An Objective Performance Evaluation of the LSTM Networks in Time Series Classification

This study presents a controlled comparison of baseline Kolmogorov-Arnold Networks (KAN), implemented via PyKAN, and Long Short-Term Memory (LSTM) networks for the forecasting of stochastic, non-stationary financial time series. The two architectures are assessed in terms of predictive accuracy, computational efficiency, and interpretability, with accuracy measured by the Root Mean Square Error (RMSE) in normalised feature space. Under a direct multi-output forecasting protocol, LSTM attains clearly superior accuracy across all tested prediction horizons, consistent with its well-established effectiveness for sequential data modelling. Baseline KAN, although offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits substantially higher error rates and limited practical applicability for time series forecasting in its standard form. Several specialised temporal variants -- including Temporal KAN and Time-Frequency KAN -- have since been proposed to address these sequential modelling limitations, but they lie outside the scope of the present study. KAN is observed to converge faster during training under the configurations tested, although direct runtime comparisons are constrained by methodological factors. These findings support the adoption of LSTM for accuracy-critical financial forecasting and establish an empirical baseline for standard KAN on stochastic sequential data, motivating further investigation of temporally-aware KAN architectures. The study benchmarks baseline KAN against baseline LSTM only; the results do not extend to specialised KAN variants designed for sequential data, nor to the broader family of temporal models.

Structured state space models (SSMs) have recently emerged as a promising foundation for sequence modeling, with Mamba-based architectures demonstrating strong performance through input-dependent state transitions, albeit at considerable complexity. However, their application to time-series classification (TSC) has been largely limited to Mamba-style architectures, leaving the broader SSM design space underexplored. We present the first systematic study spanning diagonal SSMs (S4D) and input-dependent SSMs (Mamba family) on large-scale TSC benchmarks, asking whether such complexity is necessary for top performance. Our results reveal a surprising finding: S4D consistently outperforms Mamba-based variants in both accuracy and efficiency, challenging the assumption that increased complexity translates to meaningful gains in TSC. Building on this, we introduce MS4, lightweight modifications to S4D via a linear input projection and channel-mixing mechanism, and MS4N, a normalized variant that stabilizes state dynamics with negligible overhead. Evaluated on 59 datasets across MONSTER (up to 60 million samples, 50K timesteps, 82 classes) and the UEA benchmark, against 15 baselines, MS4 and MS4N consistently outperform Mamba-based models while remaining more efficient, and MS4N matches or surpasses competing deep learning models that are roughly 2x and 10x larger in parameters. These results position lightweight structured SSMs as a compelling alternative to scaling complexity for TSC.

Despite recent advances in state space models (SSMs) such as Mamba across various sequence domains, research on their standalone capacity for time series classification (TSC) has remained limited. We propose MambaSL, a framework that minimally redesigns the selective SSM and projection layers of a single-layer Mamba, guided by four TSC-specific hypotheses. To address benchmarking limitations -- restricted configurations, partial University of East Anglia (UEA) dataset coverage, and insufficiently reproducible setups -- we re-evaluate 20 strong baselines across all 30 UEA datasets under a unified protocol. As a result, MambaSL achieves state-of-the-art performance with statistically significant average improvements, while ensuring reproducibility via public checkpoints for all evaluated models. Together with visualizations, these results demonstrate the potential of Mamba-based architectures as a TSC backbone.