S-GAI initializes MLPs using spectral geometry from data, improving performance.
problem Lack of guidance on initial weights encoding data geometry.
method S-GAI uses SVD to estimate spectral class geometry, initializing MLPs from training data.
result S-GAI-initialized MLPs start from a more informative hidden state and achieve comparable accuracy.
Temporal Functional Circuits explain KAN forecasts with interpretable edge functions.
problem Lack of mechanistic explanations in KAN forecasting.
method Transform KAN edge functions into faithful, temporally grounded explanations using a gated residual KAN.
result Gated KAN achieves lower MSE than linear-only models on regime-switching signals.
Introduces Causal Energy Minimization to understand Transformer layers.
problem Empirical parameterization of Transformer blocks remains largely unexplored.
method Causal Energy Minimization framework that recasts Transformer layers as optimization steps on conditional energy functions.
result Identifies design space for Transformer layers including weight sharing and energy-based interpretations.
Bilinear MLPs offer a new way to interpret deep learning models without complex nonlinearities.
problem Lack of mechanistic understanding in how MLPs compute.
method Introduced bilinear MLPs without element-wise nonlinearities, analyzed their weights using tensor and eigendecomposition.
result Bilinear MLPs provide interpretable weight structures and enable adversarial attacks and overfitting analysis.
Closed-form polynomial approximations replace MLPs in transformers, enabling new interpretability methods.
problem Replacing MLPs with polynomial approximations for transformer models.
method Theoretical derivation of closed-form least-squares approximations of MLPs and GLUs using polynomial functions.
result Polynomial approximations explain over 95% of MLP and GLU outputs' variance, enabling interpretability.
Classifier-based AI safety gates fail in self-improvement, even with advanced verification methods.
problem Maintaining reliable oversight of AI systems as they improve over iterations.
method Comprehensive empirical testing on neural controllers and MuJoCo benchmarks, using various classifiers and verification methods.
result Classifier-based safety gates fail in maintaining reliable oversight, even with advanced verification methods.
This paper presents a new family of backpropagation-free neural architectures, Gated Linear Networks (GLNs). What distinguishes GLNs from contemporary neural networks is the distributed and local nature of their credit assignment mechanism; each neuron directly predicts the target, forgoing the ability to learn feature…
In this paper we propose solving localized multiple kernel learning (LMKL) using LMKL-Net, a feedforward deep neural network. In contrast to previous works, as a learning principle we propose {\em parameterizing} both the gating function for learning kernel combination weights and the multiclass classifier in LMKL usin…
Deep Q-learning is investigated as an end-to-end solution to estimate the optimal strategies for acting on time series input. Experiments are conducted on two idealized trading games. 1) Univariate: the only input is a wave-like price time series, and 2) Bivariate: the input includes a random stepwise price time series…
Kolmogorov-Arnold Networks enable ultrafast online learning with fixed-point quantization.
problem Efficient online learning for high-frequency systems with strict memory constraints.
method Fixed-point online training on FPGAs exploiting B-spline locality in KANs.
result Kolmogorov-Arnold Networks are more efficient and expressive than MLPs for low-latency tasks.
N-BEATS-MOE improves time series forecasting by adapting to series characteristics.
problem Forecasting heterogeneous time series with varying characteristics.
method Mixture-of-Experts layer with dynamic block weighting.
result Consistent improvements across 12 benchmark datasets, especially for heterogeneous series.
Transformers without skip connections collapse token representations to a single direction.
problem Rapid convergence of token representations to a single direction in self-attention-only Transformers.
method Analysis of layer normalization, residual connections, and multi-head attention mechanisms.
result Residual connections prevent rank collapse in real Transformers, while MLPs generate new feature directions.
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.
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.
Interpolated-MLPs control inductive bias for better performance in low-compute tasks.
problem Low-compute performance gap between MLPs and CNNs.
method Introduced Interpolated MLP (I-MLP) approach to control inductive bias incrementally.
result Continuous logarithmic relationship between inductive bias and performance in low-compute tasks.
Hierarchical pretraining with slow-fast ODEs
problem Causal self-attention vs. slow-fast ODEs
method Instantiating fast-slow ODE formalism as a concrete neural network
result Equilibrium manifold x=φ(y) is exactly the master-equation (ME) stationary distribution ES-MLP combines Graph-MLP with edge splitting for node classification on both homophilic and heterophilic graphs.
problem Node classification on graphs with mixed homophilic and heterophilic properties.
method Combines Graph-MLP with edge splitting mechanism from ES-GNN to learn two adjacency matrices based on relevant and irrelevant feature pairs.
result ES-MLP achieves performance comparable to homophilic and heterophilic models without using edges during inference.
A new GNM model outperforms MLP for tabular data.
problem Learning with tabular data.
method Proposes Graph Neural Machine (GNM) replacing MLP's graph representation with a nearly complete graph and using synchronous message passing.
result GNM outperforms MLP in classification and regression tasks.
This study compares GNNs and GA-MLPs, finding GA-MLPs can distinguish graphs but not count walks.
problem Comparing expressive power and graph isomorphism testing capabilities of GNNs and GA-MLPs.
method GA-MLPs augment node features with multi-hop operators and apply MLPs node-wise; GNNs are compared as a baseline.
result GA-MLPs can distinguish almost all non-isomorphic graphs but cannot count attributed walks, unlike GNNs.
KANs replace fixed MLP weights with learnable edge functions, improving accuracy and interpretability.
problem Lack of interpretability and scalability in MLPs.
method KANs use learnable activation functions on edges instead of fixed weights, replacing weights with spline functions.
result KANs outperform MLPs in accuracy and interpretability with smaller models.
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…
Revisits neural collaborative filtering vs. matrix factorization, showing dot product superiority.
problem Comparing neural collaborative filtering to matrix factorization in recommendation systems.
method Revisited experiments using MLPs as similarity functions, comparing dot product to MLP outputs.
result Simple dot product outperforms MLP-based learned similarities in practical settings.
Study uses MLP models to predict large-cap US stocks, finding 2-3 hidden layers more flexible.
problem Predicting asset prices for large-cap US stocks.
method Applied MLP models with dynamic structure to factor models, focusing on firm characteristics.
result MLP models with 2-3 hidden layers more flexible in modeling factors, better for downside risk control.
SpArX creates faithful explanations of neural networks' decision-making.
problem Challenges in explaining neural networks' decisions.
method Sparsifies MLPs while maintaining structure, then translates into QAFs for argumentative explanations.
result SpArX provides more faithful explanations than existing methods.
This paper proposes a new approach to Transformers by integrating hierarchical associative memory with MetaFormers.
problem Theoretical framework for Transformers and MLP-Mixers remains underdeveloped.
method Integrating hierarchical associative memory with MetaFormers to create a parallelized MLP-Mixer.
result Symmetry-breaking effects improve the performance of the MLP-Mixer in image recognition tasks.
Designs an MLP from LDA for multi-Gaussian class classification.
problem Classifying inputs with multiple Gaussian distributions.
method Interprets MLP as generalized LDA, using LDAs for half-space partitioning, neurons for subspace isolation, and merging for class-wise representation.
result Automatic feedforward design for MLP architecture and weights.
The paper studies 4-qubit Clifford states and their properties.
problem Understanding the set and properties of 4-qubit Clifford states.
method Analyzing the 293760 4-qubit Clifford states, splitting them into 18 groups, and studying the action of CNOT gates and local gates.
result There are 293760 4-qubit Clifford states with specific entanglement entropies, and any pair can be connected with local gates and at most 3 CNOT gates.
m-arcsinh improves SVM and MLP reliability and speed in scikit-learn.
problem Improving SVM and MLP reliability and speed in scikit-learn.
method Modified arcsinh function for kernel and activation in SVM and MLP.
result Competitive classification performance and reliability of SVM and MLP with m-arcsinh.
Improved logistic MoE with sigmoid gate shows better sample efficiency.
problem Improving sample efficiency in logistic MoE models.
method Comprehensive analysis of multinomial logistic MoE with modified sigmoid gate, incorporating temperature parameter and using Euclidean score.
result The sigmoid gate leads to lower sample complexity than softmax gate for both parameter and expert estimation.
New method prepares 3-qubit states using local gates and controlled-Z gates.
problem Preparation of 3-qubit states using quantum gates.
method Uses Ry(θ) gates and controlled-Z gates, with an optimal number of controlled-Z gates. result Optimal number of controlled-Z gates for preparing 3-qubit states is four. This study compares MLPs and KANs in low-data regimes, finding MLPs with personalized activation functions outperform KANs.
problem Comparing MLPs and KANs in low-data regimes.
method Introduced an effective technique for designing MLPs with unique, parameterized activation functions for each neuron.
result MLPs with personalized activation functions achieve significantly higher predictive accuracy with only a modest increase in parameters, especially in low-data regimes.
Sigmoid gating is more sample efficient than softmax in mixture of experts.
problem Softmax gating leads to unnecessary competition among experts, causing representation collapse.
method Theoretical analysis of a regression framework with mixture of experts, identifying identifiability conditions and convergence rates.
result Sigmoid gating requires fewer samples to achieve the same expert estimation error as softmax gating.
In quantum computation, series of quantum gates have to be arranged in a predefined sequence that led to a quantum circuit in order to solve a particular problem. What if the sequence of quantum gates is known but both the problem to be solved and the outcome of the so defined quantum circuit remain in the shadow? This…
New approach finds minimum width for deep, narrow MLPs.
problem Finding the minimum width for deep, narrow MLPs to approximate continuous functions.
method Proposes a framework to simplify finding minimum width into determining a geometrical function w(dx,dy) based on input and output dimensions. result Proves that w(dx,dy) equals the optimal minimum width for deep, narrow MLPs to achieve universality. Investigates transfer learning in spatial statistics.
problem Applying transfer learning to spatial statistics.
method Simple MLP models for spatial data.
result Potential of transfer learning in spatial statistics.
Hybrid model improves wind speed prediction accuracy using MLP and WOA.
problem Improving wind speed prediction accuracy for renewable energy control.
method Combining MLP with Whale Optimization Algorithm (WOA) for data preprocessing and model optimization.
result The hybrid MLP-WOA model outperformed standalone MLP model in wind speed prediction accuracy.
ResNets promote smoother interpolations than MLPs, enhancing generalization.
problem Understanding the difference in smoothness between ResNets and MLPs.
method Neural Tangent Kernel (NTK) analysis during gradient descent training.
result ResNet's NTK results in smoother interpolations than MLPs.
Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing m…
Topo-MLP learns network representations without message passing.
problem Lack of efficient higher-order network modeling methods.
method Proposes Topo-MLP, a simplicial neural network algorithm using MLP and HONC loss.
result Demonstrates improved robustness and efficiency in representation learning.
Gated attention improves model curvature, enhancing performance on nonlinear tasks.
problem Understanding the geometric implications of gating in attention mechanisms.
method Modeling attention outputs as Gaussian distributions and analyzing Fisher--Rao geometry.
result Gated attention enables non-flat geometries, including positively curved manifolds.
Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant M…
MLPs can approximate any function in context, challenging the importance of in-context universality.
problem Understanding why transformers are more effective than classical models.
method Proved MLPs with trainable activation functions are universal in context.
result Transformer success is likely due to factors other than in-context universality.
Gated attention improves performance by using a hierarchical mixture of experts.
problem Improving performance of self-attention mechanisms in Transformers.
method Rigorously show that gated attention can be modeled as a hierarchical mixture of experts, providing a theoretical justification for its benefits.
result Gated attention is more sample-efficient than multi-head self-attention, requiring fewer data points to achieve the same estimation error.
Given the success of the gated recurrent unit, a natural question is whether all the gates of the long short-term memory (LSTM) network are necessary. Previous research has shown that the forget gate is one of the most important gates in the LSTM. Here we show that a forget-gate-only version of the LSTM with chrono-ini…
Improved HMoE models using Laplace gating function enhance expert specialization and performance.
problem Improving performance of hierarchical mixture of experts models.
method Used Laplace gating function instead of Softmax in hierarchical mixture of experts models.
result Laplace gating function accelerates expert convergence and enhances specialization.
Transformers show better in-context learning resilience under distribution shifts than simple MLPs.
problem Understanding in-context learning under varying distribution shifts.
method Comparing transformers and set-based MLPs on linear regression tasks.
result Transformers better emulate OLS performance and exhibit better resilience to mild distribution shifts.
Transformers with MLP heads outperform linear baselines in in-context learning.
problem Understanding in-context learning in Transformers with nonlinear MLP heads.
method Analyzing a model with two-layer MLPs trained via gradient steps and fully optimized, under high-dimensional asymptotics.
result Nonlinear MLPs enhance ICL performance, particularly on nonlinear tasks.
The paper evaluates three variants of the Gated Recurrent Unit (GRU) in recurrent neural networks (RNN) by reducing parameters in the update and reset gates. We evaluate the three variant GRU models on MNIST and IMDB datasets and show that these GRU-RNN variant models perform as well as the original GRU RNN model while…