Model Cooperation Coherer (MCC)

• Model Cooperation Coherer (MCC) is a dual-branch adapter that aligns retrieval-informed features with both numerical and LLM-based time-series forecasting models.
• It transforms outputs from the Multi-grained Series Interaction Learner into residual fused numeric sequences for non-LLM models and structured prompts for LLM-based models.
• MCC underpins zero-shot forecasting in QuiZSF by ensuring coherent integration of cross-domain retrieval data, enhancing performance and mitigating gradient issues.

Model Cooperation Coherer (MCC) is the dual-branch adaptation component within QuiZSF ("Quick Zero-Shot Time Series Forecaster") that aligns retrieval-derived knowledge with two classes of time-series pre-trained models (TSPMs): non-LLM models and LLM-based models. In the QuiZSF pipeline, MCC sits after retrieval and representation learning, receiving MSIL outputs and converting them into model-compatible conditioning: residual-semantic fusion inputs for numerical forecasters and structured prompts for language-model forecasters. Its role is therefore not to perform retrieval or forecasting directly, but to make those stages coherent, trainable, and operationally compatible in zero-shot time-series forecasting (ZSF) (Ma et al., 9 Aug 2025).

1. Architectural placement and formal role

QuiZSF organizes forecasting as a staged pipeline:

$$\text{CRB} \rightarrow \text{HHTR} \rightarrow \text{MSIL} \rightarrow \text{MCC} \rightarrow \text{TSPM} \rightarrow \text{forecast}.$$

Within that sequence, ChronoRAG Base (CRB) and HHTR retrieve relevant historical series from large cross-domain databases, while the Multi-grained Series Interaction Learner (MSIL) transforms the target series and retrieved neighbors into interaction-aware representations. MCC is the point at which these representations are converted into the input modality expected by the base forecasting model (Ma et al., 9 Aug 2025).

The paper defines MCC as “a dual-branch Model Cooperation Coherer (MCC) that aligns retrieved knowledge with two kinds of TSPMs: Non-LLM based and LLM based. MCC constructs residual-semantic fusion inputs for numerical models and structured prompts for LLMs, while supporting end-to-end optimization across modalities.” In this sense, MCC functions as a modality-aware adapter. For non-LLM TSPMs, it preserves a numerical interface; for LLM-based TSPMs, it produces textual conditioning. A common misconception is to treat MCC as a forecasting backbone in its own right. The formulation in QuiZSF does not support that interpretation: MCC is an integration mechanism between retrieval-informed representations and an existing TSPM.

Its inputs are produced by MSIL. The normalized target series is

$$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$

and each retrieved series is normalized as

$$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$

MSIL then computes an interaction pattern

$$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$

an average pattern

$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$

and a fused representation through cross-attention:

$$\mathbf{Q} = \mathbf{W}_q \mathbf{T}^{\text{norm}}, \quad \mathbf{K} = \mathbf{W}_k \mathbf{P}_{\text{avg}}, \quad \mathbf{V} = \mathbf{W}_v \mathbf{P}_{\text{int}},$$

$$\mathbf{R}_{\text{fused}} = \text{Softmax}\!\left(\frac{\mathbf{Q}\mathbf{K}^{\top}}{\sqrt{d}}\right)\mathbf{V}.$$

MCC consumes these outputs rather than raw retrievals.

2. Dual-branch design

MCC has two branches tailored to two TSPM families: a Numerical Coherer for non-LLM models such as TTM, TimesFM, and Moirai, and a Language Coherer for LLM-based models such as Time-LLM, LLMTime, and GPT4TS (Ma et al., 9 Aug 2025).

Branch	Target models	Output form
Numerical Coherer	TTM, TimesFM, Moirai	Residual-fused numeric sequence
Language Coherer	Time-LLM, LLMTime, GPT4TS	Structured textual summaries and prompt

The Numerical Coherer is used when the base TSPM operates directly on numerical sequences. Its purpose is to inject retrieval-informed information without disrupting the existing behavior of the numerical forecaster. The paper states that “for numerical TS pre-trained models, we apply a residual connection to fuse the normalized target sequence $\mathbf{T}^{\text{norm}}$ with the MSIL-fused representation $\mathbf{R}_{\text{fused}}$, then feed it into the forecasting model.” The core form is

$$\widehat{\mathbf{T}} = \mathcal{F}_{\text{N}}\bigl(\mathbf{R}_{\text{fused}}, \mathbf{T}^{\text{norm}}\bigr).$$

The description further interprets this in a classic residual form,

$$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$0

where $$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$1 is a small learnable network. The resulting sequence is then treated as the final input to the numerical TSPM, which outputs the forecast.

The Language Coherer addresses a different constraint: LLM-based TSPMs operate exclusively on text. Direct use of $$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$2, $$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$3, or $$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$4 is therefore infeasible. MCC resolves this modality gap by mapping numerical features into prompt text:

$$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$5

where $$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$6 is a structured prompt. Forecasting is then expressed as

$$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$7

with $$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$8 denoting the numeric sequence encoded in the input format expected by the LLM-based forecaster, and $$\mathbf{T}^{\text{norm}} = \frac{\mathbf{T} - \text{loc}_T}{\text{scale}_T},$$9 denoting the MCC-generated prompt. The appendix clarifies that these summaries capture essential characteristics of the retrieved series, such as trends and patterns, and combine them with instruction prompts specifying the forecasting task.

3. Cooperation, coherence, and alignment mechanisms

MCC is the stage at which retrieved knowledge is made operationally relevant to the downstream forecaster. The cooperation path is explicit: CRB and HHTR retrieve cross-domain neighbors, MSIL converts them into multi-grained target-conditioned features, and MCC injects those features into the forecast model in a modality-appropriate form (Ma et al., 9 Aug 2025).

In the non-LLM branch, cooperation occurs through residual fusion. This means retrieval-informed features alter the target representation through a residual pathway rather than a full replacement. The significance of that design is stated directly: the residual module “enhances expressiveness and mitigates gradient vanishing.” The same structure also permits the system to back off toward the original target representation when retrieved information is less useful. This suggests a controlled integration mechanism rather than unconditional reliance on retrieval.

In the LLM branch, cooperation is prompt-mediated. The Language Coherer converts $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$0, $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$1, and $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$2 into structured textual summaries, places them into a template with separate fields for target series description, retrieved patterns, task description, and output format, and appends an instruction-style prompt such as predicting the next $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$3 points. The paper describes this as a way to present retrieved patterns as contextual knowledge about the current target series rather than as arbitrary text.

The paper also states that there is no explicit auxiliary alignment loss between target and retrieved representations. Instead, coherence is enforced by three mechanisms. First, MSIL cross-attention ensures that retrieval-derived features are target-conditioned:

$$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$4

Second, MCC’s residual fusion modulates how strongly retrieval affects the numerical representation. Third, the structured prompt in the LLM branch frames retrieved patterns as relevant guidance. A common misunderstanding is therefore to interpret MCC as implementing a separate explicit alignment objective. In QuiZSF, alignment is architectural and distributional rather than an independent target-retrieval loss.

4. Training objectives and optimization behavior

For the numerical branch, MCC participates in joint optimization with MSIL and the base TSPM. The training objective combines mean squared error with Maximum Mean Discrepancy (MMD) regularization (Ma et al., 9 Aug 2025).

Let $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$5 be the predicted sequence and $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$6 the ground-truth future sequence. In an RKHS $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$7 with feature map $$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$8,

$$\mathbf{S}_i^{\text{norm}} = \frac{\mathbf{S}_i - \text{loc}_{S_i}}{\text{scale}_{S_i}}.$$9

Using the kernel trick with $$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$0, the empirical estimate is

$$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$1

The total loss is

$$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$2

The paper characterizes the MMD term as encouraging the global distribution of predictions to match the distribution of true targets, thereby reducing pathological patterns or distributional drift. In the non-LLM setting, gradients from this loss backpropagate through the TSPM, the residual fusion module $$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$3, the MSIL attention and MLP layers, and retrieval-related projections, while CRB itself remains non-parametric.

The LLM branch is different. In the reported experiments, Time-LLM and LLaMA-7B are used with structured prompts, and MCC’s Language Coherer is described as a template-based, deterministic text generator with no learnable parameters inside MCC. The paper therefore distinguishes two optimization regimes: the numerical branch is fully differentiable and end-to-end trainable, whereas the LLM branch relies primarily on prompt-based steering, with the LLM backbone being pre-trained and usually frozen or lightly fine-tuned.

5. Empirical function in zero-shot forecasting

MCC is central to how QuiZSF operationalizes zero-shot forecasting under domain transfer, extreme conditions, and data-scarce settings. The abstract reports that QuiZSF, when paired respectively with non-LLM and LLM-based TSPMs, ranks Top1 in $$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$4 and $$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$5 of prediction settings while maintaining high efficiency in memory and inference time (Ma et al., 9 Aug 2025). MCC is not ablated separately for the numerical branch, but it is indispensable because MSIL outputs would not reach the TSPM without it.

For the LLM branch, the ablation evidence is direct. A variant labeled QuiZSF$$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$6-w/o-Coherer removes structured prompt conversion and instead directly concatenates MSIL features with the target sequence. On the transfer settings ETTm1 $$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$7 ETTh2 and ETTm1 $$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$8 ETTm2, the reported MSE values are:

Variant	ETTm1 $$\mathbf{P}_{\text{int}} = \text{MLP}_1\!\left( \frac{\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}} {\left\|\prod_{i=1}^{n} \mathbf{S}_i^{\text{norm}}\right\|} \right),$$9 ETTh2	ETTm1 $$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$0 ETTm2
QuiZSF$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$1-w/o-RAG	0.394	0.296
QuiZSF$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$2-w/o-MSIL	0.387	0.286
QuiZSF$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$3-w/o-Coherer	0.388	0.289
QuiZSF$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$4	0.382	0.281

The paper states that removing the Coherer causes about $$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$5 MSE degradation on those transfer tasks and comments that “without converting numerical time series into LLM-understandable tokens using the prompt template, the LLM's performance is inferior.” This establishes that, at least for the LLM modality, MCC is not a peripheral formatting layer but a substantive performance-critical interface.

The paper also attributes robustness under domain shift and scarce-data conditions partly to MCC. In the non-LLM branch, retrieval-enhanced residual inputs allow the TSPM to borrow patterns from similar historical sequences in CRB. In the LLM branch, textual descriptions of retrieved patterns help the LLM avoid hallucinations and anchor predictions in realistic behaviors. The case study is described as showing that RAG plus MCC smooths noisy predictions and avoids unrealistic fluctuations.

6. Implementation, limitations, and broader perspective

The paper does not provide layer-by-layer specifications of the residual module $$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$6 or the exact text template used by the Language Coherer (Ma et al., 9 Aug 2025). It does, however, characterize the design as lightweight. For QuiZSF$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$7, the learnable modules in retrieval and feature extraction are said to involve very few additional parameters, and both retrieval and feature extraction rely heavily on efficient dot products. MCC’s Numerical Coherer is therefore presented as a small residual adapter with minor time and memory overhead relative to the base TSPM. Figure analysis is described as showing that QuiZSF$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$8 is only slightly slower than bare TTM$$\mathbf{P}_{\text{avg}} = \text{MLP}_2\!\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{S}_i^{\text{norm}} \right),$$9 while remaining competitive in model size and inference time.

For the Language Coherer, the overhead is primarily token length rather than trainable parameters, because the prompt generator is template-based and MSIL compresses retrieval results into patterns. The paper also notes that there is no dedicated MCC-specific hyperparameter, but its efficacy depends on upstream settings that determine the quality of the features MCC receives: retrieval count $$\mathbf{Q} = \mathbf{W}_q \mathbf{T}^{\text{norm}}, \quad \mathbf{K} = \mathbf{W}_k \mathbf{P}_{\text{avg}}, \quad \mathbf{V} = \mathbf{W}_v \mathbf{P}_{\text{int}},$$0, local-domain proportion $$\mathbf{Q} = \mathbf{W}_q \mathbf{T}^{\text{norm}}, \quad \mathbf{K} = \mathbf{W}_k \mathbf{P}_{\text{avg}}, \quad \mathbf{V} = \mathbf{W}_v \mathbf{P}_{\text{int}},$$1, and database scale. The reported best settings are $$\mathbf{Q} = \mathbf{W}_q \mathbf{T}^{\text{norm}}, \quad \mathbf{K} = \mathbf{W}_k \mathbf{P}_{\text{avg}}, \quad \mathbf{V} = \mathbf{W}_v \mathbf{P}_{\text{int}},$$2, $$\mathbf{Q} = \mathbf{W}_q \mathbf{T}^{\text{norm}}, \quad \mathbf{K} = \mathbf{W}_k \mathbf{P}_{\text{avg}}, \quad \mathbf{V} = \mathbf{W}_v \mathbf{P}_{\text{int}},$$3 around $$\mathbf{Q} = \mathbf{W}_q \mathbf{T}^{\text{norm}}, \quad \mathbf{K} = \mathbf{W}_k \mathbf{P}_{\text{avg}}, \quad \mathbf{V} = \mathbf{W}_v \mathbf{P}_{\text{int}},$$4, and CRB-Medium as a trade-off.

The main limitations attributed to MCC are dependency-related rather than purely architectural. Its performance depends on retrieval quality: noisy retrieval produces noisy MSIL features, which residual fusion or prompting cannot fully repair. It also depends on the expressiveness of the base TSPM, since MCC does not replace the forecast model. In the LLM branch specifically, the Language Coherer is non-trainable and uses fixed templates, limiting its ability to adapt prompt construction through gradient updates.

The paper situates MCC conceptually alongside retrieval-augmented generation and multimodal fusion. The Numerical Coherer resembles learned fusion of retrieved embeddings with model inputs, while the Language Coherer resembles retrieval-aware prompt engineering. From that perspective, MCC is a modality bridge between numerical time-series representations and text-based forecasting interfaces. Future work proposed in the paper includes multi-granularity sequential learning methods for pattern transfer between different sub-sequences, further complexity reduction, and exploration of sparse connections in retrieval and fusion; all of these would plausibly affect MCC’s future design.