Mamba Forecaster Overview

• Mamba Forecaster is a family of state-space-based models using input-dependent dynamics to maintain long-range temporal structure with linear complexity.
• These models replace quadratic attention with linear-time recurrences enhanced by patching, decomposition, and hybrid attention integration.
• Their design enables state-of-the-art performance in multivariate, probabilistic, and domain-specific forecasting, validated across diverse empirical benchmarks.

Mamba Forecaster denotes a family of forecasting models that use the Mamba selective state space architecture as the primary sequence module, either replacing attention entirely or operating inside hybrid encoder blocks. In the time-series literature, these models are used for long-horizon multivariate forecasting, zero-shot foundation-model forecasting, probabilistic forecasting, minute-level financial prediction, and spatio-temporal traffic prediction. Their shared premise is that input-dependent state-space recurrences can preserve long-range temporal structure with linear complexity in sequence length, while auxiliary mechanisms such as patching, decomposition, spectral gating, semantic embeddings, or expert routing compensate for the limitations of vanilla Mamba on non-stationary, multi-scale, or cross-series data (Wang et al., 2024, Ma et al., 2024, Bhethanabhotla et al., 2024).

1. State-space foundation and forecasting formulation

The mathematical core of a Mamba forecaster is the state space model. Several forecasting papers use the continuous-time formulation

$h'(t) = A h(t) + B x(t), \qquad y(t) = C h(t),$

with zero-order-hold discretization

$$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$

and discrete recurrence

$$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$

In Mamba, parts of this system become input-dependent, so the state update is selective rather than fixed (Ma et al., 2024, Wang et al., 2024).

This selectivity is typically implemented by making quantities such as $B_t$, $C_t$, and $\Delta_t$ functions of the current token. In AdaMamba, for example, the Mamba block is summarized as

$$\mathbf{s}_t = \overline{\mathbf{A}_t}\mathbf{s}_{t-1} + \overline{\mathbf{B}_t}\mathbf{x}_t,\qquad \mathbf{y}_t = \mathbf{C}_t \mathbf{s}_t,$$

with $$\mathbf{B}_t,\mathbf{C}_t,\Delta_t = \mathrm{Linear}(\mathbf{x}_t)$$, emphasizing that the recurrence is conditioned on input content rather than being purely linear time-invariant (Jeon, 7 Dec 2025).

In forecasting, this machinery is embedded inside a mapping from a historical window to a future horizon. Typical formulations are direct multi-step mappings such as

$$f_\theta : \mathbf{X}_{1:L} \mapsto \mathbf{Y}_{L+1:L+T},$$

for multivariate long-term forecasting (Wang et al., 2024), or one-step-ahead regression on minute-level stock data

$\hat{P}_{t+1} = f_\theta(x_{t-59}, \dots, x_t)$

with a 60-minute input window (Kadiyala et al., 14 Sep 2025). Zero-shot foundation models follow the same formal structure but keep parameters fixed after pretraining and apply the model to new datasets without target-domain fine-tuning (Bhethanabhotla et al., 2024, Ma et al., 2024).

The main architectural attraction is computational. Across these papers, Mamba-based forecasters are repeatedly positioned against Transformer self-attention by exploiting linear rather than quadratic scaling in sequence length. This advantage is central in long-horizon forecasting, high-frequency financial prediction, and large-scale multivariate settings with many sensors or channels (Wang et al., 2024, Kadiyala et al., 14 Sep 2025, Bhethanabhotla et al., 2024).

2. Canonical architectural patterns

Although the term covers a broad family rather than a single model, the literature has converged on several recurring design patterns: channel-independent encoding, patch-based tokenization, bidirectional or variable-direction scans, decomposition or normalization front-ends, and hybridization with attention, mixtures of experts, or graph modules.

Model	Forecasting setting	Distinctive design
S-Mamba	Multivariate LTSF	bidirectional Mamba for inter-variate correlations + FFN for temporal dependencies
MambaTS	Multivariate LTSF	Variable Scan along Time, Temporal Mamba Block, variable permutation training, VAST
Mamba4Cast	Zero-shot univariate forecasting	Mamba2 + multi-scale causal CNN + single-pass multipoint prediction
TSMamba	Foundation-model forecasting	forward/backward Mamba encoders + patch-wise autoregressive pretraining
AdaMamba	Long-horizon multivariate forecasting	adaptive normalization + multi-scale trend decomposition + patch MoE encoding
ms-Mamba	Multivariate TSF	parallel Mamba blocks with different sampling rates

S-Mamba tokenizes each variate autonomously via a linear layer, treats variables as tokens, and applies a bidirectional Mamba layer to extract inter-variate correlations while delegating temporal dependency learning to a feed-forward network (Wang et al., 2024). MambaTS modifies vanilla Mamba more aggressively: it introduces Variable Scan along Time, removes the original causal convolution inside the Mamba block, applies dropout directly to selective parameters, and learns scan order through variable permutation training and Variable-Aware Scan along Time (Cai et al., 2024). This is a direct response to the observation that Mamba’s order-sensitive scan can be problematic when variable order is arbitrary.

Patching is another dominant pattern. AdaMamba normalizes and detrends the raw sequence, splits it into non-overlapping patches, embeds each patch, and then feeds patch tokens into a Mamba-enhanced Transformer layer with a mixture-of-experts feed-forward block (Jeon, 7 Dec 2025). TSMamba also adopts 1D-convolutional patching, but uses forward and backward Mamba encoders pretrained through patch-wise autoregressive prediction before fine-tuning a forecasting head (Ma et al., 2024). Mamba4Cast extends the same idea into a zero-shot setting: a causal CNN front-end with dilations $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$0 feeds a Mamba2 encoder, and the model predicts the entire horizon in one pass rather than autoregressively (Bhethanabhotla et al., 2024).

A second major trend is explicit multi-scale handling. ms-Mamba replaces the single sampling rate of ordinary Mamba with multiple parallel Mamba blocks using different $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$1, then averages the resulting representations (Karadag et al., 10 Apr 2025). AdaMamba uses multi-scale convolutions and squeeze-and-excitation recalibration to extract trend before Mamba processing (Jeon, 7 Dec 2025). DMamba separates seasonal and trend components and assigns different model classes to each: a variable-direction Mamba encoder for seasonal interactions and a lightweight MLP for trend (Chen et al., 9 Feb 2026). ASGMamba inserts a lightweight Adaptive Spectral Gating module before Mamba and combines it with a three-branch patch hierarchy and node embeddings (Li et al., 2 Feb 2026).

Hybrid models preserve Mamba’s linear-time sequential backbone while reintroducing explicit global context modules where necessary. MAT combines Mamba for long-range dependencies with Transformer self-attention for short-range dependencies on weather data (Zhang et al., 2024). DC-Mamber uses a dual-channel design in which Bi-Mamba operates on channel-independent variable tokens while a linear Transformer operates on channel-mixing temporal tokens, and then fuses the two streams (Fan et al., 6 Jul 2025). This suggests that “Mamba forecaster” is best understood as a design space centered on selective SSMs rather than as a single canonical architecture.

3. Forecasting regimes and application domains

The most common regime is supervised long-term multivariate forecasting on benchmarks such as ETTh1/2, ETTm1/2, Electricity, Weather, Traffic, Exchange, Solar-Energy, and PEMS. S-Mamba, ms-Mamba, AdaMamba, DMamba, and ASGMamba all target this setting, but they differ in where they apply Mamba: along variables, along patches, across multi-scale branches, or only on decomposed seasonal components (Wang et al., 2024, Karadag et al., 10 Apr 2025, Jeon, 7 Dec 2025, Chen et al., 9 Feb 2026, Li et al., 2 Feb 2026).

A second regime is foundation-model forecasting. Mamba4Cast is a univariate zero-shot model trained purely on synthetic data generated from a 70% GP and 30% ForecastPFN mixture; it uses Mamba2 and predicts all future steps in a single forward pass (Bhethanabhotla et al., 2024). TSMamba is a multivariate foundation model that transfers from a pretrained Mamba LLM through a two-stage procedure: patch-wise autoregressive backbone adaptation followed by forecasting-head training and refinement (Ma et al., 2024). ss-Mamba pushes the foundation-model idea toward cross-series semantic conditioning by injecting semantic index embeddings from pretrained LLMs and spline-based KAN temporal encodings into the selective SSM input gate (Ye, 3 Jun 2025).

A third regime is probabilistic forecasting. Mamba-ProbTSF keeps Mamba as a deterministic mean predictor and adds a second network for predictive standard deviation, training both under a Gaussian negative log-likelihood. The model assumes

$$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$2

and evaluates calibration through standardized residuals, coverage, and KL divergence (Pessoa et al., 13 Mar 2025). AdaMamba is not itself probabilistic, but its authors explicitly describe it as compatible with probabilistic extensions (Jeon, 7 Dec 2025).

The application range extends beyond generic benchmarks. In minute-level stock prediction, a shallow Mamba model with one Mamba block, $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$3, $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$4, and $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$5 is combined with intraday technical indicators and one LLM-derived sentiment stream (Kadiyala et al., 14 Sep 2025). HIGSTM uses Mamba inside a stock-specific hierarchical framework with index-guided frequency decomposition and dynamic/global cross-stock graphs (Yan et al., 14 Mar 2025). MCST-Mamba uses separate temporal and spatial Mamba pathways for multichannel traffic prediction over sensor networks, simultaneously forecasting speed, flow, and occupancy (Hamad et al., 5 Jul 2025). These cases show that the term also covers domain-specialized forecasters in which Mamba is embedded inside broader financial or spatio-temporal systems.

4. Empirical performance and efficiency

The empirical record is strong but heterogeneous. S-Mamba reports leading performance on thirteen public datasets while maintaining low computational overhead; on Traffic its average MSE/MAE over horizons is $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$6, compared with $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$7 for iTransformer, and on Weather its average is $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$8, compared with $$\bar{A} = \exp(\Delta A), \qquad \bar{B} = (\Delta A)^{-1}(\exp(\Delta A)-I)\cdot \Delta B,$$9 for iTransformer (Wang et al., 2024). MambaTS further argues that naïvely replacing attention by Mamba inside PatchTST or iTransformer is insufficient, and that its redesigned scan order and block structure are needed to achieve new state-of-the-art performance (Cai et al., 2024).

Among foundation models, Mamba4Cast is notable for its scale-to-efficiency ratio: it uses about 27M parameters, is trained only on synthetic data, achieves a baseline MASE of 1.153 in single-pass multipoint mode, and is reported as competitive with Chronos-Base at 200M parameters while scaling much better with prediction length (Bhethanabhotla et al., 2024). TSMamba likewise reports zero-shot averages of $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$0 MSE/MAE on ETTm2 and $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$1 on Weather, while in full-shot mode it reports $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$2 on Weather and $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$3 on ILI (Ma et al., 2024).

Several later variants show that raw Mamba backbones can be substantially improved by preprocessing or specialization. AdaMamba reports the best MSE on ETTh1 (0.4419), ETTh2 (0.3722), ETTm1 (0.3788), and ETTm2 (0.2825), and second-best Weather performance (0.2538) behind iTransformer at 0.2530 (Jeon, 7 Dec 2025). ms-Mamba reports average MSE 0.406 with fixed scales and 0.402 with learnable scales on Traffic, improving over S-Mamba at 0.414 (Karadag et al., 10 Apr 2025). DMamba reports ETTh2 average MSE 0.318 versus 0.381 for S-Mamba and PEMS08 average MSE 0.099 versus 0.148 for S-Mamba, attributing the gain to assigning Mamba only to the seasonal branch (Chen et al., 9 Feb 2026). ASGMamba reports 21 first-place MSE scores and 27 first-place MAE scores across its benchmark suite while keeping strict $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$4 complexity (Li et al., 2 Feb 2026).

Domain-specific systems show the same pattern. In minute-level stock forecasting with LLM sentiment, Mamba is reported as faster and better than Reformer for every LLM source tested, with the best configuration reaching MSE 0.1367 using LLaMA 3.3–70B sentiment (Kadiyala et al., 14 Sep 2025). In multichannel traffic prediction, MCST-Mamba reports MAE/RMSE $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$5 on PEMS-D4 and $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$6 on PEMS-D8 while using 0.49M parameters and predicting speed, flow, and occupancy jointly (Hamad et al., 5 Jul 2025). In stock cross-sectional forecasting, HIGSTM reports IC 0.0791, 0.0708, and 0.0918 on CSI500, CSI800, and CSI1000, respectively, together with the best Sharpe ratio on all three datasets (Yan et al., 14 Mar 2025).

Probabilistic evaluation adds a different perspective. Mamba-ProbTSF reports KL divergence on the order of $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$7 for synthetic data and $$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$8 for real-world data, and finds that on electricity and traffic the true trajectory stays within the predicted uncertainty interval at the two-sigma level about 95% of the time (Pessoa et al., 13 Mar 2025). This is a different notion of forecasting quality from pointwise MSE, but it reinforces the view that Mamba forecasters can be extended beyond deterministic regression.

5. Design tensions, misconceptions, and failure modes

The literature does not support the view that simply replacing attention with Mamba is sufficient. MambaTS explicitly reports that directly swapping Mamba into PatchTST or iTransformer degrades performance, and then attributes the degradation to causal-convolution mismatch, overfitting of selective parameters, and scan-order sensitivity (Cai et al., 2024). Likewise, S-Mamba performs best on large-$$h_t = \bar{A} h_{t-1} + \bar{B} x_t, \qquad y_t = C h_t.$$9, strongly correlated, often periodic datasets, but on low-dimensional or weak-correlation datasets such as parts of ETT and Exchange, linear models or iTransformer remain competitive (Wang et al., 2024). A plausible implication is that Mamba’s linear-time advantage does not by itself resolve the representation problem; tokenization, scan geometry, and inductive bias remain decisive.

A second misconception is that selective SSMs automatically handle non-stationarity. Several later models are built around the opposite claim. AdaMamba argues that raw or lightly normalized Mamba still “sees the raw series” and therefore benefits from adaptive multi-scale detrending before sequence modeling (Jeon, 7 Dec 2025). DMamba argues that trend and seasonal components should not share the same model complexity, and reports worse results when Mamba is assigned to the trend branch or to both branches indiscriminately (Chen et al., 9 Feb 2026). ASGMamba argues that vanilla Mamba can waste state capacity on high-frequency noise, then introduces local spectral gating to suppress those components before they reach the recurrent state (Li et al., 2 Feb 2026). Collectively, these results suggest that successful Mamba forecasters often rely on front-end conditioning rather than on the SSM alone.

A third tension concerns global context. MAT frames Mamba as strong on long-range temporal structure but weaker on short-range dependencies, and therefore combines it with Transformer attention (Zhang et al., 2024). DC-Mamber makes a related but more specific claim: Mamba is effective for channel-independent intra-variable modeling, whereas linear attention is better suited to channel-mixing global temporal aggregation (Fan et al., 6 Jul 2025). These hybrid models do not reject Mamba; rather, they delimit the conditions under which pure selective SSMs are sufficient.

Uncertainty modeling exposes additional limitations. Mamba-ProbTSF finds that using S-Mamba as the variance network leads to severely over-estimated and unstable uncertainty on real data, so the recommended design is a dual-network system with Mamba for the mean and a fully connected network with softplus for the variance (Pessoa et al., 13 Mar 2025). The same paper also identifies Brownian motion as a failure case: the model does not correctly learn the $B_t$0 growth law and yields poor calibration. This indicates that a Mamba forecaster can be well matched to “deterministic dynamics + noise” yet poorly matched to purely stochastic dynamics.

6. Research directions and broader significance

The research trajectory points toward three broad directions. The first is foundation-model generalization. Mamba4Cast shows that synthetic-prior pretraining with Mamba2 can support zero-shot forecasting across 17 datasets without any target-domain fine-tuning (Bhethanabhotla et al., 2024). TSMamba shows that transfer from a pretrained Mamba LLM can reduce the amount of time-series pretraining data required for a competitive foundation model (Ma et al., 2024). ss-Mamba adds semantic index embeddings and KAN-based time encoders, suggesting a path toward cross-series generalization that is conditioned not only on values and timestamps but also on series identity semantics (Ye, 3 Jun 2025).

The second direction is structured conditioning. HIGSTM conditions Mamba’s selective parameters on macro information derived from index-guided decomposition (Yan et al., 14 Mar 2025). MCST-Mamba conditions forecasting on adaptive spatio-temporal embeddings and separate temporal/spatial Mamba pathways (Hamad et al., 5 Jul 2025). ASGMamba conditions Mamba inputs on patchwise spectral energy (Li et al., 2 Feb 2026). This suggests that future Mamba forecasters are likely to become increasingly context-aware, with external or latent signals entering the selective SSM through $B_t$1, $B_t$2, $B_t$3, or related gating paths.

The third direction is modular probabilistic and hybrid forecasting. AdaMamba is described as compatible with probabilistic extensions (Jeon, 7 Dec 2025), while Mamba-ProbTSF provides one concrete route through Gaussian likelihood training (Pessoa et al., 13 Mar 2025). Hybrid Mamba-attention systems such as MAT and DC-Mamber indicate that selective SSMs and attention need not be treated as mutually exclusive (Zhang et al., 2024, Fan et al., 6 Jul 2025). This suggests that the long-term significance of the Mamba forecaster may lie less in a single winning architecture than in a broad reorganization of forecasting models around linear-time state-space cores, with decomposition, graph learning, semantic conditioning, or attention layered on top when the task requires them.

In that sense, Mamba Forecaster is best understood as a research program: an attempt to retain the representational advantages of modern sequence models while replacing quadratic attention with selective state-space dynamics, and then compensating for the resulting inductive-bias gaps through carefully designed normalization, tokenization, decomposition, or hybridization.