Linear Transformers and State Space Models have emerged as efficient alternatives to softmax Transformers for causal sequence modeling, enabling parallel training via matrix multiplication and efficient RNN-style inference. However, despite their success in causal tasks, no unified framework exists for applying Linear Transformers to bidirectional sequence modeling. We introduce LION, the first framework to systematically extend Linear Transformers to the bidirectional setting. LION generalizes three core representations commonly used in the causal case--full Linear Attention, bidirectional RNN, and chunkwise parallel form--to the bidirectional setting. These forms are theoretically equivalent and enable models to exploit the strengths of each during training and inference. We prove that a broad class of Linear Transformers can be extended using LION and validate our framework via three core examples based on the choice of decay type: LION-LIT, the bidirectional extension of [25]; LION-D, based on [44]; and LION-S, a variant using selective decay [34, 13]. Across standard bidirectional tasks, LION enables models to match or exceed the performance of softmax Transformers, while offering significantly faster training and more efficient inference than existing State Space Models.

A key question in sequence modeling with neural networks is how to represent and learn highly nonlinear and probabilistic state dynamics. Operator theory views such dynamics as linear maps on Hilbert spaces containing mean embedding vectors of distributions, offering an appealing but currently overlooked perspective. We propose a new approach to sequence modeling based on an operator-theoretic view of a hidden Markov model (HMM).

Linear Transformers and State Space Models have emerged as efficient alternatives to softmax Transformers for causal sequence modeling, enabling parallel training via matrix multiplication and efficient RNN-style inference. However, despite their success in causal tasks, no unified framework exists for applying Linear Transformers to bidirectional sequence modeling. We introduce LION, the first framework to systematically extend Linear Transformers to the bidirectional setting. LION generalizes three core representations commonly used in the causal case--full Linear Attention, bidirectional RNN, and chunkwise parallel form--to the bidirectional setting. These forms are theoretically equivalent and enable models to exploit the strengths of each during training and inference. We prove that a broad class of Linear Transformers can be extended using LION and validate our framework via three core examples based on the choice of decay type: LION-LIT, the bidirectional extension of [25]; LION-D, based on [44]; and LION-S, a variant using selective decay [34, 13]. Across standard bidirectional tasks, LION enables models to match or exceed the performance of softmax Transformers, while offering significantly faster training and more efficient inference than existing State Space Models.

Recent work has demonstrated the effectiveness of formulating decision making as supervised learning on offline-collected trajectories. Powerful sequence models, such as GPT or BERT, are often employed to encode the trajectories. However, the benefits of performing sequence modeling on trajectory data remain unclear. In this work, we investigate whether sequence modeling has the ability to condense trajectories into useful representations that enhance policy learning. We adopt a two-stage framework that first leverages sequence models to encode trajectory-level representations, and then learns a goal-conditioned policy employing the encoded representations as its input.

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Recently, there has been a renewed interest in using linear RNNs for efficient sequence modeling.

In this work, we aim to establish a strong connection between two significant bodies of machine learning research: continual learning and sequence modeling.That is, we propose to formulate continual learning as a sequence modeling problem, allowing advanced sequence models to be utilized for continual learning.Under this formulation, the continual learning process becomes the forward pass of a sequence model.By adopting the meta-continual learning (MCL) framework, we can train the sequence model at the meta-level, on multiple continual learning episodes.As a specific example of our new formulation, we demonstrate the application of Transformers and their efficient variants as MCL methods.Our experiments on seven benchmarks, covering both classification and regression, show that sequence models can be an attractive solution for general MCL.

With latent variables, stochastic recurrent models have achieved state-of-the-art performance in modeling sound-wave sequence. However, opposite results are also observed in other domains, where standard recurrent networks often outperform stochastic models. To better understand this discrepancy, we re-examine the roles of latent variables in stochastic recurrent models for speech density estimation. Our analysis reveals that under the restriction of fully factorized output distribution in previous evaluations, the stochastic variants were implicitly leveraging intra-step correlation but the deterministic recurrent baselines were prohibited to do so, resulting in an unfair comparison. To correct the unfairness, we remove such restriction in our re-examination, where all the models can explicitly leverage intra-step correlation with an auto-regressive structure. Over a diverse set of univariate and multivariate sequential data, including human speech, MIDI music, handwriting trajectory, and frame-permuted speech, our results show that stochastic recurrent models fail to deliver the performance advantage claimed in previous work.