New bounds on neural network capacity for treelike sign perceptrons using RDT.
problem Determining the capacity of treelike sign perceptrons neural networks.
method Random Duality Theory (RDT) to establish upper bounds.
result Mathematically rigorous bounds on network capacity for any number of neurons.
Improved neural network capacity analysis using simplified RDT.
problem Analyzing the memorization capabilities of sign perceptron neural networks.
method Developed a simplified, partially lifted Random Duality Theory (fl RDT) approach.
result Concrete capacity bounds universally improve over previous best known ones.
Study shows how activation functions impact the storage capacity of treelike neural networks.
problem Understanding the role of activation functions in neural network expressive power.
method Analysis of treelike two-layer networks with various activation functions in the infinite-width limit.
result Activation functions affect storage capacity and robustness, with nonlinearity increasing capacity and decreasing robustness.
New analysis shows capacity of treelike neural networks with various activations.
problem Analyzing the capacity of treelike neural networks with diverse activations.
method Utilized Random Duality Theory and its partially lifted version to handle various activations.
result The capacity of treelike neural networks decreases for large network width but converges to a constant value.
New Coxeter groups have unique boundary structures.
problem Understanding boundaries of Coxeter groups.
method Recursive construction and amalgamation of CAT(0) groups.
result Totally disconnected Morse boundaries for new Coxeter groups.
Perceptrons have been known for a long time as a promising tool within the neural networks theory. The analytical treatment for a special class of perceptrons started in seminal work of Gardner \cite{Gar88}. Techniques initially employed to characterize perceptrons relied on a statistical mechanics approach. Many of su…
Wide hidden layer TCM nets capacity analyzed using RDT and fl RDT.
problem Capacity analysis of wide hidden layer TCM nets.
method Employed Fully Lifted Random Duality Theory (fl RDT) for capacity characterization.
result Explicit, closed form capacity characterizations for a generic class of hidden layer activations.
Paper proposes online algorithms for multiclass classification with partial labels.
problem Classifying data with partial labels.
method Avg Perceptron, Max Perceptron, Avg Pegasos, Max Pegasos algorithms.
result Mistake bounds for Avg Perceptron and regret bound for Avg Pegasos.
This paper proposes an improved design of the perceptron unit to mitigate the vanishing gradient problem. This nuisance appears when training deep multilayer perceptron networks with bounded activation functions. The new neuron design, named auto-rotating perceptron (ARP), has a mechanism to ensure that the node always…
We comment on the fact that gradient ascent for logistic regression has a connection with the perceptron learning algorithm. Logistic learning is the "soft" variant of perceptron learning.
We study and provide exposition to several phenomena that are related to the perceptron's compression. One theme concerns modifications of the perceptron algorithm that yield better guarantees on the margin of the hyperplane it outputs. These modifications can be useful in training neural networks as well, and we demon…
A note proves the binary perceptron's capacity is less than 0.847.
problem Determining the capacity of the binary perceptron.
method Conditional first moment method combined with known results on the spherical perceptron.
result Proves the binary perceptron's capacity is less than 0.847.
Quantum algorithms improve perceptron learning efficiency.
problem Improving quantum algorithms for perceptron learning.
method Revisiting and correcting a flawed quantum version space perceptron algorithm, proposing quantum-enhanced cutting-plane algorithms.
result Improved complexity bounds for quantum perceptron learning.
Efficient algorithms find solutions in a rare well-connected cluster at low constraint densities.
problem Finding solutions in the symmetric binary perceptron at low density.
method Formal proof of existence of a subdominant connected cluster and application of an efficient multiscale majority algorithm.
result An efficient algorithm can find solutions in a subdominant connected cluster with high probability.
Bayesian Perceptron offers fully Bayesian neural networks without complex computations.
problem Lack of uncertainty quantification in neural networks.
method Bayesian inference framework for perceptron training and predictions in closed-form.
result Analytical expressions for perceptron's output and weight learning provided.
A new algorithm finds a separating hyperplane with fewer updates.
problem Finding a separating hyperplane with minimal updates.
method Optimistic Perceptron algorithm.
result The Optimistic Perceptron finds a separating hyperplane with no more than $ rac{1}{γ}$ updates.
Perceptron is a classic online algorithm for learning a classification function. In this paper, we provide a novel extension of the perceptron algorithm to the learning to rank problem in information retrieval. We consider popular listwise performance measures such as Normalized Discounted Cumulative Gain (NDCG) and Av…
Perceptrons are neuronal devices capable of fully discriminating linearly separable classes. Although straightforward to implement and train, their applicability is usually hindered by non-trivial requirements imposed by real-world classification problems. Therefore, several approaches, such as kernel perceptrons, have…
We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits quantum information processing to determine a separating hyperplane using a number …
Binary perceptron's instability linked to replica symmetry breaking.
problem Understanding the relationship between algorithmic instability and replica symmetry breaking in binary perceptron learning.
method Established the connection between algorithmic instability and replica symmetry breaking by comparing the instability condition around the fixed point to the instability for breaking the replica symmetric solution of the free energy function.
result The instability condition around the algorithmic fixed point is identical to the instability for breaking the replica symmetric saddle point solution of the free energy function.
We propose a new type of hidden layer for a multilayer perceptron, and demonstrate that it obtains the best reported performance for an MLP on the MNIST dataset.
Unified framework for accelerated Perceptron and related problems.
problem Finding optimal linear threshold functions for classification.
method Modern acceleration techniques, specifically optimistic online learning.
result Improved convergence rates for various Perceptron-related problems.
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.
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.
Modified Perceptron handles strategic agents with limited position changes.
problem Learning linear classifiers in the presence of strategic agents that can manipulate their positions.
method Developed a modified Perceptron algorithm with bounded mistakes under various manipulation costs.
result The modified Perceptron achieves bounded mistakes even when manipulation costs are unknown.
Study analyzes learning dynamics in nonlinear perceptrons using stochastic-process approach.
problem Understanding the roles of nonlinearity and input-data distribution in neural network learning.
method Stochastic-process approach to derive flow equations for learning dynamics in nonlinear perceptrons.
result Input-data noise affects learning speed differently under supervised and reinforcement learning.
A new geometric perceptron model improves 3D shape classification.
problem Challenges in geometric tasks involving point clouds using machine learning.
method Introduces multilayer geometric perceptron (MLGP) with geometric neurons.
result MLGP outperforms vanilla MLP in 3D shape classification and noise resistance.
The study analyzes multi-class teacher-student perceptron performance and generalization errors.
problem Analyzing multi-class classification with the teacher-student perceptron.
method Deriving asymptotic expressions for Bayes-optimal and empirical risk minimization (ERM) generalization errors.
result Regularised cross-entropy minimization yields close-to-optimal accuracy for multi-class classification.
The paper analyzes phase transitions in transfer learning for perceptrons.
problem Understanding when transfer learning from a source task to a target task is beneficial.
method Theoretical analysis of a pair of related perceptron learning tasks.
result Reveals a phase transition from negative to positive transfer as task similarity changes.
Geometric vector perceptrons improve protein structure learning.
problem Learning from protein structure with efficient and natural representations.
method Introducing geometric vector perceptrons to extend dense layers for Euclidean vectors, integrating geometric and relational reasoning.
result Improves model quality assessment and computational protein design over existing methods.
It has been known for a long time that the classical spherical perceptrons can be used as storage memories. Seminal work of Gardner, \cite{Gar88}, started an analytical study of perceptrons storage abilities. Many of the Gardner's predictions obtained through statistical mechanics tools have been rigorously justified. …
The paper analyzes a simple neural network model with algebraic methods.
problem Finding minima of a ridge-regularized mean squared error for ReLU perceptrons.
method Developed a Divide-Enumerate-Merge strategy using computational algebra.
result Identifies both isolated and connected minima of the RR-MSE.
Study shows perceptrons with random labels perform similarly to Gaussian data.
problem The assumption of Gaussian input data is often seen as a limitation in machine learning.
method Analyzed generalized linear classification (perceptron model) with random labels.
result Minimum training loss is independent of data covariance for high-dimensional input data.
This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however we show that, if we choose as cost function the logarithm of the determinant of t…
PAC-Bayesian bounds for MLPs with cross entropy loss validated.
problem Generalization bounds for MLPs with cross entropy loss.
method Introduced probabilistic explanations and proved PAC-Bayesian bounds using ELBO.
result MLPs with cross entropy loss inherently guarantee PAC-Bayesian generalization bounds.
Artificial Neural Networks(ANN) has been phenomenally successful on various pattern recognition tasks. However, the design of neural networks rely heavily on the experience and intuitions of individual developers. In this article, the author introduces a mathematical structure called MLP algebra on the set of all Multi…
Breast cancer is the most frequently reported cancer type among the women around the globe and beyond that it has the second highest female fatality rate among all cancer types. Despite all the progresses made in prevention and early intervention, early prognosis and survival prediction rates are still unsatisfactory. …
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the online and batch settings. First, we propose a perceptron-like algorithm for learnin…
We utilize Wi-Fi communications from smartphones to predict their mobility mode, i.e. walking, biking and driving. Wi-Fi sensors were deployed at four strategic locations in a closed loop on streets in downtown Toronto. Deep neural network (Multilayer Perceptron) along with three decision tree based classifiers (Decisi…
New method lowers spherical perceptron capacity using fully lifted random duality theory.
problem Tackles the negative spherical perceptron capacity, a long-standing open problem.
method Develops fully lifted random duality theory (fl RDT) to characterize capacity.
result Shows remarkable closed-form analytical relations for practical capacity values.
WavPool improves deep neural networks with wavelet-based pooling.
problem Improving efficiency and performance of deep neural networks.
method Introducing WavPool, a wavelet-transform-based pooling layer.
result WavPool outperforms existing network architectures by 10% on CIFAR-10.
Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory…
Study potential computational gaps in symmetric binary perceptrons using fl-RDT.
problem Potential statistical-computational gaps in symmetric binary perceptrons.
method Parametric utilization of fully lifted random duality theory (fl-RDT).
result Observation of a computational gap SCG=αc−αa in SBP. New method constructs equivariant neural networks for arbitrary matrix groups.
problem Challenges in constructing equivariant neural networks for complex groups.
method Completely general algorithm for solving equivariant layers of matrix groups.
result Constructs multilayer perceptrons equivariant to multiple groups including O(1,3), O(5), Sp(n), and Rubik's cube group.
A new model of learning corrects for chance to improve learning outcomes.
problem The importance of chance-corrected measures in learning.
method Developed two models: Informatron and AdaBook, based on empirical psychological results.
result Chance correction facilitates learning, as shown by computational results.
We present a neural-network valuation of financial derivatives in the case of fat-tailed underlying asset returns. A two-layer perceptron is trained on simulated prices taking into account the well-known effect of volatility smile. The prices of the underlier are generated using fractional calculus algorithms, and opti…
We prove lognormal distribution for symmetric perceptron model, solving key conjectures.
problem Understanding the performance of learning algorithms in neural networks.
method Lognormal distribution characterization and small graph conditioning method.
result Established lognormal distribution and several conjectures for the symmetric perceptron model.
Proposes using MLP for predicting optimal penalty in changepoint detection.
problem Predicting optimal penalty for changepoints in sequences.
method Uses a multilayer perceptron (MLP) with ReLU activation function to predict penalty.
result Improves accuracy and F1 score compared to existing models.