New insights into neural network complexity reveal better generalization performance.
problem Mysterious generalization in deep models despite high parameter counts.
method Effective dimensionality as a measure of parameter space complexity.
result Double descent behavior in generalization as a function of parameters explained.
Counting spheres in hyperbolic space with effective methods.
problem Counting spheres in Apollonian and Kleinian packings.
method Spectral methods and orbit counting, extending Kontorovich and Lax-Phillips techniques.
result Best-known effective error rate for sphere packing counting problems.
Proposes a new DNN framework for count data with high-cardinality features.
problem Real-world data often have correlations and high-cardinality categorical features that traditional DNNs overlook.
method Introduces a hierarchical likelihood learning framework with gamma random effects for Poisson DNNs.
result Improves prediction performance by capturing nonlinear effects and subject-specific cluster effects.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
Pruning at initialization fails to find sparse subnetworks, revealing information-theoretic barriers.
problem Difficulty in finding sparse subnetworks without training the full model.
method Analysis of effective parameter count and mutual information between sparsity mask and data.
result Pruning at initialization cannot find sparse subnetworks due to high mutual information.
New phases identified in neural scaling laws with compute limits.
problem Understanding neural scaling laws under compute constraints.
method Solved neural scaling model with stochastic gradient descent, derived loss curves, analyzed model-parameter-count phases.
result Identified 4 phases (+3 subphases) in data-complexity/target-complexity phase-plane, derived exponents.
New approach shows why overparameterized neural nets generalize well.
problem Understanding why overparameterized neural nets generalize well in practice.
method An alternative notion of capacity for attention-based models based on the effective rank of attention matrices.
result Generalization bound matches empirical scaling laws observed in large language models.
Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.
problem Understanding effective default correlation in corporate defaults.
method Temporal coarse-graining of latent default-probability paths, applied to corporate default-count data.
result Temporal coarse-graining provides a scale-consistent baseline that improves identifiability and reduces over-allocation of long-horizon fluctuations.
Transformer learns to estimate negative binomial parameters efficiently.
problem Parameter estimation for over-dispersed count data in large screens.
method Pre-trained transformer trained on synthetic data generation to invert parameter to count transformation.
result Method of moments provides faster, more efficient, and better-calibrated estimates.
Temporal aggregation reveals latent default correlation from monthly data.
problem Understanding effective default correlation from monthly default data.
method Temporal coarse-graining of latent default-probability paths.
result Temporal coarse-graining improves identifiability and reduces over-allocation of long-horizon fluctuations.
Bayesian model fuses diverse microbiome data types.
problem Challenges in fusing different types of microbiome data.
method Flexible multinomial-Gaussian generative model with variational EM algorithm.
result Inferred latent variables provide common dimensionality reduction and predictive posterior distribution.
Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neur…
A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time (t−1) as the shape parameters of those at time t, which are linked …
Generalization in nonlinear least squares can be studied via algorithmic stability and effective dimension.
problem Generalization in nonlinear least squares models
method Deriving error bounds for local minimizers using algorithmic stability and effective dimension
result Bounds depend on learned geometry rather than parameter count
New findings challenge the traditional U-shaped curve of model complexity and error, revealing a second descent in error as model size increases.
problem The traditional U-shaped curve of model complexity and prediction error is incomplete, with recent work suggesting a second descent in error as model size increases.
method Careful consideration of multiple complexity axes and a nonparametric statistics perspective were used to interpret the observed double descent curves.
result The observed double descent curves in classical statistical machine learning methods fold back into traditional convex shapes, resolving tensions with statistical intuition.
The article applies Occam's Razor to non-parametric model building, minimizing the number of bits for data encoding.
problem Overlooking the role of model parameters in data encoding leads to inefficient probability density estimators.
method Extends bit counting to model parameters, providing a true measure of complexity for parametric models.
result Minimizing total bit requirement leads to smoother, more efficient probability density estimates and fewer relevant parameters.
Flow Matching for count data improves sample quality and efficiency.
problem Mapping between count distributions across batches or time points in high-dimensional count data.
method count-FM, a flow-matching framework based on a continuous-time birth-death process with local unit jumps.
result count-FM achieves better sample quality than representative baselines while using fewer parameters.
Estimates point counts in Teichmüller space for mapping class groups.
problem Counting points in Teichmüller space under mapping class group actions.
method Quantitative estimates with power saving error terms for Teichmüller metric balls.
result Effectivizes asymptotic counting results of Athreya et al.
Polynomial-time methods count and sample DAGs from Markov classes.
problem Counting and sampling Markov equivalent DAGs.
method Polynomial-time algorithms for DAGs from Markov classes.
result Long-standing open problem solved, making practical infeasible strategies feasible.
NGD models have higher effective dimension than SGD models.
problem Measuring model complexity accurately.
method Comparison of NGD and SGD models using effective dimension measures.
result NGD models have a higher effective dimension than SGD models.
Estimates surface count with prescribed foliations.
problem Counting square-tiled surfaces with specific foliations.
method Effective estimate with power saving error term.
result Strengthens asymptotic counting formulas.
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately IR2log22(I) non-zero counts. The paper models and predicts co-occurrence counts using Gamma regression.
problem Predicting relevance between items or users from high-dimensional sparse co-occurrence count data.
method Shared parameter alternating zero-inflated Gamma regression models (SA-ZIG) with Fisher scoring and learning rate adjustment.
result SA-ZIG with learning rate adjustment performs satisfactorily in predicting relevance.
New findings show tool-augmented models can recall unlimited facts, outperforming purely memorized models.
problem Limitations of purely memorized models in recalling large amounts of factual information.
method Demonstrated the benefits of in-tool learning (external retrieval) over in-weight learning (memorization) for factual recall.
result Proved that tool-use enables unbounded factual recall via a simple and efficient circuit construction.
The main result of this paper is an effective count for Apollonian circle packings that are either bounded or contain two parallel lines. We obtain this by proving an effective equidistribution of closed horospheres in the unit tangent bundle of a geometrically finite hyperbolic 3-manifold of infinite volume, whose fun…
The paper explores curvature-free effects in manifolds with volume growth and ends-counting.
problem Investigating curvature-free effects in manifolds with volume growth and ends-counting.
method Establishing two main theorems about volume growth and ends-counting.
result Proves the existence of smooth bounded mean-concave exhaustion and escaping geodesic lines.
New approach improves black-box planning efficiency by discovering focused macros.
problem Difficulty of deterministic planning increases exponentially with depth.
method Discovering macro-actions with focused effects to improve goal-count heuristics.
result Focused macros dramatically improve black-box planning efficiency.
Pruning is a standard technique for removing unnecessary structure from a neural network to reduce its storage footprint, computational demands, or energy consumption. Pruning can reduce the parameter-counts of many state-of-the-art neural networks by an order of magnitude without compromising accuracy, meaning these n…
Counting is a fundamental task in biomedical imaging and count is an important biomarker in a number of conditions. Estimating the uncertainty in the measurement is thus vital to making definite, informed conclusions. In this paper, we first compare a range of existing methods to perform counting in medical imaging and…
Non-negative tensor factorization models enable predictive analysis on count data. Among them, Bayesian Poisson-Gamma models can derive full posterior distributions of latent factors and are less sensitive to sparse count data. However, current inference methods for these Bayesian models adopt restricted update rules f…
Time series of counts arise in a variety of forecasting applications, for which traditional models are generally inappropriate. This paper introduces a hierarchical Bayesian formulation applicable to count time series that can easily account for explanatory variables and share statistical strength across groups of rela…
Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in na…
ENTED efficiently decomposes binary and count tensors using nonparametric Gaussian processes.
problem Handling high-dimensional and sparse binary and count data with traditional tensor decompositions.
method ENTED uses nonparametric Gaussian processes and sparse orthogonal variational inference to handle binary and count tensors.
result ENTED outperforms traditional methods in binary and count tensor completion tasks.
Proposes a robust EM algorithm for analyzing incomplete panel count data.
problem Missing reports in panel count data.
method Functional EM algorithm for non-parametric counting process mean function estimation.
result Robust to misspecification of Poisson process assumption and missing completely at random.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
PHIBP models complex microbiome data with shared parameters.
problem Complex, sparse count data in microbiome analysis.
method Bayesian nonparametric framework with shared species parameters.
result Flexible multivariate count model with tractable inference.
The paper improves count data regression models for overdispersed data.
problem Improving regression models for overdispersed count data.
method Double ℓ1-regularized negative binomial regressions. result Oracle inequalities and consistency for Lasso estimators of partial regression coefficients.
Polynomial-time methods count and sample DAGs from equivalence classes.
problem Counting and sampling DAGs from Markov equivalence classes.
method Polynomial-time algorithms for DAGs.
result Counting and sampling can be done in polynomial time.
Capsule network (CapsNet) was introduced as an enhancement over convolutional neural networks, supplementing the latter's invariance properties with equivariance through pose estimation. CapsNet achieved a very decent performance with a shallow architecture and a significant reduction in parameters count. However, the …
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and e…
Proposes PSCCA for estimating correlations and canonical correlations in sparse count data.
problem Estimating correlations and canonical correlations in sparse count data from next-generation sequencing.
method Probabilistic approach for sparse count data sets (PSCCA).
result PSCCA outperforms other methods in estimating true correlations and canonical correlations at the natural parameter level.
Graphical estimation of count time series dependencies.
problem Estimating dependencies between multivariate count time series.
method Parameter-driven generalized linear model with l1-type regularization and MCEM algorithm.
result Characterization of disease spread interdependence and sources/sinks in Greater Mumbai.
Artificial neural networks (ANNs) may not be worth their computational/memory costs when used in mobile phones or embedded devices. Parameter-pruning algorithms combat these costs, with some algorithms capable of removing over 90% of an ANN's weights without harming the ANN's performance. Removing weights from an ANN i…
The ability to detect and count certain substructures in graphs is important for solving many tasks on graph-structured data, especially in the contexts of computational chemistry and biology as well as social network analysis. Inspired by this, we propose to study the expressive power of graph neural networks (GNNs) v…
In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface S, and fix a number of points F on its boundary. We ask: how many configurations of disjoint arcs are there on S whose boundary is F? We find that thi…
We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this fil…
Precision medicine aims for personalized prognosis and therapeutics by utilizing recent genome-scale high-throughput profiling techniques, including next-generation sequencing (NGS). However, translating NGS data faces several challenges. First, NGS count data are often overdispersed, requiring appropriate modeling. Se…
Estimates the number of closed curves on surfaces with power-saving error terms.
problem Counting closed curves on surfaces with given properties.
method Effective dynamics of mapping class group on Teichmüller space and space of closed curves, introducing novel methods.
result Proves estimates with power-saving error terms for filling closed curves and curves with respect to a current.