent space.
result The new prior significantly increases model capacity with only one additional scalar parameter.
Analyzes how ReLU affects neural network capacity and solution space geometry.
problem Understanding the effects of ReLU on neural network capacity and solution space.
method Analytical and numerical studies of two-layer neural networks with ReLU activations.
result The capacity of ReLU networks remains finite as the number of hidden neurons increases, unlike for threshold units.
This paper extends financial theory to measure learnable market structure under computational constraints.
problem Understanding learnable market structure under bounded computational capacity.
method Introduces financial epiplexity as a measure of learnable market structure, extending classical information theory.
result Proves that equal entropy does not imply equal epiplexity and derives thresholds for useful regimes.
Flexible VAEs using FIFs improve model likelihood on image datasets.
problem Limitations of diagonal Gaussian posteriors in VAEs.
method Regularized Free-form Injective Flow (FIF) for flexible posterior.
result Full covariance VAEs outperform diagonal Gaussian posteriors.
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.
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.
We propose a decentralized Maximum Likelihood solution for estimating the stochastic renewable power generation and demand in single bus Direct Current (DC) MicroGrids (MGs), with high penetration of droop controlled power electronic converters. The solution relies on the fact that the primary control parameters are se…
LDTA expands LDA's topic modeling capacity with tree-structured priors.
problem Limited expressiveness of Dirichlet priors in LDA for complex topic relationships.
method Introduces Latent Dirichlet-Tree Allocation (LDTA) with Dirichlet-Tree (DT) priors, and develops universal mean-field variational inference and Expectation Propagation.
result LDTA enables expressive, tree-structured priors over topic proportions, expanding modeling capacity of LDA.
New method allows a robot to perceive space dimensions without prior knowledge.
problem Limitation of previous methods in perceiving space dimensions with small movements.
method Non-linear dimension estimation method.
result Robots can now perceive space dimensions with larger movements.
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…
The article introduces gamma-Psi-dimensions for margin multi-category classifiers.
problem Margin multi-category classifiers' generalization performance under minimal learnability hypotheses.
method Derives gamma-Psi-dimensions, handles capacity measures, and establishes upper bounds on metric entropies and Rademacher complexity.
result Gamma-Psi-dimensions improve over fat-shattering dimension and offer a promising alternative for multi-class to binary transitions.
Extends capacity analysis to neural networks, showing how capacity is distributed across layers.
problem How capacity is distributed in neural networks with non-linear layers.
method Introduces layer decoupling to quantify non-linear activation's impact, and uses a markovian rule for capacity propagation in deep networks.
result Shows that under certain conditions, capacity allocation in neural networks is equivalent to linear capacity allocation in an extended input space.