Paper extends sparse alternatives to softmax for continuous domains, enabling efficient attention mechanisms.
problem Efficiently assigning zero probability to irrelevant categories in continuous domains.
method Extend alpha-entmax to continuous domains, introducing continuous-domain attention mechanisms.
result Continuous attention allows attending to time intervals and compact regions, improving text classification, machine translation, and visual question answering.
New model prevents forgetting in continual learning.
problem Learning from a continuous stream of tasks without forgetting.
method Bayesian Optimized Continual Learning with Attention Mechanism (BOCL).
result BOCL outperforms state-of-the-art in preventing catastrophic forgetting and fitting new tasks better.
The paper quantifies the regularity of attention operations.
problem Quantifying the regularity of attention operations.
method Proposes a new mathematical framework using measure theory and integral operators.
result Proves attention operation is Lipschitz continuous on compact domains and provides an estimate of its Lipschitz constant.
Lipschitz normalization boosts deep attention models, especially for graph neural networks.
problem Gradient explosion in deep graph attention networks leads to poor performance.
method Enforcing Lipschitz continuity by normalizing attention scores.
result Deep GAT models with LipschitzNorm achieve state-of-the-art results for tasks with long-range dependencies.
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.
The paper shows how continuous attention can lead to better object representations.
problem Learning good representations from data without labeled examples.
method Integrating unsupervised learning and reinforcement learning with intrinsic motivation.
result The proposed algorithm improves object recognition in few-shot settings.
Paper introduces kernel deformed exponential families for sparse continuous attention.
problem Creating efficient attention mechanisms for sparse data.
method Developed kernel deformed exponential families, theoretically and experimentally.
result Kernel deformed exponential families can attend to multiple compact regions of data.
Mathematical framework for understanding attention in neural networks.
problem Lack of theoretical understanding of attention in neural networks.
method Proposes a measure-theoretic model of attention and interprets self-attention as a system of self-interacting particles.
result Shows that attention is Lipschitz-continuous under suitable assumptions.
Deep neural networks, including recurrent networks, have been successfully applied to human activity recognition. Unfortunately, the final representation learned by recurrent networks might encode some noise (irrelevant signal components, unimportant sensor modalities, etc.). Besides, it is difficult to interpret the r…
New model recognizes emotions with missing modalities, improving accuracy.
problem Handling missing modalities in emotion recognition.
method Transformer-based architecture with cross-attention and self-attention mechanisms.
result Improvement of 37% in predicting arousal values and 30% in valence values compared to baseline.
This paper develops sparse alternatives to continuous distributions, including new types of Gaussians and attention mechanisms.
problem Creating flexible continuous distributions with varying support for machine learning applications.
method Defining Ω-regularized prediction maps and Fenchel-Young losses for arbitrary domains, and deriving new types of Gaussians and attention mechanisms. result Sparse alternatives to continuous distributions, including deformed exponential families and β-Gaussians, are introduced. We replace the Hidden Markov Model (HMM) which is traditionally used in in continuous speech recognition with a bi-directional recurrent neural network encoder coupled to a recurrent neural network decoder that directly emits a stream of phonemes. The alignment between the input and output sequences is established usin…
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
GOAT improves attention mechanisms by learning better priors.
problem Standard attention mechanisms use a naive uniform prior, limiting flexibility and generalization.
method GOAT introduces a trainable, continuous prior that replaces the uniform assumption, maintaining compatibility with optimized kernels.
result GOAT avoids representational trade-offs and learns an extrapolatable prior that combines positional flexibility with length generalization.
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. 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.
Rough Transformers improve time series modeling with lower costs and better performance.
problem Inefficient modeling of irregularly sampled time series data.
method Signature patching for continuous-time representations, reducing computational costs.
result Rough Transformers outperform vanilla Transformers and Neural ODE models.
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.
We propose the Gaussian attention model for content-based neural memory access. With the proposed attention model, a neural network has the additional degree of freedom to control the focus of its attention from a laser sharp attention to a broad attention. It is applicable whenever we can assume that the distance in t…
Transformers can approximate any sequence-to-sequence function, surprising given their complexity.
problem Understanding the expressive power of Transformer models for sequence-to-sequence functions.
method Established that Transformers are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, and extended this to arbitrary functions using positional encodings.
result Transformers are universal approximators of arbitrary continuous sequence-to-sequence functions on a compact domain.
Transformers can predict new tokens based on any number of context tokens, approximating continuous mappings with fixed resources.
problem Handling an arbitrarily large number of context tokens in transformers.
method Mathematical analysis of transformer's expressivity using Wasserstein distance and continuous mappings.
result Deep transformers are universal and can approximate continuous in-context mappings to arbitrary precision, uniformly over compact token domains.
Hybrid model predicts flow and pressure in water systems.
problem Predicting flow and pressure in water distribution systems with complex spatial-temporal correlations.
method Hybrid dual-stage spatial-temporal attention-based recurrent neural networks (hDS-RNN).
result Our model outperformed 9 baseline models in flow and pressure series prediction.
SNI framework for mixed-type data imputation interprets and explains missing values.
problem Missing data in mixed-type databases skew analysis results.
method SNI couples statistical priors with neural attention to impute and explain missing values.
result SNI provides interpretable feature dependency diagnostics and soft regularization of attention.
SE(3)-Transformers maintain equivariance for 3D data under rotations and translations.
problem Ensuring stable and predictable performance in 3D data under transformations.
method Introducing a self-attention module that is equivariant under continuous 3D roto-translations.
result The SE(3)-Transformer outperforms non-equivariant and non-attention models on real-world datasets.
With the improvement of medical data capturing, vast amount of continuous patient monitoring data, e.g., electrocardiogram (ECG), real-time vital signs and medications, become available for clinical decision support at intensive care units (ICUs). However, it becomes increasingly challenging to model such data, due to …
Machine learning models that can exploit the inherent structure in data have gained prominence. In particular, there is a surge in deep learning solutions for graph-structured data, due to its wide-spread applicability in several fields. Graph attention networks (GAT), a recent addition to the broad class of feature le…
EFA extends self-attention to handle mixed data types and dynamic relevance.
problem Handling high-dimensional, mixed data types with dynamic relevance.
method Probabilistic generative model using self-attention and latent factor model.
result EFA consistently outperforms existing models in complex latent structure capture and reconstruction.
New analysis shows RPE-based Transformers can't approximate all functions.
problem Understanding the limitations of RPE-based Transformers in approximating continuous functions.
method Mathematical analysis and development of a novel attention module (URPE) to overcome limitations.
result RPE-based Transformers can't approximate all continuous sequence-to-sequence functions, even with depth and width.
Study reveals attention mechanism's similarity computation parallels traditional machine learning.
problem Understanding the essence and principles of attention mechanism in deep learning.
method Examined classic metrics and vector space properties in manifold learning, clustering, and supervised learning to identify key characteristics of similarity computation and information propagation.
result Self-attention mechanism in deep learning adheres to the same principles but operates more flexibly and adaptively.
We examine the dependence of the deformation obtained by bending quasi-Fuchsian structures on the bending lamination. We show that when we consider bending quasi-Fuchsian structures on a closed surface, the conditions obtained by Epstein and Marden to relate weak convergence of arbitrary laminations to the convergence …
Survey of continuous volatility models, focusing on fractional and rough methods.
problem Stylized facts driving continuous volatility modeling.
method Historical development and fractional/rough methods.
result Characterization of landmark models and recent advances.
The paper identifies patterns in language model weights used for memorizing paragraphs.
problem Locating the specific mechanisms and weights used by language models to memorize paragraphs.
method Examined gradients and attention patterns in language models to identify memorized paragraphs.
result Gradients of memorized paragraphs have a distinguishable spatial pattern, and localized attention heads are involved in paragraph memorization.
New Performer model tackles long-sequence protein modeling.
problem Challenges of training complex Transformer models for long sequences.
method Linearly scalable long-context Transformer architecture, Performer.
result Performer provides strong theoretical guarantees and is effective for protein sequence modeling.
New method embeds time span into self-attention for better temporal pattern recognition.
problem Capturing temporal patterns in event sequences without recurrent networks.
method Functional time representation learning with Bochner's and Mercer's Theorems.
result Proposed methods outperform baseline models in various continuous-time event sequence prediction tasks.
DAFT models attention as a dynamical system to make neural networks more interpretable.
problem Uninterpretable features learned by neural networks without human priors.
method DAFT models attention as a continuous dynamical system using neural ODEs.
result DAFT reduces the number of reasoning steps while maintaining similar performance.
Network embedding represents nodes in a continuous vector space and preserves structure information from the Network. Existing methods usually adopt a "one-size-fits-all" approach when concerning multi-scale structure information, such as first- and second-order proximity of nodes, ignoring the fact that different scal…
Analyzes non-Markovian environments in stochastic approximation.
problem Understanding learning mechanisms in non-ergodic, non-Markovian settings.
method Analytic framework for transformer learning and continual learning.
result Proposes a new approach to transformer and continual learning.
Zero-Copy Architecture Detects Cross-Company Financial Signals Instantly.
problem Financial models miss cross-company disruptions due to static data.
method Heterogeneous Rust-Python streaming architecture that maps cross-company attention as a continuous-time graph.
result Zero-copy parsing and inference process delivers real-time cross-company signal detection.
Graph embedding methods represent nodes in a continuous vector space, preserving information from the graph (e.g. by sampling random walks). There are many hyper-parameters to these methods (such as random walk length) which have to be manually tuned for every graph. In this paper, we replace random walk hyper-paramete…
New method tackles anomaly detection in video surveillance using continual learning.
problem Challenges in continual learning for high-dimensional applications like video surveillance.
method Transfer learning and continual learning for online anomaly detection.
result Significantly reduces training complexity and continual learning from recent data.
Rough Transformers improve efficiency for medical time-series data.
problem Efficiently modeling irregularly sampled, long-range time-series data.
method Introducing Rough Transformers, a Transformer variant with continuous-time representations and multi-view signature attention.
result Rough Transformers outperform vanilla Transformers while using less computational resources.
As energy markets begin clearing at sub-hourly rates, their interaction with load control systems becomes a potentially important consideration. A simple model for the control of thermal systems using market-based power distribution strategies is proposed, with particular attention to the behavior and dynamics of elect…
Disease progression models are instrumental in predicting individual-level health trajectories and understanding disease dynamics. Existing models are capable of providing either accurate predictions of patients prognoses or clinically interpretable representations of disease pathophysiology, but not both. In this pape…
Proposes SAHP for better Hawkes process modeling.
problem Predicting occurrence patterns of event sequences.
method Leverages self-attention to modify Hawkes process intensity function.
result Demonstrates effectiveness on real-world datasets.
New Transformers maintain Lipschitz continuity for robustness.
problem Ensuring robustness in Transformers for safety-sensitive applications.
method Introducing gradient-descent-type in-context Transformers with explicit Euler steps of negative gradient flows.
result Universal approximation theorem for Lipschitz continuous Transformers.
Bitcoins and Blockchain technologies are attracting the attention of different scientific communities. In addition, their widespread industrial applications and the continuous introduction of cryptocurrencies are also stimulating the attention of the public opinion. The underlying structure of these technologies consti…
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show t…
A new model tackles language generation issues by using discrete variational attention.
problem Information under-representation and posterior collapse in variational autoencoders.
method Proposes a discrete variational attention model with categorical distribution over attention mechanism.
result Enhances latent space for language generation and avoids posterior collapse.