Single-layer GCN model improves recommendation performance with less complexity.
problem Severe computational burden and excessive model parameters in existing GCN models.
method Proposes a single-layer GCN architecture with a simplified aggregation step using DA similarity.
result Significantly outperforms existing GCN models and achieves up to a few orders of magnitude speedup.
Lookahead pruning extends single-layer optimization to multi-layer, outperforming magnitude-based pruning.
problem Pruning neural networks to reduce computational cost and memory usage.
method Developed a multi-layer optimization approach extending the single-layer optimization of magnitude-based pruning.
result Consistently outperforms magnitude-based pruning on various networks, especially in high sparsity.
Understanding the representational power of Restricted Boltzmann Machines (RBMs) with multiple layers is an ill-understood problem and is an area of active research. Motivated from the approach of \emph{Inherent Structure formalism} (Stillinger & Weber, 1982), extensively used in analysing Spin Glasses, we propose a no…
Transformers with multiple layers learn to estimate bigram distributions, while single-layer models often get stuck in unigram local minima.
problem Understanding the sequential modeling capabilities of transformers using Markov chains.
method Introducing a new framework to analyze transformers via Markov chains, characterizing their loss landscapes.
result Single-layer transformers often get stuck in local minima representing the unigram distribution, while deeper models reliably converge to the ground-truth bigram.
Relational Networks (RN) as introduced by Santoro et al. (2017) have demonstrated strong relational reasoning capabilities with a rather shallow architecture. Its single-layer design, however, only considers pairs of information objects, making it unsuitable for problems requiring reasoning across a higher number of fa…
GroSS enables efficient search for grouped convolutional architectures.
problem Training grouped convolutional architectures efficiently and effectively.
method GroSS: Group-Size Series Decomposition for Grouped Architecture Search.
result Simultaneous training of differing numbers of groups within a single layer and all possible combinations between layers.
Single-layer Transformer can approximate any sequence mapping.
problem Lack of theoretical understanding of Transformers.
method Review of linear algebra, probability, and optimization concepts; detailed analysis of Transformer architecture.
result A single-layer Transformer can approximate any continuous sequence-to-sequence mapping to arbitrary precision.
Neural ODEs simplified using Chen-Fliess series for Rademacher complexity analysis.
problem Analyzing the complexity of neural ODE models.
method Using Chen-Fliess series to frame neural ODEs as infinite-width nets, where weights are signature of control input and features are Lie derivatives.
result Derived compact expressions for the Rademacher complexity of ODE models.
Graph classification receives a great deal of attention from the non-Euclidean machine learning community. Recent advances in graph coarsening have enabled the training of deeper networks and produced new state-of-the-art results in many benchmark tasks. We examine how these architectures train and find that performanc…
Random feature maps improve forecasting with cheaper computation.
problem Improving forecasting accuracy with random feature maps.
method Developed a hit-and-run algorithm to select optimal internal weights.
result Optimal internal weights lead to superior forecasting skill.
Optimal stock price prediction model using recurrent neural networks with RMSprop optimizer.
problem Stock price prediction using neural networks.
method Comparison of fully connected, convolutional, and recurrent architectures; inclusion of three optimization techniques.
result Single layer recurrent neural network with RMSprop optimizer produces optimal results with validation and test MAE of 0.0150 and 0.0148 respectively.
Study shows neural networks trained with GD converge to Gaussian processes with polynomial decay.
problem Understanding convergence of neural networks to Gaussian processes during training.
method Explicit upper bounds on quadratic Wasserstein distance between trained networks and Gaussian approximations.
result Polynomial decay of approximation error with network width and training time.
We study the interplay between memorization and generalization of overparameterized networks in the extreme case of a single training example and an identity-mapping task. We examine fully-connected and convolutional networks (FCN and CNN), both linear and nonlinear, initialized randomly and then trained to minimize th…
OLS is a special case of Transformer, revealing its linear nature.
problem Understanding the statistical essence of Transformer architecture.
method Algebraic proof and spectral decomposition of covariance matrix.
result Attention mechanism in Transformers is mathematically equivalent to OLS.
Convolution and pooling improve kernel methods in image classification.
problem Understanding the interplay between approximation and generalization in convolutional architectures.
method Characterized RKHS of kernels with convolution, pooling, and downsampling, computed generalization error.
result Convolution and pooling operations trade off approximation with generalization power.
Enhanced ELM reduces randomness in neural network training.
problem Challenges in ELM architecture design and sensitivity to random weight initialization.
method Introduces Effective Non-Random ELM (ENR-ELM) incorporating signal processing concepts.
result ENR-ELM simplifies architecture design and eliminates random weight selection.
Paper proposes an efficient method to optimize neural networks without backpropagation.
problem Computational inefficiency and scalability issues in neural network optimization.
method Derives explicit solutions to optimize neural networks, reducing computational costs.
result Explicit solutions achieve near-optimality and can discover better optima than backpropagation.
Investigates the benefits of multi-head attention in Transformers, deriving convergence and generalization guarantees.
problem Underexplored dynamics of multi-head attention in Transformer training and generalization.
method Derives convergence and generalization guarantees for gradient-descent training of a multi-head self-attention model.
result Establishes conditions for initialization that ensure multi-head attention's realizability.
Gradient descent on LSE objectives implicitly performs EM, leading to collapse without volume control.
problem Gradient collapse in autoencoders without volume control.
method Introduced a single-layer encoder with an LSE objective and InfoMax regularization for volume control.
result Gradient--responsibility identity holds exactly; LSE alone collapses; variance prevents dead components; decorrelation prevents redundancy.
Dropout training, originally designed for deep neural networks, has been successful on high-dimensional single-layer natural language tasks. This paper proposes a theoretical explanation for this phenomenon: we show that, under a generative Poisson topic model with long documents, dropout training improves the exponent…
New analysis shows PE in Transformers increases generalization gap and vulnerability.
problem Understanding the impact of PE on Transformer generalization and robustness.
method Generalization analysis and adversarial Rademacher bounds for a single-layer Transformer with trainable PE.
result PE systematically enlarges the generalization gap and makes models more vulnerable to attacks.
Study reveals self-attention's role in learning and generalizing interactions.
problem Understanding self-attention's theoretical role in neural architectures.
method Interacting entities analysis, including multi-agent RL and genetic sequences.
result Self-attention efficiently represents, learns, and generalizes pairwise interactions.
Traditionally, when generative models of data are developed via deep architectures, greedy layer-wise pre-training is employed. In a well-trained model, the lower layer of the architecture models the data distribution conditional upon the hidden variables, while the higher layers model the hidden distribution prior. Bu…
GNNs improve graph signal discrimination by adding nonlinearities.
problem Improving graph signal discrimination in physical networks.
method Analyzing the discriminability of GNNs and their relation to graph filter banks.
result GNNs are at least as discriminative as linear graph filter banks.
We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary synapses in single layer networks. The standard statistical analysis shows that this…
Neural networks trained with Q-learning converge to optimal control.
problem Optimal control of reinforcement learning with neural networks.
method Analysis of a limit differential equation derived from Q-learning.
result The limit differential equation has a unique stationary solution that is optimal.
Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.
problem Understanding when and why Transformers outperform other neural network architectures.
method Analyzing a sequence-to-sequence data generating model with dynamic sparsity, proving sample complexity differences between feedforward, recurrent, and Transformers.
result Transformers can learn dynamic sparsity models with lower sample complexity than feedforward and recurrent networks.
Establishes connection between MTDNN and multitask GP, revealing weight correlation as key to task sharing.
problem Limited theoretical understanding of information sharing in MTDNN.
method Derives multitask GP kernels for MTDNN and MTBNN, showing shared hyper-parameters and last layer weights.
result Information sharing in MTDNN is due to weight correlation, not intermediate layer weights.
New model combines physics and machine learning for ocean dynamics.
problem Discovering hidden laws governing ocean dynamics.
method Develops Deep Neural Numerical Models (DNNMs) to learn hidden variables of physical laws.
result Illustrates DNNMs applied to Sea Surface Height dynamics, connecting to QG model.
Recent work has shown that topological enhancements to recurrent neural networks (RNNs) can increase their expressiveness and representational capacity. Two popular enhancements are stacked RNNs, which increases the capacity for learning non-linear functions, and bidirectional processing, which exploits acausal informa…
Post-training quantization saves resources for neural networks.
problem Implementing neural networks in resource-constrained hardware.
method Generalized post-training quantization method (GPFQ) with modifications for sparsity and error analysis.
result Error decays linearly with over-parametrization, showing minor loss of accuracy.
Paper introduces ICGNs to model convex gradients.
problem Modeling convex gradients efficiently.
method Integrates Jacobian-vector product in a neural network.
result Single layer ICGN outperforms single layer ICNN in fitting.
Unified framework for studying softmax attention under large prompts.
problem Challenges in theoretical analysis of softmax attention.
method Measure-based framework for finite and infinite prompts.
result Softmax attention converges to linear attention in the large-prompt regime.
The paper analyzes SGD in high-dimensional networks, revealing new scaling limits.
problem Understanding SGD dynamics in high-dimensional networks.
method Analyzing the effective dynamics of SGD using recent work on the subject.
result A new correction term emerges at the critical scaling regime, changing the phase diagram.
Study SGD dynamics in sequence models, revealing training phases and influence of sequence length.
problem Understanding SGD in sequence models like attention networks.
method Derived closed-form population loss and analyzed SGD dynamics for SSI models.
result Two distinct training phases: escape from uninformative initialization and alignment with target subspace.
Shallow diffusion models learn hidden low-dimensional structures effectively.
problem Learning from high-dimensional signals like images and video.
method Analysis of shallow diffusion models over the Barron space of single layer neural networks.
result Shallow diffusion models can adapt to simple low-dimensional structures, overcoming the curse of dimensionality.
KAPLAN-HR models survival data without manual interactions, outperforming existing methods.
problem Survival analysis challenges with complex covariates and time-varying effects.
method Kolmogorov-Arnold Networks (KAN) for nonparametric hazard estimation.
result KAPLAN-HR matches or exceeds existing methods in clinical survival data.
Transformers can learn noisy linear systems with depth and IID data.
problem Learning noisy linear dynamical systems with transformers.
method Theoretical analysis of multi-layer and single-layer transformers with respect to L2-testing loss. result Single-layer transformers have a non-diminishing lower bound on approximation error, suggesting depth separation.
Transformers struggle to learn Markovian dynamics, showing NP-hard optimization challenges.
problem Understanding transformers' limitations in learning Markovian dynamical functions.
method Investigated through a structured ICL setup, analyzing loss landscapes and parameter optimization.
result Recovering optimal transformer parameters for Markovian functions is NP-hard.
Recently, with convolutional neural networks gaining significant achievements in many challenging machine learning fields, hand-crafted neural networks no longer satisfy our requirements as designing a network will cost a lot, and automatically generating architectures has attracted increasingly more attention and focu…
Many real-world complex systems across natural, social, and economical domains consist of manifold layers to form multiplex networks. The multiple network layers give rise to nonlinear effect for the emergent dynamics of systems. Especially, weak layers that can potentially play significant role in amplifying the vulne…
PixelCNN models can achieve state-of-the-art results on CIFAR-10 with exact likelihood computation.
problem Dequantization gap in modeling discrete data like images.
method Introducing subset flows to allow exact computation of likelihoods for discrete data.
result PixelCNN models trained with exact likelihood computation achieve state-of-the-art results on CIFAR-10.
Probabilistic bounds on neuron death in deep networks, showing depth can be increased indefinitely.
problem Understanding neuron death in deep rectifier networks and its impact on model trainability.
method Deriving upper and lower bounds on neuron death probability as a function of model hyperparameters.
result The probability of neuron death decreases as network depth increases, provided width increases proportionally.
ELM speeds up financial machine learning tasks.
problem Efficiently solving time-sensitive financial tasks with machine learning.
method Single-layer neural networks with random initialization and convex optimization.
result ELM achieves significant computational efficiency in financial applications.
Olshausen and Field (OF) proposed that neural computations in the primary visual cortex (V1) can be partially modeled by sparse dictionary learning. By minimizing the regularized representation error they derived an online algorithm, which learns Gabor-filter receptive fields from a natural image ensemble in agreement …
In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems (or, more generally, nested systems) offer a way to generate complex mappings usin…
ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.
problem Approximating ergodic dynamical systems using ESNs.
method Tikhonov least squares regression on ESNs trained on observations from an ergodic dynamical system.
result ESNs trained with Tikhonov least squares approximate the target function in the L2(μ) norm.
Biological neural network mimics CCA for multi-channel data.
problem Implementing CCA in a biologically plausible neural network.
method Derive an online CCA algorithm with local synaptic updates for multi-compartmental neurons.
result The derived neural network architecture and synaptic updates resemble cortical pyramidal neuron behavior.