New approach improves linear-time attention for language models.
problem Challenges of quadratic attention in long-sequence modelling, especially for discrete data.
method Reinterpreting linear attention through latent probabilistic graphical models, introducing asymmetric structure and recurrent parameterisation.
result Our model achieves competitive performance and outperforms existing linear attention variants on language modelling benchmarks.
Linear attention in Transformers can be interpreted as dynamic VAR models.
problem Misalignment between Transformers and autoregressive forecasting objectives.
method Interpreting linear attention as VAR, rearranging MLP, attention, and flow.
result SAMoVAR improves performance, interpretability, and efficiency.
A method to automatically choose feature dimensions in linear attention for better approximation quality.
problem Choosing the feature dimension in linear attention to balance quality and efficiency.
method Statistical degrees of freedom for determining feature dimension, layer-wise training strategy.
result Our method achieves smaller approximation error compared to fixed dimensions and improves model performance.
Multi-head attention outperforms single-head in in-context linear regression tasks.
problem Comparing performance of transformer with single-/multi-head attention in in-context learning.
method Theoretical analysis of performance of transformers with different attention mechanisms in linear regression tasks.
result Multi-head attention with a substantial embedding dimension outperforms single-head attention in in-context linear regression tasks.
ZeroS improves Transformers by adding negative weights, matching or beating softmax attention.
problem Limited performance of linear attention methods, especially in long context sequences.
method Proposes Zero-Sum Linear Attention (ZeroS) that removes the zero-order term and reweights zero-sum softmax residuals.
result ZeroS matches or exceeds standard softmax attention across various benchmarks, theoretically expanding representable functions.
LoLCATs improves linearized LLM quality with less memory and compute.
problem Linearizing large language models (LLMs) often degrades model quality and requires expensive training.
method Two-step method: attention transfer and low-rank adaptation.
result Significant improvement in linearizing quality with 20+ points on 5-shot MMLU.
The softmax content-based attention mechanism has proven to be very beneficial in many applications of recurrent neural networks. Nevertheless it suffers from two major computational limitations. First, its computations for an attention lookup scale linearly in the size of the attended sequence. Second, it does not enc…
Transformers with linear space and time complexity for accurate attention estimation.
problem Efficiently estimating attention in large-scale tasks without relying on priors.
method Performers use Fast Attention Via positive Orthogonal Random features (FAVOR+) for linear approximation of softmax attention.
result Performers achieve competitive results on various tasks, demonstrating the effectiveness of their attention-learning approach.
Unified framework for non-linear attention using modern Hopfield networks.
problem Improving transformer model's understanding of complex relationships and efficiency.
method Proposes an energy functional based on Modern Hopfield Networks (MNH) to unify linear and non-linear attention mechanisms.
result Context wells encapsulate contextual relationships among tokens, offering a richer representation of non-linear data.
Transformer attention layers solve single-location regression tasks.
problem Understanding token-wise sparsity and internal linear representations in attention-based models.
method Introduce single-location regression task and a simplified predictor based on self-attention layers.
result Transformer attention layers are asymptotically Bayes optimal and can learn underlying structures effectively.
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.
Paper investigates Lipschitz constants of self-attention modules in neural networks.
problem Lipschitz constants of self-attention modules in neural networks.
method Proved standard dot-product self-attention is not Lipschitz for unbounded input domain. Proposed L2 self-attention that is Lipschitz. Derived upper bound on L2 self-attention's Lipschitz constant.
result Proved standard self-attention is not Lipschitz for unbounded input domain and proposed an alternative L2 self-attention that is Lipschitz.
Linformer reduces transformer complexity to linear, improving efficiency.
problem High cost of training and deploying large transformer models for long sequences.
method Approximates self-attention with low-rank matrix, proposing Linformer with O(n) complexity. result Linformer performs similarly to standard transformers but is more memory- and time-efficient.
Paper connects MoE and self-attention, proposing active-attention.
problem Improving efficiency and performance of self-attention mechanisms.
method Established connection between MoE and self-attention, analyzed quadratic gating functions, proposed active-attention mechanism.
result Active-attention outperforms standard self-attention in various tasks.
We demystify attention patterns in multi-head softmax models for linear data.
problem Understanding the training dynamics and emergent patterns in multi-head softmax attention models.
method Extensive empirical experiments and rigorous theoretical analysis.
result Multi-head softmax attention models approximate a debiased gradient descent predictor, outperforming single-head attention and achieving near-Bayesian optimality.
LUNA improves linear attention for long sequences without sacrificing accuracy.
problem Quadratic computational cost of softmax attention in long-sequence domains.
method LUNA learns a learnable kernel feature map to reduce attention cost to linear while maintaining accuracy.
result LUNA achieves state-of-the-art performance on the LRA and excels at post-hoc conversion.
Linearized attention fails to converge to NTK limit even at large widths.
problem Understanding the convergence of attention mechanisms to the kernel regime.
method Analyzes linearized attention and its relationship to the NTK limit, considering practical widths and conditions.
result Linearized attention does not converge to its NTK limit at any practical width, revealing a fundamental trade-off.
This work analyzes self-attention matrices using random matrix theory.
problem Understanding the theoretical behavior of self-attention layers in neural networks.
method Asymptotic spectral analysis of the attention matrix, Gaussian equivalence, and linearization.
result The singular value distribution of the attention matrix is asymptotically characterized by a linear model.
AReLU uses attention-based rectification to improve neural network performance.
problem Improving neural network performance through better activation functions.
method Integrates attention mechanism with rectified linear unit (ReLU) to learn and scale feature maps.
result AReLU significantly boosts performance of most network architectures with minimal changes.
Transformers become faster by linearizing self-attention.
problem Quadratic complexity of transformers makes them slow for long sequences.
method Expressed self-attention as a linear dot-product and used matrix product associativity to reduce complexity.
result Linear transformers are up to 4000x faster on long sequences.
A-MMSE uses attention to learn efficient OFDM channel estimation.
problem Accurate OFDM channel estimation requires second-order statistics, which are hard to obtain in practice.
method A-MMSE is a model-based DNN framework that learns linear MMSE filters via Attention Transformer, reducing inference complexity.
result A-MMSE outperforms other methods in normalized MSE across various SNR conditions.
FEM improves attention mechanisms by applying value-driven log-linear tilts.
problem Standard attention mechanisms read via convex average, limiting channel-wise selection.
method Free Energy Mixer (FEM) applies a value-driven, per-channel log-linear tilt to a fast prior over indices.
result FEM outperforms strong baselines on NLP, vision, and time-series tasks.
Skeinformer accelerates self-attention for long sequences with linear complexity.
problem Efficiency of Transformer models in processing long sequences.
method Matrix sketching and column sampling to reduce quadratic complexity to linear.
result Skeinformer outperforms alternatives with smaller time/space footprint.
This paper analyzes the interpolation error of nonlinear Attention compared to linear regression.
problem Understanding the interpolation error of nonlinear Attention in high-dimensional settings.
method Derives explicit expressions for mean-squared interpolation error using signal-plus-noise model and random matrix theory.
result Nonlinear Attention generally incurs a larger interpolation error than linear regression, but this gap can be reversed with structured signals.
Linear Transformer Block combines MLP and linear attention for near-optimal ICL in linear regression.
problem Achieving near-optimal in-context learning (ICL) risk for linear regression with a Gaussian prior.
method Combines linear attention and MLP components in a Linear Transformer Block (LTB). Establishes correspondence with one-step gradient descent estimators (GDext−β). result LTB achieves nearly Bayes optimal ICL risk for linear regression with a Gaussian prior.
AGBoost uses attention weights to improve GBM for regression problems.
problem Improving gradient boosting machine for regression tasks.
method Attention-based modification of GBM with trainable attention weights.
result AGBoost achieves better performance on regression datasets.
Bayesian theory explains abrupt emergence of copy subcircuit in attention.
problem Understanding the abrupt emergence of the copy subcircuit in attention during training.
method Deriving a closed-form posterior over the attention matrix and reducing it to a low-dimensional order parameter space.
result Derive a phase transition in the amount of training data.
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
Study algebraic invariants from lightning self-attention models.
problem Understanding polynomial coefficients of self-attention mechanisms.
method Identify algebraic invariants using polynomial coefficients and coordinate geometry.
result Found linear and nonlinear families of algebraic invariants.
LNUCB-TA improves MAB performance by dynamically adjusting exploration rates and recognizing spatiotemporal patterns.
problem Suboptimal performance in environments with rapidly changing reward structures and static exploration rates.
method Hybrid model combining linear and nonlinear estimation, with adaptive k-NN for temporal attention.
result Significantly outperforms state-of-the-art algorithms in cumulative and mean reward, convergence, and robustness.
A new LSTM architecture improves time series forecasting efficiency.
problem Efficiency and accuracy in time series forecasting using linear models.
method Attention-free LSTM architecture for time series prediction.
result Improved prediction capacity and efficiency compared to LSTM.
KATA improves associative recall by optimizing feature maps derived from nonnegative attention weights.
problem Linear attention's poor performance on associative recall tasks.
method Formulates attention recall as a spherical-packing problem and introduces Kernelized Linear Attention Activations (KATA).
result KATA features offer a favorable capacity-interference tradeoff, enabling efficient associative recall.
Self-attention optimizers converge to optimal weights, revealing bias patterns.
problem Understanding the implicit bias in self-attention mechanisms.
method Analysis of gradient-based optimization in self-attention layers.
result Adaptive step-size strategies can accelerate convergence to optimal weights.
Unified framework for sequence models using test-time regression.
problem Designing efficient sequence models with associative memory.
method Formalizing associative recall as regression over input tokens, deriving various sequence models.
result Clarifies the effectiveness of query-key normalization in softmax attention and offers new generalizations.
Bidirectional attention is shown to be equivalent to a continuous bag of words model with mixture-of-experts.
problem Understanding the statistical underpinnings of bidirectional attention.
method Exploring bidirectional attention as a mixture-of-experts model and reparameterizing it.
result Bidirectional attention can be viewed as a continuous bag of words model with mixture-of-experts weights.
New framework shows cross-attention improves multi-modal in-context learning.
problem Understanding multi-modal in-context learning in neural networks.
method Mathematical framework and linearized cross-attention mechanism.
result Cross-attention mechanism is provably optimal for multi-modal in-context learning.
Adapts attention to supervised learning for personalized predictions.
problem Personalized predictions for each data point with model simplicity.
method Local model fitting with attention weighting for tabular data.
result Attention weighting improves predictive performance and preserves interpretability.
Neural networks using transformer-based architectures have recently demonstrated great power and flexibility in modeling sequences of many types. One of the core components of transformer networks is the attention layer, which allows contextual information to be exchanged among sequence elements. While many of the prev…
Paper studies how few pretraining tasks are needed for a linear model to solve new tasks.
problem How many pretraining tasks are needed for a linear model to solve new tasks?
method Pretrained a linear attention model for linear regression with a Gaussian prior.
result Effective pretraining requires a small number of independent tasks, and the model closely matches Bayes optimal.
The Linear Attention Recurrent Neural Network (LARNN) is a recurrent attention module derived from the Long Short-Term Memory (LSTM) cell and ideas from the consciousness Recurrent Neural Network (RNN). Yes, it LARNNs. The LARNN uses attention on its past cell state values for a limited window size k. The formulas ar…
WildCat efficiently compresses neural network attention mechanisms.
problem Expensive quadratic runtime of attention mechanisms in neural networks.
method Uses a weighted coreset with a fast subsampling algorithm to approximate attention with near-linear time complexity.
result Approximates exact attention with super-polynomial error decay and near-linear runtime.
This study examines how sequential correlations affect in-context learning in sequence models.
problem Understanding how in-context learning works with sequentially correlated data.
method Extended linear regression model to sequentially correlated data, tested on transformer architectures.
result Sequential correlations alter the effective context length and attention architecture effectiveness.
Paper proposes linear transformers for efficient in-context learning without context length limitations.
problem Quadratic complexity of softmax transformers limits data processing speed.
method Investigates linear transformers under domain generalization, showing they learn mappings from context distributions to response functions.
result Linear transformers achieve in-context learning with a linear complexity in context length, offering a dimension-independent convergence rate.
Single-head attention approximates any function under various norms.
problem Universal approximation of functions using attention mechanisms.
method Interpreting attention as partitioning and summing linear transformations.
result Single-head attention can approximate any continuous function under L∞-norm and Lebesgue integrable functions under Lp-norm. Attention mechanism learns to focus on sparse tokens efficiently.
problem Detecting weak, rare, and sparsely located features in long sequences.
method Theoretical analysis and training of a single-layer attention classifier in a sparse-token classification model.
result A single-layer attention classifier can achieve vanishing test error with logarithmic signal strength growth, unlike linear classifiers requiring linear growth.
The study provides precise asymptotic theory for in-context learning by Transformers.
problem Understanding the sample complexity, pretraining task diversity, and context length for successful in-context learning.
method An exactly solvable model of linear regression task by linear attention, deriving sharp asymptotics.
result Double-descent learning curve with increasing pretraining examples, phase transition between low and high task diversity regimes.
Models use embeddings and attention for better claim severity prediction.
problem Improving predictive modeling of claim severity with categorical data.
method Developed neural networks and attention-based architectures with embeddings.
result Attention-based models enhance predictive performance with contextual augmentation.
Random forests with attention and self-attention improve regression performance.
problem Improving regression model performance on various datasets.
method Proposes new models using attention and self-attention mechanisms to solve regression problems.
result The models improve model performance on many datasets.