arXiv CSopen access

RAVEN: A Regime-Aware Variable-context Expert Network for Financial Time Series Forecasting

RAVEN: A Regime-Aware Variable-context Expert Network for Financial Time Series Forecasting Cheng He1,2 , Zhenyu Guan2 , Xijie Liang2 , Defu Lian1∗ , Jiajia Li3∗ , Enhong Chen1 , Patrick P. C. Lee4 , Geng Hu5 , Zehao Chen2 1 University of Science and Technology of China, China

2 Shanghai Black Wing Asset Management Co., Ltd., China

3 College of Sciences, Shanghai University, China 4 The Chinese University of Hong Kong, China

arXiv:2606.24062v1 [cs.LG] 23 Jun 2026

5 Qitan Technology Co., Ltd., China

reformulate the problem as the regression of log-returns: rt = ln(Ct /Ct−1 ) [13], [15]. This transformation shifts the modeling objective from tracking absolute values to capturing price innovations [15], the unpredictable stochastic components driven by the arrival of new market information. While logreturns are statistically more stable than raw prices, they still exhibit exceptionally low SNR and heavy-tailed distributions, making accurate regression a challenging task [13]. Historically, financial time-series analysis has been dominated by tree-based ensembles such as XGBoost [6] and LightGBM [17], descendants of the gradient boosting framework [12]. They excel at modeling non-linear interactions over handcrafted technical features, but treat each forecast as a static tabular problem and ignore the inherent temporal topology of market regimes. Subsequent deep-learning architectures, from MultiLayer Perceptron through Recurrent Neural Networks [10] to Long Short-Term Memory networks [16] and Gated Recurrent Unit [7], restore a notion of temporal memory through recurrence and gating, yet remain biased toward recent observations and often fail to distinguish transient market noise from longterm structural regime shifts. Recently, Transformer-based models, from Informer [45], PatchTST [26], TimesNet [36], and iTransformer [22] to frequency-domain variants such as FredFormer [27], and WPMixer [25], have enhanced general time-series forecasting by leveraging attention to capture long-range dependencies. However, when applied to financial markets, these models inherit a structural bottleneck that is rarely examined: the I. I NTRODUCTION reliance on a fixed-length historical context window L. In Financial time series forecasting is a cornerstone of quanti- non-stationary financial environments, a static L creates an tative investment, supporting tasks from risk management to irreconcilable conflict: a short window lacks memory to span automated trading. Unlike well-known benchmark datasets in structural regime shifts, while a long window unavoidably the general time series domain, such as ETTh, ETTm, Weather, mixes stale information from a prior regime into the current Electricity, or Traffic [37], which often exhibit clear periodic prediction as additive noise. Classical econometric models already hinted at the value patterns and deterministic trends, financial data is noisy and non-stationary [23]. In this adversarial environment, predicting of adaptive multi-horizon reasoning. The Heterogeneous raw price levels Ct at time t is impractical: prices are not scale- Autoregressive model of realized volatility (HAR-RV) [8], invariant and cross-asset comparable, typically follow a random originally introduced for volatility forecasting, captures longwalk, and exhibit extremely high autocorrelation, leading to memory structure by linearly aggregating daily, weekly, and spurious regression and inflated in-sample performance. To monthly rolling averages, demonstrating that multiple fixed capture meaningful predictive signals, existing approaches look-back horizons carry complementary temporal information that no single-horizon model can subsume. HAR-RV and *Corresponding authors its descendants, however, commit to a designer-fixed set of

Abstract—Financial time series forecasting presents structural challenges absent from standard benchmarks. Log-returns are nonstationary, exhibit exceptionally low signal-to-noise (SNR) ratios, and are governed by regime-dependent temporal dependencies. We identify a key limitation of state-of-the-art (SOTA) time series models in financial settings. A fixed context window is mismatched to the time-varying optimal look-back of non-stationary price processes. We propose the Regime-Aware Variable-context Expert Network (RAVEN), a Mixture-of-Experts framework designed to adaptively determine the temporal context for each input sample. Instead of relying on a fixed look-back horizon, RAVEN constructs a hierarchy of nested contiguous windows whose lengths are determined by the data itself. Specifically, RAVEN scores patches by learned importance in reverse chronological order and applies the Cumulative Importance Thresholding (CIT) mechanism to derive nested prefix windows, each routed to a scale-specialized expert. A Global Compressed Representation (GCR) branch runs in parallel over the full context, preserving global temporal coherence that local experts cannot guarantee. Because the nested routing induces structured overlap among expert inputs, we introduce a Correlation-Aware Weighting (CAW) to align variable-length expert outputs and penalize pairwise cosine similarity prior to aggregation. Experiments on cumulative logreturn prediction (HS300, S&P500) and fund sales forecasting demonstrate that RAVEN achieves SOTA performances, improves Pearson correlation by 9.2% on HS300 and 20.2% on S&P500, and reduces MSE by 18.2% on fund sales forecasting, while achieving the best results in 14 of 16 metrics on four PEMS traffic benchmarks. Index Terms—Financial Time Series Forecasting, Mixture-ofExperts, Adaptive Context Selection, Non-stationary Financial Data

work designed for adaptive context modeling in financial time series forecasting. The core of RAVEN lies in its learnable patch weighting and selection mechanism. Unlike static methods that adopt a single fixed context length, RAVEN dynamically evaluates the importance of each historical patch. It accumulates these scores in reverse chronological order against Cumulative Importance Thresholding (CIT) based thresholds, and generates a nested sequence of consecutive look-back windows. Each window is routed to a dedicated expert working at its corresponding temporal scale. All windows are anchored at the most recent patch, ensuring temporal coherence of positional attention within each expert. To ensure that local specialization does not come at the cost of global coherence, we introduce a Global Compressed Representation (GCR) branch that runs in parallel over the full context. It distills a holistic global view that complements the local experts’ selective, scale-specific processing. Furthermore, the nested routing topology creates structured overlap across expert inputs. To address this issue, we propose the shape-aligned fusion with Correlation-Aware Weighting (CAW) strategy. It decorrelates expert representations prior to aggregation and eliminates redundant noise, yielding reliable multi-resolution forecasts.

(a) HS300 constituent 600176.SS (daily log-returns, 2020–2024)

(b) PEMS03 traffic flow (5-min)

Figure 1: CWT scalograms for multi-scale analysis. Financial data (a) exhibits non-stationary energy distribution with no fixed periodicity, while traffic data (b) shows stable, periodic patterns.

Our main contributions are summarized as follows: • Dynamic Context Paradigm: We identify the critical

horizons and to a linear functional form; the complementary horizons themselves, and the optimal way to combine them, remain hand-crafted. More recent deep-learning multi-period research, e.g. MLF [42], extend this multi-period intuition with sophisticated attention mechanisms and serves as our most competitive alternative. Nevertheless, MLF still relies on pre-defined periods and equally distributed patches. Such static designs prevent it from adaptively perceiving the optimal context in dynamic markets. To empirically verify this claim, we apply the Continuous Wavelet Transform (CWT) as a multi-scale diagnostic:   Z +∞ 1 ∗ t −b W f (a, b) = p f (t) ψ dt, a |a| −∞

limitations of static, fixed-length context windows in nonstationary financial environments and propose RAVEN. This framework adaptively adjusts the receptive field to time-varying market dynamics. It learns data-dependent look-back windows by accumulating patch importance in reverse order under CIT-based thresholds. • Dual-View Architecture: We design a dynamic MoE backbone augmented with a GCR branch. The architecture balances local specialization and global context modeling. Experts with distinct scales handle variable-length patches for fine-grained local perception. Meanwhile, the GCR branch captures holistic historical information to preserve global coherence. • Redundancy Mitigation Strategy: We introduce ShapeAligned Fusion and CAW. By dynamically compressing and decorrelating heterogeneous expert outputs, this strategy explicitly filters noise from overlapping input segments, enabling efficient utilization of MoE parameters under the low SNR of financial time series. • Extensive Evaluation and Deployment progress: We conduct extensive evaluations on cross-market cumulative log-return prediction. Compared with SOTA baselines, RAVEN improves the Pearson correlation by 9.2% on HS300 and 20.2% on S&P500, and reduces MSE by 18.2% in fund sales forecasting. Cross-domain tests on four PEMS traffic datasets further verify its generalization ability, achieving best performance results across 14 out of 16 evaluated metrics. Under realistic backtest conditions, RAVEN-driven strategies outperform our production baseline by over 10% in cumulative returns, and the system is currently advancing through final online integration.

where scale a is inversely proportional to frequency and b denotes temporal position. Figure 1 visualizes the scalograms of two representative series. For the HS300 constituent 600176.SS (Figure 1a), energy concentration migrates unpredictably across scales within the five-year horizon. High-frequency components dominate in 2020, shift toward lower-frequency bands from 2021 to 2022, and return to high-frequency dominance by late 2023. No stable periodic structure persists at any scale. In contrast, the PEMS03 traffic series (Figure 1b) exhibits time-invariant energy bands at scales ranging from 200 to 260, reflecting a fixed daily periodicity that holds uniformly across the entire observation period. This divergence reveals that the dominant temporal scale governing predictive information in financial data is itself non-stationary. Thus, a fixed context window mechanism introduces an inductive bias that is mismatched to the underlying data-generating process. To bridge this gap, we propose RAVEN (Regime-Aware Variable-context Expert Network), a novel MoE-based frame-

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Table I: Summary of notations.

Objective. The goal of RAVEN is to learn a mapping fθ : RLmax ×D → R, parameterized by θ , such that the prediction (H) ŷt = fθ (Xt ) accurately approximates the true cumulative return (defined in Equation 3) over the out-of-sample test distribution [9], [35].

Notation

Explanation / Description

D Lmax H B Xt Ct rt (H) yt (H) ŷt

Total dimension of the input channels Maximum historical look-back window length Forecast horizon for cumulative log return prediction Batch size Market state input matrix observed at time t Asset closing price at time t One-step log-return The H-period true cumulative log-return The H-period forecasted log-return

plen N d E

Fixed patch length Total number of patches derived via ⌊Lmax /plen ⌋ Embedded feature dimension Joint patch embedding matrix

si s̃i K τk Ψi Gk ℓk hk

Raw importance score assigned to the i-th embedded patch Softmax-normalized patch importance Total number of experts The k-th cumulative sum threshold Chronological reverse-cumulative patch importance score Monotone patch index prefix subset to the k-th expert Dynamic selected patch number for expert k Variable-length output hidden sequence

zk R rk αk wk λ zlocal zglobal

Dimension-aligned representation vector Expert cosine similarity to evaluate representation overlap Accumulated expert redundancy penalty score Routing confidence of each expert Final adaptive gate weight Learnable redundancy penalty Aggregated representation synthesized from local experts Compressed holistic feature vector from the global branch

LMSE Lent Ldiv

Log return forecasting loss utilizing mean squared error Router negative-entropy regularization penalty Expert representation diversity regularizer

B. Overall Architecture Figure 2 illustrates the overall architecture of RAVEN. Given a look-back window X ∈ RLmax ×D , the model produces a scalar (H) H-period cumulative log-return forecast ŷt through three functionally distinct stages: • Preprocessing (§II-C) normalizes the input instances, processes each channel independently, and partitions the lookback window into an embedded patch sequence E = [e1 , . . . , eN ] ∈ RN×d . • Dual-Branch Backbone (§II-D) consumes E through two parallel pathways. The local branch routes nested contiguous patch prefixes to K scale-specialized experts via a CITthresholded router. The global branch distills the entire lookback window into a single compressed representation. • Output Projection (§II-E) aligns the variable-length expert outputs to a common dimensionality, aggregates them via a CAW scheme, fuses the result with the global representation, and projects to the scalar forecast through an MLP head. We elaborate on each module in the following sections. C. Preprocessing Instance normalization. We normalize each input instance to zero mean and unit variance over the temporal dimension of the look-back window. This removes sample-level distributional shift, a well-known obstacle in non-stationary financial series, while preserving the temporal structure of returns [18].

II. RAVEN D ESIGN A. Problem Formulation We consider the task of multi-horizon return forecasting from multivariate financial time series. Let xt ∈ RD denote the D-dimensional market state observed at time t, comprising standard market variables (e.g., OHLCV, bid-ask spread) and engineered factors. From the closing price Ct , we derive the one-step log-return: rt = ln(Ct /Ct−1 ),

Channel-independent processing. The normalized window X ∈ RLmax ×D may contain heterogeneous channels, e.g., OHLCV bars, bid-ask spreads, engineered factors. Following [26], we process each channel independently through shared linear projections. This design prevents spurious information leakage across semantically distinct channels and allows the model to learn channel-specific temporal dynamics.

(1)

Patch partitioning. We segment the look-back window into N = ⌊Lmax /plen ⌋ non-overlapping patches {P1 , . . . , PN } [26] arranged in reverse chronological order (most recent patch first). Each patch Pi ∈ R plen is linearly projected to a ddimensional embedding and augmented with a sinusoidal positional encoding:

which encodes price innovations induced by the arrival of new market information [13], [15]. Input. Given a maximum look-back length Lmax , an input instance at time t is defined as Xt = [xt−Lmax +1 , . . . , xt ]⊤ ∈ RLmax ×D .

(2)

ei = PatchEmbed(Pi ) + PE(i) ∈ Rd , i = 1, . . . , N.

Target. Given a forecast horizon H, the prediction target is the H-period cumulative log-return: (H)

yt

(4)

The resulting sequence E = [e1 , . . . , eN ] ∈ RN×d serves as the shared input to both branches of the backbone.

H

= ∑ rt+h = ln(Ct+H /Ct ) ∈ R,

D. Dual-Branch Backbone

(3)

h=1

The backbone comprises two parallel branches that jointly consume E: a local branch that performs dynamic, scale-aware MoE routing over nested patch prefixes, and a global branch

which corresponds to the realized holding-period return of a position entered at t and liquidated at t + H.

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Figure 2: Overview of RAVEN. The pipeline consists of three modules. Preprocess applies instance normalization, channel-independent processing, and patch partitioning to produce embedded patches E = [e1 , . . . , eN ]. Backbone operates via two parallel branches. (i) The local adaptive branch scores patch importance and accumulates scores in reverse chronological order against CIT-based thresholds, generating K nested contiguous look-back windows {Gk }. Each window is processed by a scale-specialized expert, and the variable-length outputs are shape-aligned via average pooling into fixed-dimensional vectors for aggregation into zlocal . (ii) The GCR branch captures holistic historical dependencies across the full sequence E via a Self-Attention layer, then distills a global context vector zglobal through average pooling. Output Projection concatenates [zlocal ; zglobal ] and projects them through an MLP head to output the final H-period cumulative log-return (H) ŷt . The nested routing topology introduces collinearity among experts, which is jointly suppressed by the CAW scheme and the expert diversity regularizer.

that maintains a holistic compressed view of the full look-back dependent cardinalities ℓk = |Gk |, always anchored at the most window. We describe each branch in turn. recent patch. Because accumulation starts from the present and Local branch: Patch-weighted MoE. The local branch proceeds backward, each expert receives the ℓk most informative contiguous patches, a property critical for positional attention comprises five steps. (i) Patch importance scoring. A lightweight two-layer MLP to remain temporally coherent. We set K=3, and the thresholds assigns each embedded patch a scalar importance score si = (τ1 , τ2 , τ3 ) = (0.3, 0.6, 0.9) by default. (iii) Scale-specialized experts. Each group Gk is processed φ (ei ) for i ∈ {1, . . . , N}, where φ (·) denotes the MLP scoring network with GeLU activation. These scores are then softmax- by an independent three-layer encoder Encoderk :
normalized over the sequence to yield a categorical distribution: hk = Encoderk {ei }i∈Gk ∈ Rℓk ×d . (7) exp(si ) s̃i = N , i = 1, . . . , N. (5) Since G1 is the shortest (most recent) prefix and GK the longest, ∑ j=1 exp(s j ) expert Encoder1 naturally specializes in short-term dynamics while Encoderk captures longer-term regime-scale structure, Intuitively, s̃i reflects the model’s learned belief about how intermediate experts span intermediate horizons. This constiinformative patch i is for the downstream forecast. tutes a fundamentally different form of specialization from (ii) CIT-thresholded routing. Unlike conventional MoE decontent-based MoE routing: RAVEN experts are differentiated signs that route individual tokens to experts [11], [30], our router by temporal scale, not by token content. Since Transformer accumulates s̃ from the most recent patch backward, constructencoders natively handle variable-length sequences, no padding ing a reverse-chronological cumulative importance curve, and is required within any expert. segments it at K ordered thresholds 0 < τ1 < τ2 < · · · < τK ≤ 1: (iv) Shape-aligned pooling. To align the outputs from i  different scale-specialized experts into a unified space for Gk = i ∈ {1, . . . , N} : Ψi ≤ τk , Ψi = ∑ s̃ j . (6) downstream fusion, we apply a parameter-free Shape-aligned j=1 Pooling that averages over the patch dimension: where k = 1, . . . , K. By construction, G1 ⊆ G2 ⊆ · · · ⊆ GK forms zk = AvgPool(hk ) ∈ Rd , (8) a monotone chain of contiguous patch prefixes with data-

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where AvgPool(·) averages over the ℓk patch embeddings in Forecasting loss. Consistent with the regression target defined hk ∈ Rℓk ×d , collapsing them into a fixed d-dimensional vector. in Eq. (3), the primary objective is the mean squared error This parameter-free design avoids overfitting risk and produces between the predicted and realized H-period cumulative loga uniform representation for the subsequent correlation-aware return: 1 B (H) (H)
2 gate. LMSE = ∑ ŷi − yi , (15) B i=1 (v) CAW_based expert aggregation. Because the expert groups are nested (G1 ⊆ · · · ⊆ GK ), their representations {zk } where B denotes the batch size. are inherently correlated: longer-horizon experts operate on supersets of the inputs to shorter-horizon experts. A naive Router entropy regularization. The CIT-thresholded router uniform or softmax gate would amplify this redundancy, operates on a softmax-normalized patch-importance distribution which is particularly harmful under the characteristically low s̃. Without regularization, the softmax parameterization tends to SNR of financial returns. To mitigate this, we compute the amplify initial score differences, concentrating all probability pairwise cosine similarity matrix R ∈ RK×K with entries mass on a few patches, typically the most recent ones. This R jk = z⊤j zk /(∥z j ∥∥zk ∥), derive the per-expert positive redun- router collapse causes the cumulative sum to reach all thresholds dancy score rk = ∑ j̸=k max(R jk , 0), and modulate a raw routing {τk } within the first few patches, truncating every expert group into nearly identical short prefixes and degenerating the MoE confidence αk with an exponential penalty: toward a single-scale model. We counteract this with a negativeαk exp(−λ rk ) entropy penalty: wk = K , λ ≥ 0 (learnable). (9) N ∑k′ =1 αk′ exp(−λ rk′ ) Lent = ∑ s̃i log s̃i , (16) i=1 The local representation is then obtained as the weighted aggregate: which is minimized at the uniform distribution. A high-entropy zlocal = ∑Kk=1 wk zk ∈ Rd . (10) routing distribution causes the cumulative importance curve to increase more gradually, yielding balanced prefix lengths Global branch: GCR. To preserve a holistic macroeconomic across experts and enabling the intended short-, medium-, and view alongside fine-grained local experts, RAVEN incorporates long-horizon specialization. a GCR module. It first captures comprehensive historical Expert diversity regularization. The nested structure G1 ⊆ dependencies across the entire sequence of embedded patches · · · ⊆ GK means longer-horizon experts observe a strict superset E ∈ RN×d via a Self-Attention layer, then compresses the of patches seen by shorter-horizon ones. Without explicit attended representations into a single vector through average encouragement, experts may converge to similar representations pooling: (representation collapse), causing zlocal to degenerate toward a Esa = Self-Attn(E), (11) single expert’s output. We penalize the off-diagonal entries of the expert cosine-similarity matrix: zglobal = AvgPool(Esa ) ∈ Rd , (12) 2 Ldiv = R − IK F , where AvgPool(·) averages over the N patch positions in Esa ∈ (17) z⊤j zk RN×d , yielding a unified global context vector. The global R jk = , ∥z j ∥2 ∥zk ∥2 branch thus serves as an information-preserving complement to the local branch’s selective, scale-specialized view. which drives expert representations toward pairwise orthogonality. While the CAW (Eq. 9) down-weights redundant experts E. Output Projection at inference time, Ldiv structurally prevents redundancy during The final prediction head fuses the two complementary training. The two mechanisms are complementary. representations via concatenation and projects to the scalar Complementary regularization. Lent and Ldiv address orthogforecast: onal failure modes. The entropy term prevents routing collapse
on the input side, ensuring every expert receives sufficiently (H) ŷt = MLP Concat(zlocal , zglobal ) ∈ R. (13) rich context. The diversity term prevents representation collapse For multi-horizon forecasting, the output dimension of the on the output side, ensuring experts produce non-redundant (H ) MLP is extended to M, yielding one prediction ŷt m per target representations despite overlapping inputs. Their joint use is critical for stable training in the low-SNR financial regime (see horizon Hm . ablation in §III-D). F. Training Objective G. System Deployment We optimize a composite loss that combines the primary Figure 3 illustrates the deployed system architecture, conregression objective with two auxiliary regularizers targeting sisting of an offline development environment and an online the specific failure modes of scale-aware MoE routing under production environment. low SNR: Offline environment. RAVEN is trained on historical priceL = LMSE + λent Lent + λdiv Ldiv . (14) volume data stored in a financial data lake. The trained model

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Table II: Dataset statistics. Ticker/Sensors denotes the number of stocks or funds in financial datasets or sensors in traffic datasets. Timepoints reports the total available data samples across all entities and time steps. Domain

Ticker/Sensors Timepoints Granularity

HS300 Financial S&P500 Fund

892 4694 306

18,836,466 104,692,416 647,892

1-Day 1-Day 1-Day

PEMS03 PEMS04 PEMS07 PEMS08

358 307 883 170

9,382,464 15,649,632 24,921,792 9,106,560

5-Min 5-Min 5-Min 5-Min

Traffic

Figure 3: Production deployment pipeline of RAVEN in a quantitative trading system. The offline phase handles model training and backtesting validation on historical data. The online phase appends newly available market data after each close, generates return predictions via daily inference, optimizes portfolio allocations, and routes orders through pre-trade risk checks to execution venues. A production monitor triggers the next offline retraining cycle upon sustained performance drift.

Dataset

A. Experimental Settings

Datasets. We conduct experiments on three categories of datasets. Table II summarizes the dataset statistics. (1) FinMultiTime [39]: A cross-market financial dataset containing daily price and volume data for 892 HS300 constituents and 4,694 S&P 500 constituents, spanning from 2009 to 2024. This dataset covers diverse market regimes, including bull markets, bear markets, and high-volatility crisis periods then undergoes rigorous backtesting that incorporates portfolio across both Chinese and US equity markets. optimization, risk constraints, and transaction cost modeling (2) Fund [42]: Daily user transaction records for mutual to validate out-of-sample performance. This offline cycle for fund subscriptions and redemptions on Alipay, spanning from model training is re-executed periodically, or when production January 2015 to January 2023. This dataset captures retail monitoring signals significant performance degradation. investor behavior dynamics and fund-level return patterns. (3) PEMS (03, 04, 07, 08) [14]: Four widely used traffic Online environment. Once deployed online, deployed forecasting models operates on a daily inference cycle. After flow datasets collected from the California Department of each market close, newly available data is appended to the Transportation Performance Measurement System (PeMS). streaming database and fed into models to generate next-period Each dataset records aggregated traffic flow measurements return predictions across the target tickers. Predictions are from highway sensor networks at 5-minute intervals. These consumed by a portfolio optimization module that solves for datasets exhibit strong temporal non-stationarity due to rushtarget allocation weights subject to risk and turnover constraints. hour patterns, weekday/weekend shifts, and seasonal variations, Optimized orders pass pre-trade risk checks at the trading serving to validate the generalizability of RAVEN beyond console before routing to execution venues via broker bridges. financial domains. A production monitor continuously tracks realized prediction Baselines. We compare against twelve representative methods accuracy and portfolio; sustained drift beyond predefined spanning diverse architectural strategies for temporal modeling: thresholds triggers the next offline retraining cycle. • Static Patching models: PatchTST [26] operates on fixed uniform patches, while Patch-Concat and Patch_Ensemble Deployment Status and Impact. At present, the offline modextend it via naive concatenation and ensembling over eling and backtesting validation phases have been completed. different lengths. Under identical and realistic backtest conditions, RAVENdriven strategies successfully outperform our single production • Predefined Multi-period models: MLF [42] utilizes explicbaseline by over 10% in cumulative returns. The system is itly predefined multi-period inputs combined with inter-period currently advancing through the final stages of live production redundancy filtering. integration, with active engineering efforts focused on online • Cross-variate interactions: iTransformer [22] and Crossstrategy ensembling and live out-of-sample monitoring prior former [43] capture global inter-sensor dependencies through to full-scale capital allocation. variate-as-token and cross-dimensional attention mechanisms. • Hierarchical Multi-resolution: PathFormer [5], Scaleformer [29], and NHits [4] extract multi-scale representations III. E XPERIMENTS internally through predefined hierarchical pathways, iterative refinement, or interpolation. We evaluate RAVEN on financial log-return prediction and general time series forecasting tasks to demonstrate the • Frequency-domain transformations: TimesNet [36], FEDeffectiveness of dynamic look-back selection and correlationformer [47], and FiLM [46] tackle temporal dynamics via aware expert aggregation. 2D-variations and spectral frequency decompositions.

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All baselines are evaluated under identical data splits and preprocessing protocols for a fair comparison. Implementation details. RAVEN uses K=3 experts with CITbased thresholds (τ1 , τ2 , τ3 ) = (0.3, 0.6, 0.9), patch length plen = 16, and embedding dimension d = 128. Each expert is a 3layer encoder. We optimize with AdamW for 60 epochs using cosine annealing. Auxiliary loss weights are λent = 0.1 and λdiv = 0.01. All experiments run on a single NVIDIA A100 40G GPU. Evaluation metrics. For HS300 and S&P500, we train on 2009– 2019 and evaluate on 2020–2024 via rolling out-of-sample prediction of H=10 day cumulative log-returns. We report three complementary metrics: (1) Pearson correlation (Corr) between predicted and realized returns, measuring directional accuracy; (2) Mean Squared Error (MSE) of normalized predictions, capturing magnitude fidelity; and (3) Information Coefficient Information Ratio (ICIR), defined as the mean of the crosssectional IC divided by its standard deviation across rebalancing periods, quantifying the stability of the predictive signal. For peryear evaluation (Table III), all three metrics are computed within each calendar year. For the overall summary (Table IV), Corr and ICIR are computed over the entire 5-year test period (2020– 2024) to reflect long-horizon stability, while MSE is reported as the multi-year average. For Fund, we forecast fund sales at horizons H ∈ {1, 5, 8, 10} days and report MSE and Weighted Mean Absolute Percentage Error (WMA for short). For general benchmarks, we adopt short-term horizons H ∈ {12, 24} and report MSE and MAE.

Figure 4: Cumulative return advantage of RAVEN over baselines on HS300, from 2020 to 2024. ∆(·) denotes the cumulative return of RAVEN minus that of baseline (·). All curves show a persistent upward trend across varying market regimes.

dataset-metric pairs. The consistently higher ICIR suggests that RAVEN produces not only stronger average predictions but also more stable predictive signals across rebalancing periods. This stability is particularly desirable for sequential decision-making systems that rely on robust ranking signals. To further validate that superior prediction accuracy translates into real-world investment gains, we conduct backtesting on HS300 from January 2020 to December 2024 using Qlib [40]. Qlib is an open-source AI-driven quantitative investment platform with standardized data pipelines and strategy simulation. We construct a cross-sectional portfolio management scheme. At each rebalancing point, i.e. every 10 trading days, constituents are ranked by predicted score in descending order, and a fixed-size portfolio of K=30 stocks is maintained. A drop-N strategy (Ndrop =30) limits turnover, as positions are only closed when their predicted rank falls significantly below the top-K threshold. Execution is simulated via Qlib’s SimulatorExecutor at daily frequency with an initial capital of 100M RMB and default transaction costs, including stamp duty and commission. We report the cumulative return of RAVEN minus that of each baseline under the identical strategy and period. Figure 4 shows the cumulative return advantage of RAVEN over each baseline. All gaps exhibit a persistent upward trend over the five-year period despite short-term fluctuations during volatile market phases, indicating sustained outperformance rather than episodic gains. The final cumulative return advantage over the strongest baseline (MLF) is +12.79%, while the gap over PatchTST reaches +38.45%. For the remaining baselines, the gaps are Patch-Ensemble (+34.41%), FiLM (+23.41%), PathFormer (+20.38%), PathConcat (+20.28%), and NHits (+19.46%). The steadily growing gaps confirm that adaptive dynamic routing delivers consistent predictive advantage across both trending and volatile market regimes.

B. Financial Time Series Forecasting Financial time series exhibit non-stationary dynamics and regime-dependent SNR ratios, making fixed look-back approaches particularly fragile. We evaluate RAVEN on two distinct financial forecasting tasks: 10-day period stock cumulative log return prediction and fund sales forecasting. Results on FinMultiTime. Table III reports per-year results on HS300 and S&P500. On HS300, RAVEN ranks first or second in every year-metric cell, achieving 7 first-place and 8 secondplace rankings out of 15. On S&P500, RAVEN achieves the highest Corr and ICIR across all 5 years, and the lowest MSE in 4 of 5 years, yielding 14 first-place rankings out of 15 cells. Overall, RAVEN obtains the top rank in 21 out of 30 total year-metric-dataset cells (70%), followed by MLF and NHits at 4 cells each. These results confirm that data-driven dynamic patch routing generalizes consistently across both datasets and all evaluation periods without manual scale configuration. Table IV summarizes the aggregated performance over the entire five-year test period from 2020 to 2024. On HS300, RAVEN achieves a Corr of 0.0390, an ICIR of 0.3932, and an MSE of 0.9905. Compared with the second-best baseline, MLF, it improves Corr by 9.2% and ICIR by 9.9%, while reducing MSE by 0.27%. On S&P500, RAVEN attains a Corr of 0.0363, an ICIR of 0.5980, and an MSE of 1.001. It outperforms MLF by 20.2% in Corr and 7.2% in ICIR, while reducing MSE by 1.5%. Across the two datasets, RAVEN ranks first in all six

Results on Fund. Table V reports fund sales predictions across four horizons, where RAVEN consistently achieves the best MSE and WMA. Specifically, RAVEN reduces the

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Table III: Performance comparison on HS300 and S&P500 (2020–2024). Corr and ICIR: higher is better (↑); MSE: lower is better (↓). Best in bold, second underlined. Dataset: HS300 Model

RAVEN MLF NHits PathFormer PatchTST Patch-Concat Patch-Ensemble FiLM

2020

2021

2022

2023

2024

Corr

MSE

ICIR

Corr

MSE

ICIR

Corr

MSE

ICIR

Corr

MSE

ICIR

Corr

MSE

ICIR

.0567 .0525 .0338 .0462 .0322 .0373 .0320 .0372

.9706 .9647 .9885 .9759 .9893 .9803 .9908 .9818

.5943 .5457 .3222 .5438 .3277 .5082 .3477 .5282

.0292 .0173 .0143 .0216 .0043 .0140 .0185 .0164

.9897 1.002 .9943 .9917 1.012 1.003 1.001 1.003

.1478 .1056 .1153 .1363 .0593 .1190 .0756 .1123

.0422 .0583 .0238 .0253 .0193 .0286 .0175 .0195

.9967 .9786 .9998 .9996 1.006 .9974 1.004 1.004

.5224 .5467 .4677 .4063 .4207 .4233 .4469 .4709

.0300 .0152 .0125 .0176 .0089 .0138 .0093 .0173

.9978 1.002 1.012 1.003 1.012 1.005 1.014 1.006

.3321 .2771 .3147 .3332 .2664 .2202 .2657 .3280

.0500 .0388 .0525 .0315 .0429 .0428 .0376 .0326

.9971 1.004 .9938 1.012 1.001 1.002 1.003 1.010

.3765 .3325 .3772 .3080 .3151 .3550 .3092 .3200

Dataset: S&P500 Model

RAVEN MLF NHits PathFormer PatchTST Patch-Concat Patch-Ensemble FiLM

2020

2021

2022

2023

2024

Corr

MSE

ICIR

Corr

MSE

ICIR

Corr

MSE

ICIR

Corr

MSE

ICIR

Corr

MSE

ICIR

.0339 .0268 .0268 .0258 .0195 .0242 .0302 .0275

1.003 1.027 1.015 1.027 1.042 1.027 1.017 1.022

.7256 .6515 .6423 .6337 .5616 .6254 .6742 .6524

.0365 .0283 .0301 .0212 .0219 .0262 .0275 .0193

.9989 1.023 1.001 1.039 1.032 1.023 1.021 1.036

.5892 .5420 .5475 .4737 .5016 .5154 .5263 .4724

.0426 .0350 .0379 .0297 .0225 .0234 .0314 .0322

.9985 1.011 .9957 1.028 1.037 1.032 1.021 1.018

.6078 .5689 .5827 .5204 .4837 .5132 .5298 .5511

.0405 .0339 .0310 .0397 .0305 .0324 .0342 .0302

1.002 1.008 1.007 1.006 1.014 1.011 1.007 1.014

.5481 .5149 .5025 .5394 .4850 .5041 .5114 .5091

.0283 .0207 .0221 .0220 .0126 .0186 .0243 .0230

1.001 1.013 1.007 1.009 1.026 1.013 1.009 1.013

.5795 .5128 .5143 .5070 .4431 .4713 .5290 .5127

Table IV: Overall average performance on HS300 and S&P500 (2020– 2024). Corr and ICIR: higher is better (↑); MSE: lower is better (↓). Best in bold, second underlined. Model RAVEN MLF NHits PathFormer PatchTST Patch-Concat Patch-Ensemble FiLM

Corr

HS300 MSE ICIR

Corr

S&P500 MSE ICIR

.0390 .0357 .0282 .0278 .0217 .0272 .0218 .0247

.9905 .9932 .9987 .9990 1.003 .9987 1.003 1.003

.0363 .0302 .0294 .0272 .0225 .0254 .0290 .0264

1.001 1.016 1.002 1.020 1.030 1.023 1.018 1.023

.3932 .3579 .3210 .3260 .2758 .3177 .2811 .3463

C. General Time Series Forecasting To evaluate the generalizability of RAVEN beyond financial domains, we conduct experiments on four traffic flow datasets, namely PEMS03, PEMS04, PEMS07, and PEMS08 [14]. As shown in Table VI, RAVEN achieves competitive results, securing the best performance in 14 of 16 evaluated metrics. The variate-as-token iTransformer emerges as the strongest secondbest baseline, consistently outperforming the pre-defined multiscale MLF. Traffic networks exhibit strict macroscopic spatial correlations, which allows iTransformer to excel by embedding historical series for global cross-sensor dependency capture. In contrast, MLF’s static temporal squeezing inadvertently disrupts these spatial connections. Despite the spatial dominance of traffic data, the overall superiority of RAVEN reveals that predictive gains from datadependent dynamic routing outweigh the lack of explicit spatial modeling. Traffic networks frequently suffer from abrupt, localized disruptions such as accidents or bottlenecks. iTransformer’s static global receptive field risks over-smoothing these transient temporal bursts. Conversely, RAVEN isolates these dynamics and adaptively assigns the optimal patch scale to each sensor’s immediate state. This confirms that even in spatially-dominated domains, granular temporal adaptability provides a crucial inductive bias for forecasting volatile sequences.

.5980 .5577 .5518 .5300 .4836 .5203 .5523 .5360

average MSE by 18.2% compared to the second-best MLF (32.42 vs. 39.62), maintaining stable gains from 14% to 21% across all horizons. Multi-scale architectures like PathFormer and Scaleformer perform similarly to single-scale methods, suggesting that implicit in-network multi-resolution modeling alone is insufficient. Explicit multi-period inputs with dynamic selection are imperative for capturing heterogeneous temporal patterns in transaction data. Moreover, fixed-window variants (Patch_E, Patch_C) consistently underperform MLF. This indicates that naively aggregating multi-period inputs without redundancy mitigation introduces correlated noise, negating the benefits of broader temporal context.

D. Ablation Study We ablate each component of RAVEN on HS300 to isolate individual contributions. Table VII reports year-by-year and

8

Table V: Performance comparison on Fund dataset. MSE (↓) and WMA (↓). Best in bold; second-best underlined. RAVEN

MLF

PatchTST

Patch-Ensemble Patch-Concat

NHits

FiLM

Scaleformer

PathFormer

MSE WMA

MSE

WMA MSE WMA MSE

WMA

MSE WMA MSE WMA MSE WMA MSE WMA MSE WMA

27.69 30.22 33.62 38.13

74.63 80.09 85.32 86.46

33.85 38.28 41.94 44.42

75.84 80.37 86.06 88.66

81.05 40.3 83.09 39.95 88.81 44.06 90.63 46.09

86.68 83.24 88.77 91.36

39.68 41.6 43.49 45.59

Avg. 32.42 81.63

39.62

82.73 41.96 85.90 42.60

87.51

42.59 87.89 44.75 86.14 45.04 90.81 43.38 87.00 41.29 85.46

1 5 8 10

36.68 40.28 44.71 46.18

85.87 87.14 88.08 90.46

36.53 40.91 44.81 56.73

80.29 83.93 89.23 91.12

46.12 96.1 35.54 80.75 42.86 85.35 40.43 83.74 39.9 82.58 44.57 89.12 43.97 87.62 44.17 88.67 46.62 92.67 45.75 89.63 45.56 89.82

Table VI: Short-term forecasting results on traffic datasets (MSE / MAE ↓). Best in bold; second-best underlined. PEMS03 Model

H = 12

RAVEN MLF PatchTST iTransformer NHits TimesNet FiLM Patch-Ensemble Patch-Concat Crossformer Scaleformer PathFormer FEDformer

PEMS04 H = 24

H = 12

PEMS07 H = 24

H = 12

PEMS08 H = 24

H = 12

H = 24

MSE

MAE

MSE

MAE

MSE

MAE

MSE

MAE

MSE

MAE

MSE

MAE

MSE

MAE

MSE

MAE

.067 .072 .099 .071 .083 .085 .089 .107 .103 .090 .086 .091 .126

.169 .184 .216 .174 .197 .192 .208 .239 .224 .203 .204 .209 .251

.091 .098 .142 .093 .112 .118 .120 .159 .131 .121 .109 .126 .149

.204 .227 .259 .201 .229 .223 .233 .285 .247 .240 .216 .237 .275

.074 .084 .105 .078 .081 .087 .079 .118 .096 .098 .088 .084 .138

.172 .194 .224 .183 .185 .195 .188 .247 .218 .218 .197 .190 .262

.093 .103 .153 .095 .098 .103 .106 .176 .157 .131 .120 .133 .177

.195 .233 .275 .205 .221 .215 .227 .290 .279 .256 .233 .231 .293

.072 .088 .095 .067 .083 .082 .092 .104 .094 .094 .096 .085 .109

.153 .165 .207 .165 .162 .181 .182 .221 .213 .200 .175 .173 .225

.086 .096 .150 .088 .094 .101 .117 .153 .143 .139 .105 .116 .125

.181 .207 .262 .190 .193 .204 .226 .267 .255 .247 .207 .219 .244

.077 .107 .168 .079 .114 .112 .124 .182 .149 .165 .131 .138 .173

.168 .192 .232 .182 .214 .212 .225 .246 .228 .214 .226 .215 .273

.110 .142 .224 .115 .169 .141 .195 .231 .192 .215 .174 .182 .210

.207 .246 .281 .219 .257 .238 .273 .298 .260 .260 .253 .258 .301

Table VII: Ablation study on HS300 (Pearson Corr ↑). Best in bold.

one full forward–backward pass over a batch and an inference iteration denotes one forward pass; memory denotes peak GPU memory during training. As shown in Figure 5, RAVEN 2020 0.0567 0.0550 0.0569 0.0573 0.0583 0.0584 0.0271 0.0260 0.0263 0.0290 0.0288 2021 0.0292 achieves a favorable balance between accuracy and efficiency. 2022 0.0422 0.0309 0.0313 0.0320 0.0321 0.0318 Compared with lightweight baselines MLF and PatchTST, 2023 0.0300 0.0193 0.0184 0.0204 0.0202 0.0199 RAVEN incurs moderate overhead in training time (77.89 ms 2024 0.0500 0.0432 0.0441 0.0434 0.0449 0.0452 vs. 52.54/55.48 ms), memory (3.23 GB vs. 2.47/2.77 GB), and All 0.0390 0.0352 0.0358 0.0360 0.0373 0.0372 inference latency (26.98 ms vs. 15.94/17.68 ms), reflecting the cost of adaptive temporal-scale routing. However, this overhead remains within the same order of magnitude, while overall Pearson correlation for six variants. Among the three architectural components, removing learned RAVEN achieves the best overall predictive performance on patch importance scoring without Adaptive Routing (AR) both HS300 and S&P500 (Table IV). Compared with heavier causes the largest degradation, with a 9.7% relative drop on multi-scale or routing baselines, RAVEN is substantially more the overall metric. Without the learnable patch importance efficient: it reduces training time by 27.4% over Scaleformer vector Ψi , the CIT mechanism degenerates into predefined and 89.1% over PathFormer, reduces peak memory by 93.1% window lengths, losing the ability to adapt look-back selection over Scaleformer and 35.1% over PathFormer, and reduces to regime-shifting dynamics. Disabling correlation-aware expert inference latency by 42.0% over Scaleformer and 78.3% over weighting (w/o CAW) degrades performance by 8.2%, vali- PathFormer. These results indicate that RAVEN obtains the dating that explicit redundancy suppression at the output side strongest predictive accuracy while maintaining computational is necessary when nested windows share overlapping patches. cost close to lightweight baselines and far below heavier The global context representation (w/o GCR) contributes 7.7%, adaptive architectures. providing a router-independent view that stabilizes predictions F. Hyperparameter Analysis when local experts disagree. The two auxiliary losses each We analyze the sensitivity of RAVEN to four key hyperpacontribute approximately 4.5% individually. rameters on HS300: number of experts K, CIT-based threshold E. Model Efficiency Analysis values, maximum look-back window length, and patch length We benchmark the computational efficiency of RAVEN plen . against four representative baselines on HS300 using a single Number of experts K. We vary K ∈ {2, 3, 4} with thresholds NVIDIA A100 (40GB) GPU, batch size 512, and a 120-day uniformly spaced between τmin =0.3 and τmax =0.9. Table VIII look-back window. Training and inference speeds are reported shows that K=3 achieves the best overall performance (0.0390), in milliseconds per iteration, where a training iteration denotes outperforming K=2 (0.0339) by 15.0% and K=4 (0.0361) by Year

RAVEN

w/o AR

w/o CAW

w/o GCR

w/o Lent

w/o Ldiv

9

Table X: Effect of maximum look-back window on HS300 (Corr ↑). Year

60

90

120

150

2020 2021 2022 2023 2024

0.0644 0.0283 0.0294 0.0197 0.0430

0.0585 0.0290 0.0322 0.0198 0.0458

0.0567 0.0292 0.0422 0.0300 0.0379

0.0584 0.0289 0.0330 0.0204 0.0452

All

0.0361

0.0378

0.0388

0.0376

Table XI: Effect of patch length plen on HS300 (Corr ↑). N denotes the number of patches per window. Figure 5: Efficiency comparison on HS300 (batch size 512, look-back window 120). Training and inference time are reported in milliseconds per iteration; memory denotes peak GPU memory during training. Table VIII: Effect of number of experts K on HS300 (Corr ↑). Year

K=2 (0.3, 0.9)

K=3 (0.3, 0.6, 0.9)

K=4 (0.3, 0.5, 0.7, 0.9)

2020 2021 2022 2023 2024

0.0533 0.0273 0.0300 0.0173 0.0421

0.0567 0.0292 0.0422 0.0300 0.0500

0.0582 0.0274 0.0321 0.0184 0.0442

All

0.0339

0.0390

0.0361

Year N

plen =8 15

plen =12 10

plen =16 7

plen =20 6

2020 2021 2022 2023 2024

0.0543 0.0303 0.0415 0.0315 0.0490

0.0557 0.0287 0.0404 0.0314 0.0473

0.0567 0.0292 0.0422 0.0300 0.0500

0.0520 0.0271 0.0353 0.0289 0.0482

All

0.0384

0.0384

0.0390

0.0372

Table IX: Effect of threshold values under K=3 on HS300 (Corr ↑). Year

(0.3, 0.6, 0.9)

(0.2, 0.4, 0.8)

(0.1, 0.5, 0.9)

2020 2021 2022 2023 2024

0.0567 0.0292 0.0422 0.0300 0.0500

0.0602 0.0304 0.0313 0.0207 0.0442

0.0583 0.0303 0.0321 0.0199 0.0449

All

0.0390

0.0380

0.0370

(a) Yearly shift of 600176.SS.

(b) Cross-ticker profiles (2023).

Figure 6: Distributions of Mean Patch Importance Score (MPIS) s̃i on HS300. Each data point represents the annual average of the learned importance at a given patch index. Patch index 1 corresponds to the most recent time segment. (a) Annual mean importance profiles of stock 600176.SS across five years, illustrating temporal regime adaptation. (b) Annual mean importance profiles of four stocks within 2023, illustrating cross-sectional heterogeneity.

8.0%. With K=2, only two scales are available, limiting the model’s ability to capture intermediate-term patterns. With K=4, adjacent experts cover highly overlapping windows, increasing redundancy without providing additional discriminative information. suggests that excessively long historical periods introduce stale Threshold values under K=3. We compare three threshold patterns that exacerbate concept drift and eventually surpass configurations: (0.3, 0.6, 0.9), (0.2, 0.4, 0.8), and (0.1, 0.5, 0.9). the filtering capacity of the CIT-based routing mechanism. As shown in Table IX, all configurations yield comparable Patch length plen . We vary plen ∈ {8, 12, 16, 20} to study the overall performance, with Corr ranging from 0.0370 to 0.0390 effect of routing granularity. As shown in Table XI, RAVEN and less than 5.2% relative variation. We further conduct paired is robust across the entire range, with overall Corr spanning t-tests on per-sample MSE using (0.3, 0.6, 0.9) as the reference. from 0.0372 to 0.0390 (less than 5% relative variation). Paired Neither (0.2, 0.4, 0.8) with p=0.66 nor (0.1, 0.5, 0.9) with t-tests on per-sample MSE using plen =16 as the reference p=0.19 shows a statistically significant difference at the 0.05 confirm no statistically significant difference for any alternative level. This insensitivity is anticipated. Since the importance (p=0.26, 0.21, 0.18 for plen =8, 12, 20 respectively). This scores s̃i are learned in an end-to-end manner, the model adjusts insensitivity arises because the learned importance scores s̃i its score distribution to compensate for different threshold adapt their distribution to the available routing granularity. With settings. Consequently, the exact threshold values are non- fewer patches, each score carries more discriminative weight, critical in practice. compensating for the coarser resolution. Maximum look-back window. As detailed in Table X, performance improves steadily as the window extends from 60 G. Case Study days (0.0361) through 90 days (0.0378) to the optimal 120 days To understand how RAVEN adapts its routing behavior, we (0.0388). However, expanding the window further to 150 days visualize the learned patch importance scores s̃i under different leads to a slight degradation (0.0376). This inflection point conditions in Figure 6.

10

(a) Temporal evolution of 605117.SS.

(b) Cross-ticker distribution(2023).

Figure 7: Empirical distributions of expert aggregation weights on HS300. Expert 1 corresponds to the short-horizon expert and Expert 3 to the long-horizon expert. Each bar shows the annual mean weight allocated to each expert. (a) Weight evolution of stock 605117.SS across five years, reflecting regime-driven reallocation. (b) Weight distribution across four stocks within 2023, reflecting asset-specific routing preferences.

Temporal heterogeneity. Figure 6a shows the annual mean importance profile of a single stock (600176.SS) across five years. In 2020, a year marked by extreme volatility, the router concentrates importance heavily on the most recent patch (s̃1 = 0.33) with steep decay toward older patches, effectively selecting short look-back windows. In contrast, years with sustained trends such as 2021, 2023, and 2024 exhibit flatter distributions that allocate meaningful weight to intermediate and distant patches. This indicates that the router leverages longer historical context when the SNR of older observations is higher. The temporal shift emerges purely from data-driven learning of s̃i , without explicit regime labels or calendar features. Cross-sectional heterogeneity. Figure 6b reveals that even within the same year (2023), different stocks exhibit markedly different annual mean importance profiles. Some stocks show steep concentration on recent patches, suggesting short-memory price dynamics, while others maintain more distributed weights across the full look-back range, benefiting from longer historical context. This cross-sectional variation demonstrates that no single fixed window length is universally optimal. Individual securities require different effective windows depending on their microstructure characteristics. RAVEN addresses this by learning per-sample importance scores that drive CIT-based adaptive routing, enabling each input to select its own effective temporal scale without manual specification. To establish a holistic understanding of RAVEN’s decisionmaking paradigm, we extend our visual inspection from the upstream patch importance curves to the downstream gate weights emitted at the expert aggregation stage. Figures 7b and 7a illustrate the statistical distributions of the routing weights across different financial assets and historical periods, respectively. Crucially, these downstream weight topologies perfectly mirror the continuous context-carving behaviors observed in the upstream patch selection phase, confirming that the data-driven CIT-thresholded routing over learned importance matrices structurally translates into scale-specialized representations. Figure 7a tracks the expert weight allocation of stock

11

605117.SS across five years. In 2020, a period of heightened volatility, Expert 1 (short-horizon) receives the largest share of weight, indicating that the model favors recent context when the market undergoes rapid structural change. In contrast, during 2021 and 2022, Expert 3 (long-horizon) dominates, as the model leverages extended historical context during relatively stable trending periods. The weight distribution shifts again in 2023 and 2024, reflecting changing market regimes. This adaptive reallocation confirms that the routing mechanism responds to non-stationary dynamics without manual intervention. Figure 7b compares the weight allocations of four stocks within 2023. Stock 605117.SS allocates nearly half of its weight to Expert 1 (short-horizon), suggesting rapid price dynamics that benefit from short look-back contexts. In contrast, 300888.SZ assigns the majority of weight to Expert 3 (longhorizon), indicating stable temporal dependencies that reward extended historical input. The remaining two stocks fall between these extremes. This cross-sectional divergence mirrors the upstream patch importance heterogeneity observed in Figure 6b, validating that the entire routing pipeline maintains consistent behavior from patch scoring through expert aggregation. IV. R ELATED W ORK Deep learning and foundation models for financial forecasting. Classical financial forecasting relies heavily on gradient boosting trees (e.g., XGBoost [6], LightGBM [17]), which capture non-linear interactions but treat forecasts as independent and identically distributed (i.i.d.) tabular problems, fundamentally discarding the temporal topology of market regimes [3]. Subsequent sequential architectures, including RNNs [10] and LSTMs [16], restored temporal memory but remain disproportionately biased toward recency, frequently conflating transient microstructure noise with structural regime shifts [28]. To address long-range dependencies, general time-series architectures have evolved rapidly. Early efficient variants (Informer [45], Autoformer [37]) paved the way for advanced representation learning, precipitating breakthroughs in channelindependent patching (PatchTST [26]), cross-variate dependencies (Crossformer [43]), inverted attention (iTransformer [22]), and robust token blending (CARD [34]). Complementary paradigms have also demonstrated strong competitiveness; notably, frequency-domain and wavelet models (FEDformer [47], TimesNet [36], FredFormer [27], WPMixer [25]) explicitly exploit spectral periodicity, while DLinear [41] and ModernTCN [24] established robust baselines using linear decomposition and modernized temporal convolutions. In the highly stochastic financial domain, specialized architectures have emerged to capture complex market dynamics via graph-based trend prediction (HIST [38]), market-guided attention (MASTER [19]), meta-learning for distribution shifts (DoubleAdapt [44]), and early forms of conditional routing (TRA [20]). However, despite their immense architectural diversity and expressive capacity, these models share a critical structural bottleneck: they strictly commit to a fixed context window or

treat look-back length as a static hyperparameter. In the exceptionally low SNR ratio (SNR) and non-stationary environment of financial markets, a static receptive field inevitably forces models to either truncate critical historical regime transitions or dilute actionable predictive signals with obsolete noise.

experts by patch content, RAVEN specializes by temporal scale through contiguous nested prefixes. Two additional components address challenges unique to this topology: (1) Shape-Aligned Fusion with CAW aligns variable-length expert outputs and penalizes redundant representations caused by prefix overlap; (2) a GCR branch summarizes the full context in parallel, providing macro-level information that localized experts may miss.

Adaptive context and non-stationarity in time series. In highly volatile and non-stationary time series domains, the temporal scale of a model’s receptive field must adaptively expand or contract to isolate meaningful predictive signals V. C ONCLUSION from transient noise. The Multi-period Learning Framework We presented RAVEN, a regime-aware MoE framework that (MLF) [42] represents a notable attempt by simultaneously replaces fixed-length context windows with sample-adaptive, fusing varying look-back lengths using Inter-period Redunvariable-length receptive fields for financial time series forecastdancy Filtering. Similarly, PathFormer [5] captures varying ing. By leveraging an importance-scoring mechanism coupled temporal dynamics by dynamically aggregating features from with CIT-based thresholds, RAVEN dynamically extracts nested a predefined set of fixed patch resolutions. More recently, look-back windows routed to scale-specialized experts, while TimeSqueeze [1] attempts to alleviate fixed-resolution bota GCR branch maintains macro-level context coherence. Furtlenecks by dynamically altering patch boundaries within a thermore, a CAW mechanism effectively decorrelates expert sequence based on local signal complexity. However, these outputs, mitigating information redundancy stemming from models fundamentally commit to either a rigidly fixed global overlapping patch inputs. look-back window or a predefined set of static scales, failing to Extensive experiments across financial and general timeperceive the optimal global context length on the fly. RAVEN series tasks, including cumulative log-return prediction on bridges this gap at the architectural level. By deploying a HS300 and S&P500, fund flow forecasting, and traffic forecastdata-driven CIT-thresholded routing mechanism over learned ing on PEMS benchmarks, demonstrate the effectiveness and patch importance scores, RAVEN dynamically generates nested, generality of RAVEN. On the two equity benchmarks, RAVEN variable-length historical windows for each sample, seamlessly ranks first across all six overall metric–dataset combinations, preserving continuous temporal evolution without humanimproving Pearson correlation by 9.2% on HS300 and 20.2% on defined scale constraints. S&P500 over the strongest baselines; on fund flow forecasting, MoE and routing topologies. Sparse MoE layers effectively it reduces MSE by 18.2%. Beyond financial data, RAVEN scale model capacity without proportionally increasing com- achieves the best result in 14 of 16 traffic forecasting metrics, putational overhead [11]. In the time-series domain, foun- indicating that adaptive temporal-scale routing is also beneficial dation models like Time-MoE [31] and Moirai-MoE [21] for general time series. Ablation studies confirm that adaptive scale this paradigm to billion parameters, employing token- routing, CAW, and the GCR branch each contribute indepenlevel sparse routing. Recent specialized architectures such as dently, while efficiency and hyperparameter analyses show TFPS [33] follow a similar token-level paradigm, utilizing that RAVEN provides a favorable balance between accuracy subspace clustering to route individual patches to pattern- and efficiency and remains stable across reasonable routing specific experts. These content-based routing mechanisms configurations. are highly effective for localized pattern matching: experts While RAVEN establishes a robust foundation for adaptive specialize in patches with similar local morphology, regardless financial modeling, several promising avenues remain. First, of where those patches appear in the sequence. However, such integrating cross-asset dependencies and macro-regime indicarouting primarily induces pattern-level specialization rather tors into the routing mechanism could better capture systemic than temporal-scale specialization. Since individual patches market co-movements. Second, generalizing the framework from different time positions may be dispatched to different to accommodate variable-resolution patching would further experts, no expert is explicitly assigned to model a contiguous enhance its multi-scale expressiveness. Finally, scaling RAVEN historical horizon. This limits the ability of each expert to to high-frequency intraday data and broader asset classes (e.g., capture how local patterns interact with medium- and long-range fixed income and commodities) represents a natural next step to temporal context, which is important for non-stationary financial validate its universal efficacy in complex financial ecosystems. forecasting. RAVEN adopts an orthogonal routing topology: temporal-scale routing. By ensuring each expert processes a contiguous, nested prefix of historical data, RAVEN preserves positional coherence within each horizon while enforcing datadriven scale specialization. Positioning of our work. Unlike fixed-context models [2], [32] and predefined multi-scale methods [1], [5], [42], RAVEN performs sample-dependent context selection via CIT-thresholded routing; unlike token-level MoE [21], [31], [33] that specializes

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