From Observations to States: Latent Time Series Forecasting

Deep learning has achieved strong performance in Time Series Forecasting (TSF). However, we identify a critical representation paradox, termed Latent Chaos: models with accurate predictions often learn latent representations that are temporally disordered and lack continuity. We attribute this phenomenon to the dominant observation-space forecasting paradigm. Most TSF models minimize point-wise errors on noisy and partially observed data, which encourages shortcut solutions instead of the recovery of underlying system dynamics. To address this issue, we propose Latent Time Series Forecasting (LatentTSF), a novel paradigm that shifts TSF from observation regression to latent state prediction. Specifically, LatentTSF employs an AutoEncoder to project observations at each time step into a higher-dimensional latent state space. This expanded representation aims to capture underlying system variables and impose a smoother temporal structure. Forecasting is then performed entirely in the latent space, allowing the model to focus on learning structured temporal dynamics. Theoretical analysis demonstrates that our proposed latent objectives implicitly maximize mutual information between predicted latent states and ground-truth states and observations. Extensive experiments on widely-used benchmarks confirm that LatentTSF effectively mitigates latent chaos, achieving superior performance. Our code is available in https://github.com/Muyiiiii/LatentTSF.

💡 Research Summary

The paper identifies a paradox in modern deep learning‑based time‑series forecasting (TSF): models that achieve low point‑wise error on the observation space often learn latent representations that are temporally disordered, a phenomenon the authors name “Latent Chaos.” Through extensive analysis on the Electricity dataset using the iTransformer backbone, the authors show that while raw observations exhibit clear temporal locality (adjacent time steps cluster together in t‑SNE visualizations), the learned latent embeddings scatter randomly, have a much larger average Euclidean distance between consecutive steps (94.03 vs. 12.94), and distort the spectral structure of the data. They argue that this arises from two complementary causes: (1) partial observability—real‑world observations are noisy, low‑dimensional projections of high‑dimensional system states, so minimizing observation‑space loss does not guarantee recovery of coherent latent dynamics; and (2) the optimization bias of point‑wise losses (MAE/MSE) which provide little inductive bias toward temporal continuity, encouraging shortcut learning of statistical regularities rather than true dynamics.

To address this, the authors propose Latent Time Series Forecasting (LatentTSF), a two‑stage paradigm that shifts the forecasting task from direct observation regression to latent‑state prediction. In Stage 1, a point‑wise AutoEncoder (AE) is pre‑trained to map each observation vector xₜ ∈ ℝ^C into an expanded latent vector zₜ ∈ ℝ^D (with D > C). The AE is trained with an L₁ reconstruction loss, encouraging robustness to noise while expanding the feature space to capture hidden system variables. After pre‑training, the encoder E and decoder D are frozen, and the entire historical and future sequences are transformed into latent sequences Z_X and Z_Y.

In Stage 2, a standard TSF backbone (e.g., iTransformer, TimeBase) is trained to predict future latent states directly: \hat{Z}_Y = F_θ(Z_X). The final forecast is obtained by decoding \hat{Z}_Y through D. Crucially, the loss is computed entirely in latent space, combining a squared‑error prediction term L_Pred = ‖Z_Y – \hat{Z}_Y‖₂² and an alignment term L_Align = 1 – ⟨Z_Y, \hat{Z}_Y⟩/(‖Z_Y‖‖\hat{Z}_Y‖), weighted by hyperparameters α and β. The prediction term enforces magnitude accuracy, while the alignment term encourages directional consistency, preventing degenerate scaling.

The authors provide an information‑theoretic justification: L_Pred and L_Align correspond to tractable lower bounds on the mutual information I(Z_Y; \hat{Z}_Y) and I(Y; \hat{Z}_Y), respectively. Maximizing these bounds ensures that the predicted latent states retain maximal shared information with both the true latent future and the observable future, thereby directly combating latent chaos.

Empirical evaluation spans six widely used benchmarks (Electricity, Traffic, Exchange‑Rate, Weather, Solar‑Energy, COVID‑ILI). Across all datasets, LatentTSF consistently outperforms strong baselines (including state‑of‑the‑art Transformers) by 5–12 % in MAE and shows comparable gains in SMAPE. Latent‑space diagnostics reveal that the average distance between adjacent latent points drops dramatically (e.g., from 94.03 to 9.25 on Electricity) and the spectral profiles of latent embeddings align closely with those of the raw data, confirming mitigation of latent chaos. Ablation studies demonstrate the importance of each component: removing the AE pre‑training, using a lower‑dimensional latent space, or omitting the alignment loss each degrades performance.

Strengths of the work include (1) a clear identification and quantification of a previously overlooked representation issue in TSF, (2) a simple yet effective architectural modification that can be applied to any existing backbone, (3) solid theoretical grounding via mutual information maximization, and (4) thorough experimental validation. Limitations involve the added computational cost of AE pre‑training, sensitivity to the choice of latent dimensionality D, and the current focus on regular multivariate time series rather than irregular or event‑based sequences.

Future directions suggested by the authors involve (a) self‑supervised or contrastive pre‑training to reduce AE overhead, (b) adaptive latent dimensionality mechanisms, (c) Bayesian extensions to model uncertainty in latent dynamics, and (d) deployment studies in real‑world systems such as power grids or traffic management where robustness to noisy, partially observed data is critical. Overall, LatentTSF offers a compelling shift in perspective: by forecasting in a structured latent space, models can learn smoother, more interpretable dynamics while achieving superior predictive accuracy.