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Revisiting Identity and Spectra Dispersion in Media-Bridged Time Series Forecasting: Linking Multivariate Signals and Narrative Flows

Jierui Lei, Wenjian Zhang, Qingyi Yang, Yuyang Hong, Fangzheng Chen, Zhengbo Zhang, Haina Tang, Shiming Xiang

arXiv:2610.11924v1cs.CVcs.LG

TL;DR

Existing TSF backbones are generally tailored to multivariate or multimodal forecasting, despite pre-alignment making a shared post-alignment backbone feasible. MIDAPN combines identity-aware graph modeling with automatically configured hierarchical temporal analysis; it reports strong results across both settings, including first place in 15 / 18 multivariate metrics.

  • Problem

    Current TSF backbones typically target either multivariate or multimodal forecasting, and input-level alignment alone does not unify modeling of heterogeneous variates.

    Source: §I · p. 1

  • Method

    MIDAPN combines an identity-aware graph that models essence, behavior, and commonality with SPConv, which uses adaptive guidance for hierarchical temporal modeling.

    Source: §I · p. 2

  • Results

    MIDAPN reports consistent improvements across multivariate and multimodal forecasting, ranking first in 15 / 18 multivariate metrics.

    Source: B. Experimental Results · pp. 9–10

  • Takeaways & Limitations

    The paper presents a shared backbone perspective linking multivariate and narrative-flow multimodal forecasting after pre-alignment.

    Source: §VII · p. 12

Abstract

from arXiv · show

Media-bridged time series forecasting is expanding to encompass traditional "multivariate" and emerging "multimodal" (e.g., through textual assistance). Existing Time Series Forecasting (TSF) models still rely on paradigm-specific relation, fusion, and temporal modules, hindering a common forecasting backbone across numerical and pre-aligned narrative-flow settings. To explore this, we propose the Multimedia Identity-Aware Prism Network (MIDAPN), a unified spatiotemporal forecasting backbone based on media-general graph adaptation and automatic temporal learning: (1) Following media pre-alignment, our Multimedia Identity-Aware Graph (MIDAG) revisits identity through static essence, dynamic behavior, and latent commonality, inducing affinities that extend variable-specific dependencies across media. Contextual Identity Modulation (CIM) further refines discriminative aggregation. (2) We develop Spectral Prism Convolution (SPConv) to automatically perform hierarchical temporal analysis, balancing coarse trends and fine-grained details. Meanwhile, its Adaptive Search Guidance configures a scale-efficient architecture for temporal-dimension reconstruction. These decoupled yet synergistic components jointly address media identity disentanglement and temporal-scale mismatch. Comprehensive evaluations involving 16 SOTA TSF models across 13 "multivariate" and 12 "multimodal" datasets, alongside targeted long-context comparisons against 14 time series foundation models and fused pretrained language models, demonstrate MIDAPN's consistent superiority and broad shared backbone compatibility. The code is available at \href{https://github.com/leijieruilq/MIDAPN/tree/main}{https://github.com/MIDAPN}.

I. INTRODUCTION

The introduction argues that input-level pre-alignment does not unify modeling because heterogeneous variates differ in meaning and evolution, while current TSF backbones remain paradigm-specific. MIDAPN proposes a shared post-alignment backbone addressing identity relations and temporal-scale adaptation.

B. Multimodal Time Series Forecasting

  • Existing backbones commonly target either numerical multivariate forecasting or text-assisted multimodal forecasting, while shared post-alignment modeling remains limited.Pre-alignment casts numerical channels and PLM-derived text representations as time-aligned variates, but does not itself unify how heterogeneous variates are modeled.Source: §I · p. 1, B. Multimodal Time Series Forecasting · p. 3

I. INTRODUCTION

  • MIDAPN revisits variate identity through essence, behavior, and commonality, with Contextual Identity Modulation preserving distinctiveness during graph-conditional aggregation.This design targets monolithic representations that weaken identity distinctiveness across heterogeneous sources.Source: §I · p. 2
  • SPConv uses frequency decomposition and Adaptive Search Guidance to configure hierarchical temporal modeling for scale-efficient reconstruction across varying forecasting horizons.The proposed search-by-construction addresses fixed convolutional hierarchies that may not adapt well to different spectral resolutions.Source: §I · p. 2
  • Across 13 multivariate and 7 multimodal benchmarks, MIDAPN shows cross-media compatibility and outperforms Aurora and VoT in multimodal-only settings.The introduction also reports that generic replacements for MIDAG or SPConv consistently increase errors.Source: §I · p. 2

III. PRELIMINARIES AND MEDIA PRE-ALIGNMENT

  • For TaTS-style multimodal inputs, PLM-encoded text is projected into auxiliary variates and concatenated with the temporal series for forecasting.The architecture extracts historical representations, maps them to the future horizon with a channel-independent MLP, then refines the forecast.Source: §III · pp. 3–4, Figure 2 · p. 4

A. Overall Architecture and Theoretical Analysis

  • MIDAG models which variables interact, whereas SPConv models how those interactions evolve across temporal scales; under stated approximation-gap conditions, the full model outperforms either ablated class.The modules are described as axis-decoupled but conditionally complementary.Source: A. Overall Architecture and… · pp. 4–5

1) Design Rationale:

MIDAG treats variate identity as multiple complementary aspects that induce graph affinities. Contextual identity modulation refines aggregation without explicitly estimating conditional mutual information.

1) Design Rationale:

  • Variate identity is decomposed into essence (what it is), behavior (how it manifests), and group-level commonality (where it belongs).The paper frames these as intrinsic properties, context-dependent dynamics, and shared commonalities.Source: 1) Design Rationale · p. 5
  • The identity aspects are factorized probabilistically to model how interdependent identities jointly induce varied graph structures.The described representations include individual identity embeddings and latent group-level cluster centers.Source: 1) Design Rationale · p. 5
  • Contextual Identity Modulation refines graph aggregation without explicitly estimating conditional mutual information.Source: 1) Design Rationale · p. 5

2) Individual Identity Learning:

Individual identity combines persistent variate properties with input-dependent dynamics, while latent cluster centers represent group commonalities. Soft assignments let each variate participate in multiple groups.

2) Individual Identity Learning:

  • A trainable embedding anchors persistent variate properties, while a dynamic learner extracts instantaneous behavior and their sum forms individual identity.The dynamic learner uses a low-rank factorization for parameter efficiency.Source: 2) Individual Identity Learning · p. 5
  • Essence identity acts as prior expectation and behavior identity as posterior update, making the combined identity a residual-like incremental update.Source: 2) Individual Identity Learning · p. 5

3) Group-Level Identity Clustering:

  • Projected variate identities receive soft assignments across latent cluster centers, preserving graded membership rather than forcing one cluster per variate.The resulting group representation is concatenated with individual identity.Source: 3) Group-Level Identity Clustering · pp. 5–6

4) Multimedia Identity-Aware Graph Construction:

MIDAG decomposes identity into individual and group traits to form affinities across variates and media. CIM then refines graph aggregation using temporal context, identity-aware gating, and residual refinement.

4) Multimedia Identity-Aware Graph Construction:

5) Contextual Identity Modulation (CIM):

  • CIM combines temporal and identity cues with graph aggregation and context-guided gating; residual refinement retains a broader spectrum while gating concentrates dominant modes.The authors report that these findings, alongside the “w/o CIM” ablation, substantiate context-guided refinement.Source: 5) Contextual Identity Modulation (CIM) · p. 6, Figure 4 · p. 6

1) Spectrum Capturing:

SPConv uses localized spectral responses to analyze temporal patterns and address variation in spectral resolution across horizons. Its hierarchical scaling trades spectral resolution for channel capacity and reconstructs the temporal dimension.

1) Spectrum Capturing:

  • The spectrum-capturing hypothesis is that salient temporal patterns can appear as compact, localized spectral responses, extracted with a learnable convolutional kernel.Source: 1) Spectrum Capturing · pp. 6–7
  • Multi-source signals are mapped to frequency bases and split into real and imaginary parts, while horizon-dependent spectral resolution motivates automatic architecture configuration.Source: 1) Spectrum Capturing · p. 7

2) Hierarchical Spectral Scaling:

  • Hierarchical average pooling and channel-expanded convolution contract spectral positions while expanding channels, trading resolution for capacity as layers adjust and fuse the temporal dimension.Source: 2) Hierarchical Spectral Scaling · p. 7

3) "Adaptive Search-Guided" Architecture Configuration:

Adaptive Search Guidance configures the architecture deterministically at initialization to meet a temporal reconstruction target. It uses a constrained mixed-order allocation to balance capacity and reconstruction needs.

3) "Adaptive Search-Guided" Architecture Configuration:

  • ASGM deterministically instantiates one architecture at initialization through “search-by-construction,” rather than evaluating candidates in a search-then-train process.Source: 3) "Adaptive Search-Guided"… · p. 7
  • ASGM sets network depth from the input horizon and uses layer-wise expansion factors to reconstruct multimedia representations.Source: 3) "Adaptive Search-Guided"… · p. 7
  • A structural cost proxy guides balanced capacity growth toward the reconstructed temporal dimension, while mixed-order search accommodates flexibility and integer constraints.Source: 3) "Adaptive Search-Guided"… · p. 7

4) Mixed-order Allocations:

Mixed-order expansion restricts layer allocations to at most two factors and selects a low-cost construction for the reconstruction target. Interleaving the selected factors yields a balanced SPConv capacity distribution.

4) Mixed-order Allocations:

  • Restricting allocations to at most two distinct expansion factors avoids exhaustive L-layer search over O(|Qd|^L) candidates.For each layer split, the procedure evaluates one floor-based candidate, then selects the lowest-cost valid solution.Source: 4) Mixed-order Allocations · p. 7
  • Across L−1 layer splits, the search costs O(L) = O(log T), and the selected factors are interleaved to avoid sharp adjacent-layer fluctuations.The floor-based construction chooses a candidate that does not overshoot the target for each split.Source: 4) Mixed-order Allocations · p. 7
  • At T = 720, the minimum-cost proxy outperforms alternative expansion strategies by avoiding redundancy from unbalanced allocations.Table II compares forecasting results for different expansion-factor strategies.Source: Table II · p. 8, 4) Mixed-order Allocations · p. 8

5) Patterns Distribution and Scale-Efficient Architecture Searching:

The section presents scale progression and a compact architecture search, then describes forecasting modules and training choices. MIDAPN interprets forecasting as estimating, evolving, and validating a dynamical-state embedding.

5) Patterns Distribution and Scale-Efficient Architecture Searching:

  • ASGM’s cost rises stepwise as reconstruction dimensions increase while remaining within a controllable horizon range, selecting a compact, balanced, less redundant reconstruction path.Fig. 5 also illustrates multi-scale progression from shallow to deep layers.Source: 5) Patterns Distribution and… · p. 8

1) Instance Normalization and Predict Residuals:

2) Historical Time Series Embedding:

4) Future Time Series Refinement:

  • The initial prediction is refined through TSEM modules to produce the final forecast.The supplied passages identify the refinement and final-forecast output.Source: 4) Future Time Series Refinement · p. 8

5) Operator-Level Interpretation:

  • The operator-level view estimates a dynamical state from observations, evolves it into a predicted state with FCI-MLP, then ensures embedding validity.The authors relate this process to classical embedding theory.Source: 5) Operator-Level Interpretation · p. 8

6) Tailored Training Loss:

  • Robust MAE is used for multivariate forecasting, while multimodal forecasting uses MSE to emphasize pointwise deviations and local temporal changes.The optional weight-decay coefficient β addresses non-overfitting.Source: 6) Tailored Training Loss · p. 8

A. Experimental Settings

Experiments span 25 public multivariate and multimodal datasets and compare MIDAPN with native forecasting models and pretrained or fused approaches. MIDAPN ranks first in 38 of 42 metrics overall, while ablations and identity visualizations examine component effects and learned structure.

1) Datasets:

  • The evaluation covers 25 public datasets across multivariate, multimodal, and combined multivariate-plus-text settings.The multimodal set includes Agriculture, Climate, Economy, Energy, Environment, Health, Security, SocialGood, and Traffic; the combined setting includes MSPG, LEU, and PTF.Source: 1) Datasets · pp. 8–9

B. Experimental Results

  • Across 25 real-world datasets, MIDAPN ranks first in 38/42 metrics and in the top two in 40/42; its multivariate improvements are 11.6% in MAE and 14.2% in MSE, ranking first in 15/18 metrics.Fig. 6 reports optimal long-context comparisons, where MIDAPN remains competitive with recent TSFMs and PLM-based methods; Fig. 7 visualizes performance across domains.Source: Table IV · p. 9, B. Experimental Results · pp. 9–10, Figure 6 · p. 9

2) Baselines:

  • The baseline set includes 16 native deep TSF models and 14 TSFMs and fused-PLM or modality-fusion approaches.The native models span Transformer, MLP, TCN, LLM, RNN, GCN, KAN, and Mamba families.Source: 2) Baselines · p. 9

3) Implementation Details:

  • For multimodal comparisons, TaTS supplies pre-alignment of numerical inputs and PLM text; dataset splits and look-back settings are specified for the benchmark comparisons.ETT and PEMS datasets use 6:2:2 train/validation/test splits, while other datasets use 7:1:2.Source: 3) Implementation Details · p. 9

C. Ablation and Replacement Results

  • Removing any core component incurs a substantial penalty; replacing MIDAG or SPConv with basic alternatives also degrades performance.Ablations attribute distinct roles to DFF, MIDAG, SPConv, and TSEM modules; removing MIDAG identity elements or contextual modulation impoverishes its identity-aware graph.Source: Table V · p. 10, C. Ablation and Replacement Results · p. 10

1) Identity-Aware Graph Adaptation:

  • MIDAG visualizations distinguish relatively loose, uniform essence identities from look-back-conditioned behavior identities, which converge; in multimodal data, behavior identities narrow inter-modal distance.The visualizations cover multivariate Traffic and multimodal Climate and MSPG.Source: 1) Identity-Aware Graph Adaptation · p. 10, Figure 8 · p. 11

2) Clustering Analysis:

  • Traffic variates in the same selected cluster show similar look-back evolution, while distant clusters correspond to differing temporal patterns; Fig. 9 presents Agriculture forecasts across declining, uncertain, and rising narrative-guided periods.The authors interpret the cluster pattern as implicit group clustering.Source: 2) Clustering Analysis · p. 10, Figure 9 · p. 11

3) Affinity Decomposition:

This section examines affinity structure, hyperparameter choices, text encoders, and efficiency, reporting MIDAPN’s forecasting performance and plug-and-play graph generality across media settings.

3) Affinity Decomposition:

  • MII reinforces TS–TS dependencies, MGG captures shared intra-media structure, and MIG/GI suppresses redundant affinities for selective TS–TS/Text alignment.The decomposition prioritizes forecast-relevant factors within compressed sentence embeddings.Source: 3) Affinity Decomposition · p. 11

4) "Narrative-Flow" Case Study:

  • MIDAPN gives the best forecast approximation for time series–text pairs across declining, uncertain, and rising periods.The periods are Jun–Aug 2020, Sep–Dec 2020, and Feb–Apr 2021, respectively.Source: 4) "Narrative-Flow" Case Study · p. 11

5) "Graph-Informed" Generality:

  • MIDAG generalizes as a plug-and-play component across mainstream TSF architectures, addressing PTF’s redundancy from identical clone nodes.The comparison covers multivariate Input-96-predict-96 and multimodal Input-8-predict-12 scenarios.Source: 5) "Graph-Informed" Generality · p. 11, Table VI · p. 11

B. Hyperparameter Analysis; 1) Sensitivity Analysis:

2) Optimal Selection in Multi-Domain:

  • For multimodal optimal selection, larger model dimensions may help representation learning, while lighter identity and graph dimensions help suppress cross-modal noise.Scaling dimensionality can amplify capacity under extensive time-step conditions such as Environment.Source: 2) Optimal Selection in Multi-Domain · p. 11, Figure 10 · p. 11

3) Text Encoder Analysis:

  • Smaller BERT and GPT2 encoders perform most robustly in predictable and challenging domains, while different PLMs vary by only 0.5%–0.7%.The authors attribute this pattern to lower embedding dimensions supporting effective projection with limited data.Source: 3) Text Encoder Analysis · p. 11, Figure 11 · p. 12

C. Efficiency Analysis

  • MIDAPN balances accuracy and efficiency, with small MIDAG identity and graph dimensions limiting D and SPConv using lightweight TCN-style operations.Adaptive Search Guidance completes its search at initialization with negligible O(L) overhead and no added training burden.Source: C. Efficiency Analysis · pp. 11–12

VII. CONCLUSION; C. Efficiency Analysis

  • Across 25 datasets, MIDAPN outperforms SOTA deep TSF, TSFM, and PLM-fused methods; Fig. 12 reports the lowest error and third- or fourth-fastest speed in both settings.Removing TSEMhis or TSEMpred gives a clear speed advantage over SOTA TSF models with marginal performance loss.Source: C. Efficiency Analysis · pp. 11–12, §VII · p. 12, Figure 12 · p. 12

APPENDIX

The appendix interprets CIM’s two paths through a conditional-information decomposition, describes dataset preparation, and surveys TSF and foundation-model approaches.

VIII. JOINT CONDITIONAL-INFORMATION VIEW OF CIM

  • CIM’s conditional-information decomposition interprets its two paths before fusion, with the residual and gated responses considered jointly given graph-aggregated context.The derivation adds and subtracts conditional entropy and invokes a conditional data-processing inequality.Source: §VIII · p. 14

IX. DATASETS DESCRIPTION

  • Dispersed time-series–text pairs from LEU, MSPG, and PTF are organized into TaTS-compatible format using Gemini 3.1 Pro.The passage also notes that 25 public datasets are summarized in Table VII.Source: §IX · p. 14

A. Basic TSF Models

  • The surveyed TSF models span Transformer, MLP, TCN, RNN, GCN, LLM, KAN, and Mamba architectures.Examples include PatchTST, TimeMixer, ModernTCN, MSGNet, Time-LLM, and TimePro.Source: A. Basic TSF Models · p. 14

B. TSFM & Multimodal PLM Frameworks

  • The foundation and multimodal PLM survey covers TSFMs, multimodal language-model frameworks, and multimodal forecasting frameworks.Examples include MOIRAI, Time-VLM, GPT4MTS, VoT, and MM-TSLib.Source: B. TSFM & Multimodal PLM Frameworks · p. 15

1) Settings:

This section specifies the evaluation setup and model configurations, discusses assignment supervision and robustness, and clarifies the media scope and ethical boundary.

1) Settings:

  • Experiments use RTX 4090 and A100-SXM4 GPUs, BERT-base-uncased for multimodal runs, and benchmark-standard train, validation, and test splits.Some missing or inconsistently configured baseline results were rerun; normalization or residual prediction could be used to mitigate sample indistinguishability.Source: 1) Settings · pp. 15–16

2) Model Configuration:

  • The default MIDAPN configuration uses two MIDAG layers, two SPConv layers, model dimension 512, 32 cluster centers, and graph dimension 32.Identity and cluster-center embedding dimensions are both 8.Source: 2) Model Configuration · p. 16

3) Forecasting Configuration:

  • Forecast horizons vary by scenario, and the stated configuration disregards real-world timestamp granularity.Multivariate long-term horizons are 96, 192, 336, and 720; multimodal horizons are 8, 10, and 12.Source: 3) Forecasting Configuration · p. 16

XI. DISCUSSION OF AUXILIARY TRAINING OBJECTIVES FOR MULTIMEDIA SCENARIOS

  • The authors omit assignment sharpening because it can weaken overlapping cluster effects, and it provides no consistent improvement over task-supervised graph learning.The graph remains sample-dependent and is dynamically updated end-to-end through the task loss.Source: §XI · p. 16, Table VIII · p. 16

XII. RESULT ROBUSTNESS

  • Robustness is assessed using means and standard deviations over five random seeds, with multimodal results averaged across horizons 8, 10, and 12.The seed runs do not search the best hyperparameter setting for each seed.Source: §XII · p. 16, Table IX · p. 16

XIII. FULL RESULTS

  • The full results are provided in separate tables for long- and short-term multivariate tasks, multimodal tasks, and TSFM and PLM comparisons.The supplied passage points to Tables XI–XV.Source: §XIII · p. 16

XIV. CLARIFICATIONS FOR MEDIA SCOPE

  • Here, media means heterogeneous information carriers structured as temporally aligned variables, including numerical variates and text-derived pseudovariates encoded by a frozen PLM.Raw images, audio, and video remain future work requiring broader aligned datasets, suitable encoders, and alignment mechanisms.Source: §XIV · pp. 16–17

XV. ETHICAL CONSIDERATIONS

  • The benchmark forecasts are intended for methodological evaluation, not direct high-stakes medical, financial, or security decisions without domain-specific validation.The experiments use publicly available, aggregated benchmark datasets.Source: §XV · p. 17
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