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arXiv research

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.

168,786 papers · 148 categories

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48 results for capacity saturation

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.

Deep ReLU networks show that 4 layers suffice for unique input recovery.

problem Injectivity capacity of deep ReLU networks.
method Developed a program connecting deep ReLU injectivity to an ll-extension of the 0\ell_0 spherical perceptrons, using random duality theory.
result Only 4 layers are needed for unique input recovery, showing expansion saturation effect.

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.

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.

CNAS optimizes neural architectures for class-incremental learning.

problem Capacity saturation in static neural architectures for class-incremental learning.
method CNAS uses reinforcement learning and network transformations to adaptively select architectures.
result CNAS outperforms static architectures and is more efficient.

Modeling alignment as resource-limited cognitive processes, researchers derive performance bounds.

problem Systematic deviations in feedback-based alignment of large language models.
method Modeling alignment as a two-stage cascade UoHoYU o H o Y given SS, with cognitive and total capacities.
result Capacity-coupled Alignment Performance Interval derived from Fano and PAC-Bayes bounds.

Paper develops an online learning algorithm for functional data models.

problem Recovering slope functions or predictors in functional data models.
method Online regularized learning algorithm in reproducing kernel Hilbert spaces with polynomially decaying step-size.
result Established fast convergence rates for estimation error without capacity assumption.

Catastrophic forgetting and capacity saturation are the central challenges of any parametric lifelong learning system. In this work, we study these challenges in the context of sequential supervised learning with an emphasis on recurrent neural networks. To evaluate the models in the lifelong learning setting, we propo…

2018-11-16abs ↗pdf ↗

We propose a novel high-performance and interpretable canonical deep tabular data learning architecture, TabNet. TabNet uses sequential attention to choose which features to reason from at each decision step, enabling interpretability and more efficient learning as the learning capacity is used for the most salient fea…

2019-08-20abs ↗pdf ↗

We propose a metric, Layer Saturation, defined as the proportion of the number of eigenvalues needed to explain 99% of the variance of the latent representations, for analyzing the learned representations of neural network layers. Saturation is based on spectral analysis and can be computed efficiently, making live ana…

2019-07-19abs ↗pdf ↗

We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the condi…

2016-09-21abs ↗pdf ↗

A homogeneously saturated equation for the time development of the price of a financial asset is presented and investigated for the pricing of European call options using noise that is distributed as a Student's t-distribution. In the limit that the saturation parameter of the equation equals zero, the standard model o…

2013-01-24abs ↗pdf ↗

Contextual PDA improves explanation of image classifications for saturated models.

problem Difficulty in explaining decisions of saturated classifiers.
method Proposes Contextual PDA, a faster method for explaining image classifications.
result Contextual PDA outperforms PDA in explaining image classifications of state-of-the-art deep networks.

This paper explores saturation effects in spectral algorithms over large dimensions.

problem Saturation effects in spectral algorithms over large dimensions.
method Improved minimax lower bound and gradient flow with early stopping strategy.
result Exact convergence rates of spectral algorithms in large dimensional settings.

Muon spectral optimizer outperforms SGD in associative memory tasks.

problem Understanding the advantage of spectral optimizers in learning associative memory.
method Linear associative memory problem, Gaussian inputs and outputs, power law frequency distribution, thresholded gradient approximation.
result Muon significantly outperforms SGD in storage capacity and recovery rates.

A new method detects and compacts saturated entries in antisparse coding.

problem Efficiently solving antisparse coding problems with \ell_\infty-norm penalties.
method Safe squeezing methodology to detect and compact saturated entries, reducing problem dimensionality.
result The method accelerates the computation of antisparse representation by detecting and compacting saturated entries.

Entrocraft addresses RL performance saturation in LLMs by customizing entropy curves.

problem Performance saturation in RL algorithms for LLMs.
method Entrocraft uses rejection sampling to bias advantage distributions for customized entropy schedules.
result Entrocraft significantly improves generalization, output diversity, and long-term training in 4B models.

New insights explain speedup saturation in distributed learning with large batches and delays.

problem Understanding and optimizing speedup in distributed learning with large batches and delays.
method Theoretical analysis of strongly convex, convex, and non-convex settings, considering data sparsity.
result Identification of a data-dependent parameter explaining speedup saturation in both batch size and gradient staleness.

Estimates the generalization error of deep neural networks without relying on capacity measures.

problem Understanding how generalization error scales with training data for deep neural networks.
method Derives estimates of generalization error for deep networks based on two assumptions: zero training error and error probability proportional to distance to nearest training point.
result Estimates the generalization error of DNNs as O(1/(δN^{1/d})), matching experimental behavior.

Service-induced congestion in memory-constrained LLM serving

problem Service-induced congestion in memory-constrained large language model (LLM) serving
method Developing a discrete-time dynamical model of memory-constrained LLM inference
result The system converges to a unique worst-case limit cycle that is asymptotically stable outside a Lebesgue-measure-zero exact-capture set, with throughput losses as large as 50%.

A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of nonlinear saturation in industrial growth can be estimated from an equipartition cond…

2009-03-02abs ↗pdf ↗

Spectral algorithms improve under covariate shift with novel weighted techniques.

problem Improving spectral algorithms' performance under covariate shift.
method Analysis of spectral algorithms in non-parametric regression over RKHS, proposing a weighted spectral algorithm with clipped weights.
result Normalized weighted spectral algorithm achieves optimal capacity-independent convergence rates, and clipped weights can approach optimal capacity-dependent rates.

As one of standard approaches to train deep neural networks, dropout has been applied to regularize large models to avoid overfitting, and the improvement in performance by dropout has been explained as avoiding co-adaptation between nodes. However, when correlations between nodes are compared after training the networ…

2018-06-26abs ↗pdf ↗

Common nonlinear activation functions used in neural networks can cause training difficulties due to the saturation behavior of the activation function, which may hide dependencies that are not visible to vanilla-SGD (using first order gradients only). Gating mechanisms that use softly saturating activation functions t…

2016-03-01abs ↗pdf ↗

Analyzes word2vec-like models revealing linear subspaces learned during training.

problem Understanding representation learning in word embeddings.
method Analytical solution of word2vec loss dynamics and final embeddings.
result Models learn orthogonal linear subspaces incrementally, representing interpretable concepts.

New examples show deletion type admissible pairs can be rigid under rational saturation.

problem Rigidity of admissible pairs of rational homogeneous spaces of Picard number one.
method Application of Mok's general criterion for non-subdiagram type admissible pairs.
result Examples of deletion type admissible pairs are rigid under rational saturation.

A theory of feature geometry using spectral analysis of weight matrices.

problem Current methods decompose neural network activations into sparse linear features, losing geometric structure.
method Develops a theory by analyzing the spectra of weight-derived matrices, introducing the frame operator.
result Features collapse onto single eigenspaces, organizing into tight frames, and admit discrete classification.

Study network equilibria in saturated systems, revealing how small shocks can trigger major losses.

problem Understanding how small shocks can lead to major losses in financial networks and games.
method Derived explicit expressions for network equilibria, proved conditions for their uniqueness, and analyzed discontinuities.
result Bifurcation phenomenon in network equilibria, showing sensitivity to small shocks.

Study shows scaling up models doesn't always improve downstream tasks.

problem Understanding why scaling up models doesn't always improve downstream performance.
method Systematic study of 4800 experiments on various models, analyzing performance on 20 downstream tasks.
result Performance on downstream tasks saturates as model size increases, revealing a nonlinear relationship.

Soft-Radial Projection solves gradient saturation in constrained deep learning.

problem Gradient saturation in deep learning models when integrating hard constraints.
method Introduces Soft-Radial Projection, a differentiable layer that maps predictions onto constraint boundaries without rank-deficient Jacobians.
result Improves convergence and solution quality over state-of-the-art methods.

The paper extends kernel ridge regression to product kernels and reveals new convergence behaviors.

problem Understanding kernel ridge regression in large dimensions with various kernels.
method Established a broad family of large dimensional kernels and derived convergence rates.
result Revealed new phenomena including minimax optimality, saturation effect, and multiple descent behavior.