Gradient descent converges geometrically to optimal self-attention parameters.
problem Training softmax self-attention layers for linear regression.
method Structure-aware gradient descent with preconditioner and regularizer.
result Gradient descent converges geometrically to global minima.
Softmax attention approximates complex functions and subsumes many known universal approximators.
problem Universal approximation of continuous sequence-to-sequence functions.
method Interpolation-based analysis of attention's internal mechanism, showing its ability to approximate ReLU functions.
result Softmax attention is a universal approximator for continuous sequence-to-sequence functions.
Unified framework for critical scaling of inverse temperature in self-attention.
problem Conflicting inverse-temperature laws for long-context self-attention.
method Counting gaps and defining an upper-tail accumulation scale.
result Critical inverse-temperature scale determined by gap-counting function.
Quaternion self-attention reduces computational cost and improves performance.
problem Existing quaternion self-attention increases computational cost and diverges attention distributions.
method Proposes a shared-score quaternion self-attention mechanism.
result Reduces score-computation multiplications by 75% and softmax operations from four to one.
Transformers learn to perform logistic regression in-context.
problem Understanding how transformers learn to perform specific tasks in-context.
method Constructed multi-layer transformers that perform in-context logistic regression through normalized gradient descent.
result Transformers can be trained to perform in-context logistic regression effectively.
Kernel PCA explains self-attention mechanisms in deep learning models.
problem Understanding and explaining self-attention mechanisms in deep learning models.
method Deriving self-attention from kernel principal component analysis (kernel PCA).
result RPC-Attention, a robust attention mechanism, outperforms softmax attention in various tasks.
Gradient flow in softmax models tends to produce low-entropy outputs.
problem Understanding the training dynamics of softmax-based models.
method Analysis of gradient flow dynamics in the value-softmax model.
result Gradient flow drives optimization towards low-entropy solutions.
New attention model removes softmax, improving sequence length bias.
problem Softmax attention's limitations and sequence length bias.
method Replaces softmax with normalization in self-attention.
result Normalization leads to more robust and bias-free attention.
Skyformer uses Gaussian kernel and Nyström method to speed up self-attention in transformers.
problem High computational cost of self-attention in transformers.
method Replaces softmax with Gaussian kernel and applies Nyström method for matrix approximation.
result Skyformer achieves comparable or better performance with fewer computation resources.
OSA overcomes instability in skipless Transformers.
problem Instability in skipless Transformers using Softmax Self-Attention.
method OSA parametrizes attention matrix to be orthogonal via skew-symmetric matrix exponential.
result OSA allows for training non-causal Transformers without skip connections and normalisation layers.
Quantum self-attention boosts automated market maker performance in crypto trading.
problem Improving automated market maker rebalancing in crypto trading.
method Quantum Adaptive Self-Attention (QASA) using variational quantum circuits and softmax attention.
result QASA-Sequence variant achieves best single-model risk-adjusted performance in crypto trading.
A new perspective on self-attention models using MLPs.
problem Improving sequence modeling with self-attention mechanisms.
method Introducing HyperMLP and HyperGLU, which use dynamic two-layer MLPs with reverse-offset layout.
result HyperMLP/HyperGLU consistently outperform softmax-attention baselines.
This work characterizes benign overfitting in Vision Transformers.
problem Understanding generalization of Vision Transformers when trained to overfit.
method Gradient descent on a data distribution model, focusing on self-attention layer and softmax.
result Established a condition to distinguish between small and large test errors based on signal-to-noise ratio.
Transformers can interpolate finite input sequences exactly.
problem Interpolating finite input sequences of arbitrary lengths.
method Constructing a transformer with alternating feed-forward and self-attention layers, and low-rank parameter matrices.
result Exact interpolation of datasets of finite input sequences in R^d with corresponding output sequences of smaller or equal length.
Develops a mean-field theory for multi-head self-attention under cross-entropy training.
problem Mean-field analysis of multi-head self-attention under cross-entropy training.
method Mean-field theory for a simplified single-layer causal multi-head self-attention model.
result Proves a static finite-head approximation bound for the optimal risk.
Paper proposes Sinkformers for Transformers with doubly stochastic attention.
problem Improving Transformer models' accuracy in vision and natural language processing.
method Using Sinkhorn's algorithm to make attention matrices doubly stochastic instead of SoftMax normalization.
result Sinkformers enhance model accuracy in vision and natural language processing tasks.
New RFs reduce kernel approximation variance and improve Transformer performance.
problem Efficient approximation of Gaussian and softmax kernels for kernel methods and Transformers.
method Parameterized, positive, non-trigonometric RFs optimized for variance reduction.
result Significant variance reduction in practice, outperforming previous methods.
Transformers can approximate Kalman Filtering in linear systems with small error.
problem Approximating Kalman Filtering using Transformers for linear dynamical systems.
method Two-step reduction: 1) Softmax self-attention block approximates Nadaraya-Watson kernel smoothing, 2) This estimator approximates Kalman Filter.
result Constructs a Transformer that implements the Kalman Filter with small additive error, uniformly bounded in time.
Study on how attention in prompt-tuning affects large language models.
problem Limited theoretical understanding of prompt-tuning and attention in LLMs.
method Exploration of prompt-tuning for one-layer attention architectures, contextual mixture-models, and self-contained prompt-attention model.
result Softmax-prompt-attention is more expressive than self-attention and linear-prompt-attention under contextual data model.
The study explores how Transformers predict the next token in a sequence.
problem Understanding the mechanism behind Transformers' autoregressive learning ability.
method Exploring the approximation ability of Transformers for next-token prediction through specific instances and a causal kernel descent method.
result Transformer models can learn context-dependent functions f for next-token prediction based on past and current observations. GSA-Nets apply group equivariance to self-attention for vision tasks.
problem Improving self-attention networks for vision tasks.
method Define group-equivariant positional encodings.
result GSA-Nets outperform non-equivariant self-attention networks on vision benchmarks.
Transformer models align words through attention weights, closely approximating Optimal Transport.
problem Understanding the internal mechanism of transformer models in language processing.
method Empirical evidence and theoretical analysis of attention weights and their relation to Optimal Transport.
result Transformer models can simulate gradient descent on the dual of entropy-regularized OT problem, providing a theoretical foundation for token alignment.
Self-attention prefers sparse functions of input sequences, reducing sample complexity.
problem Understanding the inductive biases of self-attention in modeling long-range dependencies.
method Theoretical analysis and synthetic experiments to probe sample complexity of learning sparse functions with Transformers.
result Bounded-norm Transformer networks can represent sparse functions of the input sequence with logarithmic sample complexity.
Self-attention models benefit equally from width and depth, but beyond a certain point, depth becomes less efficient.
problem Understanding the optimal balance between depth and width in self-attention models.
method Theoretical predictions and empirical ablations on networks of varying depths and widths.
result An optimal width of 30K is recommended for a 1-Trillion parameter network, marking a significant width for self-attention models.
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.
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.
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.
Softmax is an output activation function for modeling categorical probability distributions in many applications of deep learning. However, a recent study revealed that softmax can be a bottleneck of representational capacity of neural networks in language modeling (the softmax bottleneck). In this paper, we propose an…
The key to a Transformer model is the self-attention mechanism, which allows the model to analyze an entire sequence in a computationally efficient manner. Recent work has suggested the possibility that general attention mechanisms used by RNNs could be replaced by active-memory mechanisms. In this work, we evaluate wh…
Self attention mechanisms have become a key building block in many state-of-the-art language understanding models. In this paper, we show that the self attention operator can be formulated in terms of 1x1 convolution operations. Following this observation, we propose several novel operators: First, we introduce a 2D ve…
Proposes a faster Transformer decoding method by truncating target-side self-attention windows.
problem Efficiency in Transformer decoding with minimal BLEU score loss.
method N-gram assumption to truncate target-side self-attention windows.
result N-gram masked self-attention model maintains BLEU score for N values from 4 to 8. The computational cost of training with softmax cross entropy loss grows linearly with the number of classes. For the settings where a large number of classes are involved, a common method to speed up training is to sample a subset of classes and utilize an estimate of the loss gradient based on these classes, known as…
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.
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.
Recent studies identified that sequential Recommendation is improved by the attention mechanism. By following this development, we propose Relation-Aware Kernelized Self-Attention (RKSA) adopting a self-attention mechanism of the Transformer with augmentation of a probabilistic model. The original self-attention of Tra…
TaLK Convolutions improve sequence modeling efficiency.
problem Efficiently modeling sequences with limited time complexity.
method Adaptive convolution operation that learns kernel size.
result Time complexity reduced to O(n), making sequence encoding linear. Revises logistic-softmax likelihood for Bayesian meta-learning in few-shot classification.
problem Inherent uncertainty in logistic-softmax leads to suboptimal performance in meta-learning.
method Redesigns logistic-softmax likelihood with a temperature parameter for better control of prior confidence.
result Achieves well-calibrated uncertainty estimates and comparable/superior performance on benchmark datasets.
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.
Paper introduces Balanced Meta-Softmax for better long-tailed visual recognition.
problem Long-tailed distribution mismatch between training and testing data.
method Balanced Meta-Softmax, an unbiased extension of Softmax, using a Meta Sampler.
result Balanced Meta-Softmax outperforms state-of-the-art solutions on visual recognition and instance segmentation.
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.
Paper introduces hierarchical softmax for global hierarchical classification tasks.
problem Improving classification accuracy in tasks with class hierarchies.
method Global hierarchical neural networks using hierarchical softmax.
result Hierarchical softmax outperforms regular softmax in multiple datasets.
Typically, Softmax is used in the final layer of a neural network to get a probability distribution for output classes. But the main problem with Softmax is that it is computationally expensive for large scale data sets with large number of possible outputs. To approximate class probability efficiently on such large sc…
Binary testing for softmax models requires many samples, similar to leverage score models.
problem Binary hypothesis testing for softmax models and leverage score models.
method Analyzing sample complexity and drawing analogies between models.
result Sample complexity is asymptotically \(O(ε^{-2})\), where \(ε\) is the distance between model parameters.
MCSAE improves speaker embedding by focusing on both high- and low-level features.
problem Reduced effect of low-level features in speaker embedding encoding.
method Masked cross self-attentive encoding using ResNet with multi-layer aggregation and random masking regularization.
result Improved speaker embedding with equal error rate of 2.63% and minimum detection cost function of 0.1453.
SANST uses self-attentive networks with spatial and temporal embeddings for better POI recommendations.
problem Next point-of-interest (POI) recommendation for users based on their history.
method SANST incorporates spatio-temporal patterns into self-attentive networks.
result SANST outperforms state-of-the-art models by up to 13.65% in nDCG@10.
Transformers' self-attention mechanism is mapped to a generalized Potts model.
problem Uncertainty in what type of data distribution self-attention can efficiently learn.
method Decouple word positions and embeddings, then show self-attention learns a generalized Potts model.
result Training self-attention is equivalent to solving the inverse Potts problem.
The paper investigates polynomial alternatives to softmax in transformer models.
problem The effectiveness of softmax attention in transformers is questioned.
method The authors explore polynomial activations as alternatives to softmax, focusing on their ability to regularize the attention matrix.
result Certain polynomials can serve as effective substitutes for softmax in transformer applications, achieving strong performance.
Softmax temperature influences model representation rank and performance.
problem Understanding and optimizing softmax function's impact on model representations.
method Investigated softmax function's role in deep neural networks, introduced rank deficit bias.
result Softmax temperature affects model representation rank and can improve performance.