Can a sequence model remain competitive with only a few thousand parameters and an explicitly auditable prediction interface? We introduce ALPHABET, a compact linear-time model that compresses temporal history into stable complex pole modes: a direct bank synthesizes its modal states back into the feature trajectory, an independent cascaded bank analyzes the transformed trajectory without resynthesis, and an affine head reads only modal energies and lag moments from both banks. We characterize the temporal information this descriptor retains: for a stationary, fully observed feature process, each mode energy is a frequency-localized measurement of the second-order spectrum, the continuum of such measurements identifies the spectrum, and almost every mode separates any fixed finite set of spectrally distinct classes. On a Gaussian control with matched low-lag statistics, the learned descriptor approaches the Bayes oracle where raw autocovariances remain at chance. Across the fixed 82-task registry, ALPHABET attains mean rank 3.97 in the complete ten-family comparison. At the common-width D=64 runtime anchor, its 6,437 parameters deliver 5.02 times faster inference and 3.93 times faster complete training steps than the nine baselines on average.
We propose a hybrid approach for user-centric modeling of transactional event sequences that combines contrastive representation learning (CoLES) with State Space Models (SSMs). While contrastive methods yield high-quality compressed user representations, existing encoders -- RNNs and Transformers -- suffer from vanishing gradients or quadratic complexity, respectively. Mamba, a selective SSM, efficiently handles long-range dependencies but remains underexplored for personalized user analysis. We investigate two integration strategies: (1)~initializing the Mamba hidden state with a CoLES embedding, and (2)~prepending the projected CoLES embedding as a prefix token to the input sequence. Both approaches supply the model with an informative user prior from the first step. Experiments on three public datasets -- Age (multiclass age-group prediction), MBD (multi-label product acquisition), and Taobao (binary purchase prediction) -- demonstrate consistent improvements over standalone Mamba and CoLES with a linear classifier, with the hybrid models converging 2--3$\times$ faster than the plain SSM baseline. Explainability analysis via discretization-step maps and Integrated Gradients reveals selective event filtering on behavior-rich datasets and identifies the most informative transaction features.
In many realistic scenarios, large volumes of time series data are generated with limited or expensive annotations. This limitation makes supervised learning methods difficult to apply and leads to the use of unsupervised approaches capable of discovering meaningful structures directly from raw data. Clustering therefore plays a crucial role in organizing time series into groups that share similar temporal patterns, enabling exploratory analysis and downstream tasks without requiring manual labeling. However, existing deep clustering methods often struggle to capture long-range temporal dependencies or rely on architectures with high computational cost. This paper introduces FMMVCC, a Mamba-based deep clustering framework for time series that leverages state space sequence modeling to efficiently learn temporal representations with linear complexity. Additionally, it utilizes multi-view self-supervised learning with temporal masking and augmentations. Experimental evaluation in 15 benchmark datasets proves that FMMVCC consistently outperforms state-of-the-art baselines, achieving the best overall performance in 29 of 60 total metric evaluations and the highest average rank in all tested scenarios.
In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics. Existing approaches typically sacrifice one of these goals: deep state space models often assume Gaussian latent transitions, limiting fit and forecasting, while diffusion models are highly expressive but lack principled inference for the underlying dynamics. To combine the strengths of both, we introduce the Diffusion-Driven State Space Model (DDSSM), which replaces the conventional Gaussian transition distribution with a diffusion model. Our DDSSM resolves the open problem of how to jointly train an autoencoder and a diffusion model on sequential data, thereby extending the literature on latent diffusion models for time series. Moreover, we find that the DDSSM empirically outperforms a state-of-the-art deep SSM at fitting and forecasting a simulated time series with multimodal transitions.
Latent state space systems are ubiquitous in statistical modelling, arising naturally when a time series is observed through a noisy measurement function, however training deep state space models (DSSM) at scale remains difficult. Two largely distinct strategies and literatures have developed around the training of DSSMs. Firstly, auto-encoding DSSMs train generative DSSMs by optimising a variational lower bound. Secondly, DSSMs trained by back-propagating the outputs of a classical sequential Monte Carlo algorithm (SMC). Such approaches can train DSSMs for discriminative as well as generative tasks, however, due to the sequentiality of their forward pass, scale poorly on modern hardware. We propose a new training method \emph{parallel variational Monte Carlo} (PVMC) that bridges the gap between the paradigms, and can be used robustly to train DSSMs for both discriminative and generative tasks. Our method achieves state-of-the-art or better results on a set of baseline experiments and trains $10\times$ faster than the fastest competing SMC approach.