time series engineers

Abstract: Efficient sequence modeling remains a fundamental challenge in machine learning. Despite the success of Transformers, recurrent neural networks (RNNs) have recently re-emerged as efficient alternatives. Particularly, Echo State Networks (ESNs) offer a compelling framework of randomized RNNs that have been extensively studied for time-series forecasting and dynamical systems. This paper presents an empirical analysis of distributional, architectural, and optimization variants of ESNs evaluated on few-shot sequence-to-sequence (seq2seq) pattern tasks. These synthetic tasks utilize discrete symbol sequences, characterized by delays, inactive phases, and triggered markers to isolate and evaluate memory and pattern recognition capabilities. The minimality of these tasks is crucial to understand the strengths and limitations of machine learning models. Furthermore, when the input signal utilizes a one-hot encoding, ESN dynamics are governed strictly by their weight distributions, offering an ideal lens through which to study reservoir computing. Our findings map the performance boundaries of ESNs relative to state-of-the-art (SOTA) models. We show that preserving a linear state regime is vital for memory tasks, such as pattern completion or simple copy. We propose a data-dependent modulation mechanism for nonlinear input injection into the reservoir (G-ESN). G-ESN functions as a statistical filter capable of solving tasks that conventional ESNs cannot (the adding problem and bracket matching). Finally, for Deep ESNs, we evaluate a shared readout mechanism across layers that outperforms conventional concatenated readouts on structural tasks, including selective copy, sorting problem, and bracket matching.

Abstract: Time-series foundation models use the same network depth for every input, although forecasting windows differ in structure and difficulty. We test whether whole Transformer blocks can be removed at inference time in two pretrained models: Chronos-Bolt and TimesFM 2.5. Our bypasses avoid the original block computation and preserve the dense model exactly when all blocks are enabled. Masks are selected only on calibration windows and evaluated on 1,088 held-out windows from ETTh1, Traffic, Weather, and Exchange. At moderate sparsity, Chronos-Bolt with 7/11 candidate blocks and TimesFM with 16/20 blocks show little change in mean relative forecasting quality across datasets while reducing median A100 batch-1 latency by 11.2% and 13.4%. More aggressive TimesFM skipping accelerates inference further but substantially harms Traffic and Weather. Across both models, different equal-budget masks win on different windows, and a retrospective oracle significantly improves over the best static mask on every dataset. However, dataset-specific masks transfer inconsistently, and Chronos representations do not support reliable unseen-domain routing. These results establish cross-architecture structured redundancy and input-dependent opportunity, but not a deployable dynamic inference method.

Abstract: Source-Free Universal Domain Adaptation (SF-UniDA) extends Universal Domain Adaptation by removing access to source data at adaptation time while still handling label-set mismatches between domains. Despite growing interest in this setting for image data, no benchmark exists for time series, which are more challenging. We present the first SF-UniDA benchmark on time series. In addition, we provide the first study of pretrained foundation models as feature extractors for time series domain adaptation. In this context, we identify a critical and previously underexplored limitation of all existing SF-UniDA methods: the inference threshold for unknown-sample rejection is highly sensitive. We address this by proposing a plug-in auto-thresholding module that can be integrated into any SF-UniDA method. Experiments on three well-known time series datasets confirm the suitability of this module. They also highlight that foundation models do not systematically outperform classical backbones and that SF-UniDA tailored for time series is yet to be developed.

Abstract: Sample-level reliability heterogeneity is common in deep time series learning. Standard training pipelines apply a uniform regularization setting to all samples, which can under-regularize corrupted samples and over-restrict clean samples. Common robustness approaches filter observations in data space or impose priors on latent representations. We propose Capacity-Centric Modulation (CCM) as a complementary, sample-adaptive regularization principle. Under this principle, we introduce SACM (Sample-Adaptive Capacity Modulation), a task-agnostic framework that exploits spectral sparsity to assign sample-wise dropout probabilities along internal activation paths. SACM integrates into existing backbones without architectural redesign and preserves the deterministic inference pipeline. Across 301 real-world dataset-backbone pairs covering 9 forecasting, 32 classification, and 4 anomaly-detection datasets, SACM reduces forecasting MSE by 6.7% on average and improves classification accuracy and point-adjusted F1 by 3.04% and 17.05%, respectively, relative to unmodified backbones, with zero test-time overhead.

Abstract: Time series foundation models (TSFMs) commonly adapt to new data by attaching a single trainable head to a frozen backbone, a one-size-fits-all setup that underfits heterogeneous regimes. Replacing the head with a mixture of experts is the standard upgrade, but on instance-normalized backbones (the dominant TSFM design class) it fails: routing entropy collapses to zero and one expert absorbs every input, a failure we call normalization-induced routing collapse. Standard MoE rescue mechanisms do not repair it, because the cause is in the router's input, not its optimization. Pre-encoder normalization strips the statistics a router would need to tell regimes apart. A mutual-information decomposition makes this precise and yields a signal-ratio that, computed before training, predicts dataset vulnerability (Spearman $ρ= -0.88$). Eight causal controls, including a vision-modality replication, isolate instance normalization as the cause. The prescription is a minimal causal intervention: Raw-Routed Mixture of Adapters (RR-MoA), which routes on the raw, pre-normalization input. Under a strictly frozen backbone, RR-MoA wins 54/54 comparisons against the strongest fixed adapter and significantly outperforms LoRA, TRACE, AdaMix, and full fine-tuning. The effect generalizes across six backbones and an imputation task. Frozen RR-MoA also beats full fine-tuning by 12-79% (the Frozen Paradox); two architecturally distinct variants confirm the principle generalizes beyond this specific router.

Abstract: Diffusion models and transformers have supplanted GANs for multivariate time series imputation, largely on grounds of GAN training instability. R3GAN (NeurIPS 2024) removes that instability via regularized relativistic losses with provable convergence, raising a natural question: do stable, modern GANs revive adversarial imputation? We adapt R3GAN to 1D temporal data with a coarse-to-fine refinement framework and a frequency-domain discriminator, and audit 14 saved configurations across 3 datasets. Because these are heterogeneous single runs, the evidence is descriptive rather than a matched causal ablation. We report a negative result. All five saved mean/zero-start configurations improve by 48.4-70.2%. Among eight eligible non-legacy linear-start configurations, the mean change is -0.7% (range -3.0% to +1.1%); a separate -21.9% legacy logging anomaly is retained for provenance but excluded from that aggregate. In a saved Weather comparison, standalone R3GAN-1D underperforms BRITS by 5.8x. Crucially, we argue the common explanation (that GANs optimize distributional rather than point-wise objectives) cannot be the whole story, since diffusion models also optimize distributional objectives yet achieve state-of-the-art imputation. Our saved reconstruction-weight sweep is consistent with the adversarial signal being inert or harmful, but cannot identify its causal contribution; a matched discriminator-removed ablation is the key next experiment. We frame the precise reason a learned discriminator fails to provide useful refinement gradients (where a learned diffusion denoiser succeeds) as an open problem, and offer practical guidance on when adversarial refinement is worthwhile.

Abstract: Encoder-based time series foundation models (TSFMs) typically rely on deep stacks of independently parameterized Transformer layers, where only the final forecast is supervised and intermediate representations have no explicit predictive role. We introduce FlowTSFM, an encoder architecture that interprets depth as a recurrent transport process: a single Transformer block is iteratively applied with shared parameters, while a quantile-flow objective supervises intermediate states along a prescribed trajectory from a prior distribution toward the final forecast. The objective combines pinball forecasting loss with path-level position matching. With only 38.8M parameters, FlowTSFM achieves competitive performance on GIFT-Eval and TIME, remaining within 1.8-4.6% MASE of stronger baselines while using approximately $3\times$ fewer parameters than a 12-layer Chronos-2 model (119.5M). Beyond accuracy, we introduce CosMean, a scale-free diagnostic measuring whether recurrent updates consistently align toward the final prediction. Under a matched intermediate-state probing protocol, FlowTSFM achieves a CosMean score of 0.919 compared with 0.350 for Chronos-2, suggesting that recurrent parameter sharing combined with path supervision is associated with substantially more structured predictive trajectories at a favorable accuracy-efficiency trade-off.