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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,051 papers · 148 categories

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48 results for Spectral RNN

Lyapunov analysis improves RNN performance prediction.

problem Uncertainty in RNN performance prediction due to hyperparameters and architecture.
method Lyapunov spectral analysis of RNNs and Autoencoder-Lyapunov Embedding Learning (AeLLE).
result AeLLE successfully correlates RNN Lyapunov spectrum with accuracy and predicts performance.

Combines Fourier methods and RNNs for efficient time series prediction.

problem Efficiently processing and predicting time series data with memory and computational constraints.
method Uses short-time Fourier transform and weight reductions through low pass filtering in a Spectral RNN.
result Predicts time series data from chaotic systems and real-world data.

SKOLR uses linear RNNs to approximate Koopman operators for time-series forecasting.

problem Nonlinear dynamical system analysis and time-series forecasting with infinite-dimensional Koopman operators.
method Established a connection between Koopman operator approximation and linear RNNs, integrating learnable spectral decomposition and MLP.
result SKOLR delivers exceptional performance in various forecasting benchmarks and dynamical systems.

The paper distills a weighted automaton from RNNs for language modeling.

problem Tackles the gap between deep learning and grammatical inference.
method Uses a spectral approach to infer a weighted automaton from a trained RNN.
result Extracted weighted automata are good approximations of the RNNs, validating the approach.

Algorithm extracts deterministic PDFA from probabilistic models with improved performance.

problem Learning deterministic models from probabilistic ones with noise.
method Adapted L* algorithm for probabilistic settings, using conditional probabilities and local tolerance.
result Achieves better performance on WER and NDCG than spectral extraction of WFAs.

In this paper, we propose a fully supervised speaker diarization approach, named unbounded interleaved-state recurrent neural networks (UIS-RNN). Given extracted speaker-discriminative embeddings (a.k.a. d-vectors) from input utterances, each individual speaker is modeled by a parameter-sharing RNN, while the RNN state…

2018-10-10abs ↗pdf ↗

Proposes a new RNN structure to improve expressivity without sacrificing stability.

problem Exploding and vanishing gradient problems in RNNs and reduced expressivity.
method Introduces a non-normal RNN structure using Schur decomposition and splitting.
result Enhances expressivity while maintaining stability and training speed.

Delayed-RNN approximates stacked and bidirectional RNNs.

problem Improving RNN expressiveness and representational capacity.
method Weight-constrained delayed-RNN, equivalent to stacked-RNNs, with partial acausality.
result Delayed-RNN can approximate stacked and bidirectional RNNs, outperforming them in some tasks.

In this paper, we explore different ways to extend a recurrent neural network (RNN) to a \textit{deep} RNN. We start by arguing that the concept of depth in an RNN is not as clear as it is in feedforward neural networks. By carefully analyzing and understanding the architecture of an RNN, however, we find three points …

2013-12-20abs ↗pdf ↗

In this work, we propose a novel recurrent neural network (RNN) architecture. The proposed RNN, gated-feedback RNN (GF-RNN), extends the existing approach of stacking multiple recurrent layers by allowing and controlling signals flowing from upper recurrent layers to lower layers using a global gating unit for each pai…

2015-02-09abs ↗pdf ↗

Gating units in GRUs and LSTMs create slow modes and control phase-space complexity.

problem Training challenges in RNNs due to exploding or vanishing gradients.
method Random matrix theory and mean-field theory applied to GRUs and LSTMs.
result Gates in GRUs and LSTMs lead to accumulation of slow modes and control phase-space complexity.

RNNs struggle with in-context retrieval, while Transformers excel.

problem In-context retrieval capability of RNNs.
method Theoretical analysis and experimental techniques (CoT, RAG, Transformer layer).
result Enhancing RNNs with techniques improves their in-context retrieval capability, closing the representation gap with Transformers.

Analyzes RNNs using ODEs to map their properties and improve stability.

problem Understanding and improving the stability of RNNs.
method Relates RNNs to ODEs, mapping their properties to integration methods.
result Establishes sufficient conditions for RNN training stability and designs new architectures.

Recurrent Neural Networks (RNNs) have long been recognized for their potential to model complex time series. However, it remains to be determined what optimization techniques and recurrent architectures can be used to best realize this potential. The experiments presented take a deep look into Hessian free optimization…

2015-10-16abs ↗pdf ↗

Study proves deep narrow RNNs can approximate any function, with minimum width independent of data length.

problem Proving universality of deep narrow RNNs with bounded widths.
method Analyzing RNNs as dynamical systems, proving universality for deep narrow structures with specific widths.
result Minimum width for universality of deep narrow RNNs is independent of data length.

Hamiltonian RNN controls hidden states gradient for long-term dependencies.

problem Challenges in learning long-term dependencies in RNNs.
method Symplectic discretization of Hamiltonian system to control gradient.
result Hamiltonian RNN outperforms other RNNs without hyperparameter optimization.

Frequentist method estimates uncertainty in RNNs without altering architecture.

problem Uncertainty quantification in RNNs for decision-making.
method Jackknife resampling and influence functions to estimate variability.
result The method provides theoretical coverage guarantees on uncertainty intervals.

RNNs struggle with chaotic dynamics due to exploding gradients, but we found a way to optimize training.

problem Challenging training of RNNs with chaotic dynamics due to exploding gradients.
method Relating loss gradients to Lyapunov spectrum to optimize training on chaotic data.
result RNNs with chaotic dynamics always have diverging gradients, while stable ones have bounded gradients.

RNNs are suboptimal at compressing past sensory inputs for future prediction.

problem RNNs do not optimally compress past sensory inputs for future prediction.
method Investigated RNNs trained with maximum likelihood and found they extract unnecessary information. Injected noise into hidden states to improve performance.
result Injecting noise into RNN hidden states improves predictive information, sample quality, likelihood, and classification performance.

RNNs learn combinatorial graph problems with sample complexity bounds.

problem Learning efficient approximations for real-valued combinatorial graph problems.
method Upper bounds the sample complexity for learning real-valued RNNs.
result Real-valued RNNs can be learned with polynomial number of samples.

Recurrent Neural Networks (RNNs), which are a powerful scheme for modeling temporal and sequential data need to capture long-term dependencies on datasets and represent them in hidden layers with a powerful model to capture more information from inputs. For modeling long-term dependencies in a dataset, the gating mecha…

2017-06-07abs ↗pdf ↗