Polynomial neural networks explore thresholds for maximum expressiveness.
problem Understanding the limits of polynomial neural networks' expressiveness.
method Introducing activation degree threshold to measure network expressiveness and proving its existence and upper bounds.
result Polynomial neural networks with equi-width architectures achieve the maximum expressiveness.
Weisfeiler-Leman struggles with graph isomorphism; enhanced architectures improve generalization.
problem Graph isomorphism problem and limited expressivity of 1-WL. method Augmenting 1-WL and MPNNs with subgraph information, employing margin theory, and introducing provable generalization kernels. result Increased expressivity of graph neural networks and kernels does not necessarily correlate with improved generalization performance.
ESAN improves graph neural networks by processing subgraphs.
problem Limitations of MPNNs in graph isomorphism.
method ESAN represents graphs as sets of subgraphs and processes them with equivariant architectures.
result ESAN increases the expressive power of GNNs and more expressive architectures.
Higher granularity in MoE models boosts expressivity exponentially.
problem Expressivity of Mixture-of-Experts models with varying granularity.
method Comparing models with different numbers of active experts (granularity).
result Exponential separation in network expressivity based on granularity.
Simplified NAS for GNN architectures improves efficiency and expressiveness.
problem Efficient and effective discovery of optimal GNN architectures.
method SNAG framework with a novel search space and reinforcement learning.
result SNAG framework outperforms human-designed and existing NAS methods.
We investigate graph neural networks for multi-relational data.
problem Understanding and improving graph neural networks for multi-relational data.
method Aligning Relational GCN and Compositional GCN with the Weisfeiler-Leman test to understand their expressive power and introduce a new k-RN architecture. result The k-RN architecture overcomes the expressiveness limitations of Relational GCN and Compositional GCN. Paper explores how GNNs can learn graph biconnectivity, finding ESAN is the only known expressive framework.
problem Understanding the expressive power of GNNs beyond the WL test.
method Introduces a novel class of expressivity metrics via graph biconnectivity and develops the GD-WL approach.
result GD-WL consistently outperforms prior GNN architectures in learning biconnectivity metrics.
Review of neural network expressivity and architectures.
problem Understanding neural network expressivity across different architectures.
method Comprehensive overview of approximation results for various neural network types.
result Deep neural networks offer advantages over shallow ones for specific function classes.
Unified framework explains geometric properties of CNNs.
problem Understanding why encoder-decoder CNNs perform well.
method Unified mathematical framework based on recent neural network theories.
result Encoder-decoder CNNs are related to nonlinear basis representation using combinatorial convolution frames.
This work analyzes how deep neural networks' expressiveness increases with depth and width.
problem Understanding the expressiveness of deep neural networks (DNNs) based on their Lipschitz constants.
method Leveraging random matrix theory, the study characterizes the expressiveness of DNNs by their Lipschitz constant, showing exponential and polynomial increases with depth and width, respectively.
result The expressiveness of DNNs increases exponentially with depth and polynomially with width, consistent with function approximation benefits.
New neural network architecture with height adds expressive power.
problem Expressiveness of neural networks limited by width and depth.
method Introduces height as a new hyper-parameter in neural network architecture.
result Neural networks with height achieve significantly better approximation of functions.
Stable ResNet stabilizes gradients in deep networks.
problem Gradient vanishing and exploding in deep ResNet architectures.
method Introducing Stable ResNet architectures with gradient stabilization and infinite depth expressivity.
result Stable ResNet maintains gradient stability and expressivity in deep networks.
Paper compares expressive power of GNNs, proving approximation guarantees for practical architectures.
problem Understanding the expressive power of Graph Neural Networks (GNNs).
method Theoretical framework comparing invariant and equivariant GNNs, proving approximation guarantees for practical architectures.
result Folklore Graph Neural Networks (FGNN) are the most expressive architectures for a given tensor order.
New architectures improve topological deep learning's ability to capture complex data features.
problem Current TDL architectures struggle with fundamental topological and metric invariants.
method Developed multi-cellular networks (MCN) and scalable MCN (SMCN) to enhance expressivity.
result SMCN outperforms HOMP and expressive graph methods in learning topological properties.
Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially…
New model generates realistic single-cell gene expression data.
problem Generating realistic single-cell gene expression profiles is challenging.
method scLDM, a latent diffusion model using Diffusion Transformers and linear interpolants.
result Superior performance in generating realistic single-cell gene expression data.
We find the maximum mutual information for neural networks and its key determinants.
problem Understanding the maximum mutual information in neural architectures.
method Derived closed-form expression for maximum mutual information across neural network families.
result Maximum mutual information stems from a generalized formula and is influenced by network width and statistical invariances.
It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from propagating to early layers. In this paper we propose a simple recurrent architecture, th…
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias.…
Deep polynomial neural networks measure their expressiveness by the dimension of their functional space.
problem Measuring the expressiveness of deep polynomial neural networks.
method Analyzing the algebraic variety defined by the polynomial neural network's weights and activations.
result The dimension of the algebraic variety is a precise measure of the network's expressiveness.
Graph Metanetworks process diverse neural architectures efficiently.
problem Processing diverse neural architectures efficiently.
method Builds metanetworks using graph neural networks to process graphs representing input neural networks.
result Proves GMNs are expressive and equivariant to parameter permutation symmetries.
ISP improves GNN expressivity by stratifying nodes based on graph invariants.
problem Graph Neural Networks struggle with expressivity and structural heterogeneity.
method Invariant-Stratified Propagation (ISP) using ISP-WL and ISPGNN.
result ISP achieves enhanced expressivity beyond 1-WL, with theoretical guarantees and practical improvements.
Stable unactivated neurons reduce expressiveness in ReLU networks.
problem Reducing expressiveness in ReLU neural networks due to stably unactivated neurons.
method Investigated the probability of neurons being stably unactivated in ReLU networks with symmetric weight and bias distributions.
result Proved the probability of a neuron being stably unactivated in the second hidden layer of a ReLU network.
einspace expands NAS search space to include diverse neural architectures.
problem NAS results are often limited to existing structures; new designs are rare.
method einspace uses a probabilistic context-free grammar to create a versatile search space.
result einspace discovers novel and improved architectures, including convolutions and attention.
k-hop GNNs improve GNNs' ability to identify graph properties.
problem GNNs' limitations in identifying fundamental graph properties.
method Proposes k-hop GNNs that aggregate information from a node's k-hop neighborhood.
result k-hop GNNs can identify fundamental graph properties.
Kernelised flows improve density estimation and generation with fewer parameters.
problem Limited expressiveness of flow-based models due to invertibility constraints.
method Integrates kernels into normalising flows to enhance expressiveness and efficiency.
result Kernelised flows outperform neural network-based flows in parameter efficiency and low-data scenarios.
Study bounds VAR model's circuit complexity, showing it's limited to TC^0 circuits.
problem Understanding the limitations of the Visual AutoRegressive model.
method Established circuit complexity bounds for the VAR model.
result VAR model is equivalent to a TC^0 threshold circuit with hidden dimension ≤ O(n).
Transformers model contextual relations using probabilistic measures, revealing their expressive power.
problem Lack of clear understanding of Transformer's ability to model contextual relations.
method Introduced a measure-theoretic framework connecting softmax attention and entropy-regularized optimal transport.
result Transformer architectures can approximate arbitrary contextual relations, and the choice of normalization affects how these relations are represented.
Graph-based NAS improves sample efficiency in architecture design.
problem Current NAS search spaces are static sequences, limiting expressiveness.
method Proposed graph-based search space with vertices and edges for iterative and branching decisions.
result Graph representation improves sample efficiency in architecture design.
This paper explores how enforcing equivariance constraints limits neural network expressivity and proposes compensatory model size increases.
problem The impact of enforcing equivariance constraints on the expressive power of neural networks.
method Examined 2-layer ReLU networks, analyzed boundary hyperplanes and channel vectors, and constructed upper bounds on model size required for compensation.
result Enforcing equivariance constraints reduces the expressive power of neural networks, but this can be compensated by increasing model size.
A new method synthesizes expressions from characteristics using GAN for healthcare.
problem Synthesizing expressions from given characteristics in high-dimensional space.
method Generative Adversarial Network (GAN) based selective ensemble learning.
result The proposed SE-CTES method effectively handles deterministic and stochastic patterns.
VQC-MLPNet combines quantum and classical elements for scalable quantum machine learning.
problem Challenges in expressivity, trainability, and noise resilience of VQCs.
method Hybrid architecture with a VQC generating weights for a classical MLP during training.
result Improved expressivity, trainability, and robustness compared to standalone quantum or hybrid approaches.
Study reveals Transformer's expressive power and mechanisms.
problem Understanding the approximation properties of Transformer for sequence modeling.
method Systematic study of Transformer's components and their combined effects, establishing approximation rates.
result Reveals roles of critical parameters in Transformer, such as number of layers and attention heads.
New method learns subspace affinity function for scalable and inductive clustering.
problem Scaling and inductiveness of self-expressiveness methods for high-dimensional data.
method Siamese neural network architecture for metric learning.
result Model scales to larger datasets and clusters out-of-sample data.
Unified framework for subgraph-enhanced GNNs, improving prediction accuracy and reducing computation time.
problem Limited understanding of subgraph-enhanced GNNs and their relation to the Weisfeiler-Leman hierarchy.
method Theoretical framework, theoretical expressivity results, and data-driven subgraph sampling methods.
result Data-driven subgraph-enhanced GNNs outperform non-data-driven methods in predictive performance.
SpeqNets improve graph neural networks by scaling and adapting to graph sparsity.
problem Graph neural networks struggle with permutation-equivariant functions and scalability to large graphs.
method Introducing sparsity-aware, permutation-equivariant graph networks with heuristics for graph isomorphism.
result Significantly improved predictive performance and reduced computation times compared to existing methods.
Each human genome is a 3 billion base pair set of encoding instructions. Decoding the genome using deep learning fundamentally differs from most tasks, as we do not know the full structure of the data and therefore cannot design architectures to suit it. As such, architectures that fit the structure of genomics should …
Flow++ improves flow-based models by dequantizing with variational methods and using expressive architectures.
problem Flow-based models have poor density estimation compared to autoregressive models.
method Variational dequantization, expressive affine flows, and improved architecture design.
result Flow++ is now the state-of-the-art non-autoregressive model for unconditional density estimation.
We explore efficient neural architecture search methods and show that a simple yet powerful evolutionary algorithm can discover new architectures with excellent performance. Our approach combines a novel hierarchical genetic representation scheme that imitates the modularized design pattern commonly adopted by human ex…
NAS-Bench-101 simplifies neural architecture search by creating a searchable dataset.
problem Difficulty in reproducing NAS experiments due to high computational costs.
method Created a compact, expressive search space with 423k unique architectures, trained and evaluated them on CIFAR-10, and compiled results into a dataset.
result Researchers can evaluate diverse models in milliseconds by querying the pre-computed dataset.
New approach reduces model size for Transformer architectures.
problem Large embedding dimensions limit model applicability.
method Identified low-rank bottleneck in multi-head attention.
result Reducing head size to sequence length improves model performance.
Sparse butterfly network replaces dense layers in neural networks, improving expressibility and performance.
problem Improving expressibility and performance of neural networks with dense layers.
method Replacing dense layers with a butterfly network architecture.
result The proposed architecture significantly reduces the number of weights from quadratic to nearly linear, with comparable or better performance.
Unified method for deriving ridgelet transforms for various neural network architectures.
problem Deriving closed-form expressions for ridgelet transforms in modern neural network architectures.
method Unified Fourier slice method to derive ridgelet transforms for diverse neural network types.
result Systematic method to derive ridgelet transforms for various neural network architectures.
MLP-Mixer achieves better performance through sparsity and wider architecture.
problem Understanding why MLP-Mixer outperforms conventional MLPs.
method Revealed sparseness as a key mechanism, showed effective expression as wider MLP, demonstrated quantitative similarities, and applied a guiding principle.
result MLP-Mixer's performance improvement through sparseness and wider architecture.
New framework explains normalizing flows' power and limitations.
problem Understanding the expressive power and limitations of normalizing flows.
method Theoretical framework for well-conditioned coupling-based normalizing flows and volume-preserving flows.
result RealNVP is distributionally universal, but volume-preserving flows are not.
Transformers struggle to approximate smooth functions, relying on piecewise constant approximations.
problem Understanding the expressivity of Transformers for function approximation.
method Theoretical analysis and experimental validation of Transformer's ability to approximate smooth functions.
result Transformers cannot reliably approximate smooth functions, relying on piecewise constant approximations.
This work explores the relationship between expressivity and generalization in GNNs.
problem Understanding the trade-off between expressivity and generalization in GNNs.
method Introducing a novel framework that connects GNN generalization to the variance in graph structures they can capture.
result Theoretical findings align with empirical results, offering a deeper understanding of how expressivity enhances GNN generalization.
This paper examines how skip connections prevent rank collapse in sequence models.
problem Rank collapse in sequence models, leading to reduced expressivity and training instabilities.
method Analytical and ablation studies of lambda-skip connections in SSMs.
result A sufficient condition to prevent rank collapse across various architectures.