---
title: 'ZooCast: A Model Zoo Framework for Zero-Shot Forecasting'
url: https://www.emergentmind.com/topics/zoocast
type: topic
---

# ZooCast: A Model Zoo Framework for Zero-Shot Forecasting

ZooCast is a model-zoo framework for zero-shot time series forecasting that treats the diversity of Time Series Foundation Models (TSFMs) as an asset rather than a nuisance. Its premise is that no single TSFM is uniformly best across all temporal regimes, so the system builds a curated zoo of TSFMs, characterizes each model’s forecasting strengths, and retrieves the most suitable model or top-\(K\) models for an unseen task through the “One-Embedding-Fits-All” paradigm. In that paradigm, both tasks and models are embedded into a unified representation space, so model selection becomes lightweight similarity matching rather than repeated forward passes through the whole zoo [2509.04208].

## 1. Problem formulation and forecasting objective

ZooCast is defined for multivariate time-series forecasting. Given a historical input window
\[
X = [\mathbf{x}_1, \dots, \mathbf{x}_T] \in \mathbb{R}^{C \times T},
\]
where \(C\) is the number of channels and \(\mathbf{x}_t \in \mathbb{R}^C\), the goal is to predict the future horizon
\[
Y = [\mathbf{x}_{T+1}, \dots, \mathbf{x}_{T+H}] \in \mathbb{R}^{C \times H}.
\]
A zero-shot TSFM \(\phi\) produces forecasts directly without task-specific tuning:
\[
\hat{Y} = \phi(X).
\]
ZooCast considers a zoo
\[
\mathcal{Z} = \{\phi_1, \phi_2, \dots, \phi_M\},
\]
and ranks these models for a new task so that it can either select one model or ensemble the top-\(K\) models [2509.04208].

The framework’s core motivation is empirical specialization. The reported examples are explicit: Chronos is especially strong on high-frequency electricity data, while VisionTS excels on cloud data with spikes. This heterogeneity is used to justify a zoo-based inference abstraction:
\[
\mathbf{r}_{\text{final}} = \mathrm{Rank}(X, \mathcal{Z}), \quad
\hat{Y} = \tfrac{1}{K} \sum_{m \in \text{TopK}(\mathbf{r}_{\text{final}})} \phi_m(X, H).
\]
The paper formulates the objective in terms of both accuracy gain and efficiency:
\[
\max \; \begin{cases}
\Delta P := 1 - \mathcal{L}(\hat{Y}) \big/ \min\limits_{m=1,\dots,M} \mathcal{L}(\phi_m(X, H)), \\[6pt]
\eta := \mathbb{E}[\Delta P] \big/ T_{\text{all}} .
\end{cases}
\]
Here \(\mathcal{L}(\cdot)\) is the forecasting loss and \(T_{\text{all}}\) is total runtime including ranking and forecasting. The framework is therefore not merely a selector; it is an efficiency-constrained selector whose purpose is to capture the benefit of specialization without paying the cost of evaluating every TSFM online.

## 2. Model characterization through advantage subsets

ZooCast begins with an offline characterization phase. It constructs a zoo characterization set \(\mathcal{D}\) of \(n\) subsequences sampled from source-specific pools drawn from the pretraining datasets of the models in the zoo. In the main benchmark, the characterization set size is \(n=1000\), and the zoo contains \(13\) TSFMs: Chronos (4 versions), Moirai (3 versions), TimesFM (2 versions), VisionTS (3 versions), and Sundial (1 version) [2509.04208].

Each model is forwarded once on \(\mathcal{D}\), producing an MSE matrix
\[
\mathbf{E} \in \mathbb{R}^{M \times n},
\]
where \(E_{m,i}\) is the MSE of model \(\phi_m\) on sample \(\mathbf{x}_i\). For each sample, the inter-model error variance is
\[
\sigma_i = \operatorname{std}\!\big(\{E_{m,i}\}_{m=1}^{M}\big).
\]
ZooCast then defines an advantage score
\[
s_{m,i} = \left(\frac{1}{M-1}\sum_{k \neq m} E_{k,i} - E_{m,i}\right) \cdot \frac{\sigma_i - \bar{\sigma}}{\hat{\sigma}},
\]
and an advantage subset
\[
\mathcal{D}_m^{\text{adv}} = \left\{\, \mathbf{x}_i \in \mathcal{D} \;\middle|\; s_{m,i} > \tau \,\right\},
\]
with \(\tau = 1\) in the main benchmark setting.

This construction uses two criteria simultaneously. A sample enters \(\mathcal{D}_m^{\text{adv}}\) only if model \(m\) is better than its peers there and if the sample is sufficiently discriminative across models. The paper’s variance-decile analysis shows that the performance gap between the best model and the average model increases sharply in high-variance deciles, which motivates emphasizing such samples during model characterization. The cardinality
\[
d_m = \big|\mathcal{D}_m^{\text{adv}}\big|
\]
also defines a model weight
\[
w_m = \frac{1}{\sqrt{d_m}},
\]
which later scales similarity scores during retrieval.

## 3. “One-Embedding-Fits-All” and consensus ranking

The key technical mechanism is a shared embedding space in which both tasks and models are represented. ZooCast trains a co-embedding extractor
\[
\psi: \mathbb{R}^{T} \rightarrow \mathbb{R}^{D},
\]
with \(D = 128\) in the main experiments. The embedding model is trained on an independent dataset \(\mathcal{D}^*\) using the objective
\[
\min_\Theta \quad \mathcal{L}_{\text{Reconstruction}} + \mathcal{L}_{\text{Constraint}} + \lambda \mathcal{L}_{\text{Transfer}},
\]
where the transfer term explicitly aligns embedding similarity with cross-task transferability. In the reported implementation, the extractor is an encoder-decoder model trained on about \(300{,}000\) subsequences from M3, M4, and Tourism, with input length \(36\), prediction length \(12\), patch size \(16\), one encoder layer, hidden dimension \(64\), learning rate \(0.001\), and 10 training epochs [2509.04208].

A model embedding is not a weight-space summary of the TSFM. Instead, it is the centroid of embeddings of the model’s advantage subset. If all samples in \(\mathcal{D}_m^{\text{adv}}\) are embedded and averaged, the result is a single vector
\[
\mathbf{r}_m \in \mathbb{R}^{D},
\]
and the full library is
\[
\mathbf{R}_{\text{zoo}} =
\left[\mathbf{r}_1, \mathbf{r}_2, \dots, \mathbf{r}_M\right]^\top \in \mathbb{R}^{M \times D}.
\]

For a target multivariate series \(X = \{\mathbf{x}_c\}_{c=1}^C\), ZooCast embeds each channel separately:
\[
\mu_c = \psi(\mathbf{x}_c) \in \mathbb{R}^D, \qquad
\mu = [\mu_1, \mu_2, \dots, \mu_C]^\top \in \mathbb{R}^{C \times D}.
\]
In the reported inference setup, each \(\mu_c\) is obtained by sampling 5 random length-36 segments per channel and averaging them. Weighted cosine similarity is then computed as
\[
\text{sim}_{m,c} = w_m \cdot \frac{\mathbf{r}_m^\top \mu_c}{\|\mathbf{r}_m\| \,\|\mu_c\|},
\quad
\mathbf{A} = [\text{sim}_{m,c}]_{C \times M}.
\]

ZooCast does not finalize ranking by simple averaging over channels. It instead applies an error-correcting consensus procedure. For each channel, it retains the top-\(r\) models, with \(r=3\), and encodes those selections in a binary matrix \(\mathbf{B} \in \{0,1\}^{C \times M}\). It then computes
\[
h_m = \sum_{c=1}^C \mathbb{I}(B_{c,m}=0),
\qquad
\mathbf{r}_{\text{final}} = \mathop{\mathrm{argsort}}_{m} h_m.
\]
Models with lower Hamming distance are preferred because they are recommended by more channels. This error-correcting output-coding style aggregation is intended to suppress noisy channel-wise mismatches. The resulting top-ranked models are used either in top-1 mode or in simple average ensembles over the top-\(K\) retrieved TSFMs.

## 4. Empirical performance on GIFT-Eval

ZooCast is evaluated on GIFT-Eval, which contains 23 datasets, 97 configurations, more than 144,000 time series, and about 177 million observations. The benchmark spans 7 domains—Energy, Economy/Finance, Healthcare, Transport, Nature, Sales, and Web/CloudOps—with frequencies ranging from 10 seconds to annual, and includes both univariate and multivariate tasks. The primary metric is sMAPE, and the paper also reports average rank across configurations [2509.04208].

The reported full-benchmark results place ZooCast ahead of both the strongest single TSFM and the naive all-model ensemble in average rank.

| Setting | Method | sMAPE / Rank |
|---|---|---|
| Full GIFT-Eval | Sundial base | \(0.430 / 4.845\) |
| Full GIFT-Eval | All-13 ensemble | \(0.445 / 5.062\) |
| Full GIFT-Eval | Top-3 ZooCast | \(0.437 / 3.688\) |
| Full GIFT-Eval | Top-5 ZooCast | \(0.431 / 3.158\) |
| Univariate subset | Top-3 LogME | \(0.377 / 5.375\) |
| Univariate subset | Top-5 LogME | \(0.369 / 4.969\) |
| Univariate subset | Top-3 ZooCast | \(0.352 / 3.688\) |
| Univariate subset | Top-5 ZooCast | \(0.353 / 3.094\) |

These results show two distinct effects. First, top-\(K\) retrieval outperforms naive ensemble-all despite using fewer models at inference. Second, the benefit is not limited to multivariate forecasting; on the univariate subset, ZooCast clearly surpasses the adapted LogME-guided ensembles. The paper also reports that Top-3 ZooCast ensemble consistently outperforms both the naive All-13 ensemble and the strongest single model, and that performance improves as \(K\) increases modestly, which the authors describe as a favorable test-time scaling law.

## 5. Efficiency, storage, and sequential model release

ZooCast’s central efficiency claim is that selection is representation-based rather than forward-based. The reported complexity comparison is:
- Random: \(\mathcal{O}(N)\)
- Enumerate all: \(\mathcal{O}(MN)\)
- Ensemble all: \(\mathcal{O}(MN)\)
- Forward-based: \(\mathcal{O}(Mn + N)\)
- Repr-based (ZooCast): \(\mathcal{O}({Mn}/{U} + N)\)

Here \(M\) is the zoo size, \(N\) is task data size, \(n \ll N\) is characterization-set size, and \(U\) is the number of future unseen tasks over which precomputation is amortized. The interpretation is that the cost of building model representations is paid once, while online selection reduces to low-dimensional similarity matching plus forecasting by only the retrieved model or ensemble [2509.04208].

The measured runtime numbers on 97 GIFT-Eval tasks and 13 TSFMs are explicit:
- Full Forward: 88,024 seconds total
- ZooCast precompute: 123 seconds one-time
- Selection: 1,042 seconds
- Forecast: 2,958 seconds

The paper also reports low storage overhead: at \(M=10\), storing \(\mathbf{E}\) and \(\mathbf{R}_{\text{zoo}}\) requires about 0.2 MB; at \(M=1000\), around 20 MB. This makes the framework suitable for large and growing model zoos.

A second practical contribution is sequential expansion. When a new model \(\phi_{M+1}\) is released, ZooCast does not recompute the whole zoo. It runs only the new model on the fixed characterization set, appends its error row to the existing matrix, computes its representation, and appends that representation to the zoo library. The appendix states that this takes under one minute to characterize a new model and under one second to append the new representation. The paper’s sequential-release experiments show that performance improves progressively as new TSFMs are added, while retaining the best rank.

## 6. Assumptions, limitations, and conceptual significance

ZooCast relies on several explicit assumptions. It assumes that model complementarity exists, that a small characterization set is sufficient to summarize model strengths, that task behavior is reflected in short local segments, that a shared embedding space can align temporal patterns with model transferability, and that consensus across channels is informative for final ranking [2509.04208].

Those assumptions determine the framework’s main limitations. It depends on the quality of the offline characterization set \(\mathcal{D}\) and on the quality of the learned embedding alignment. Task embeddings are built from short windows of length 36, so the method may be weaker when suitability depends on very long context or on rare regime changes not visible in sampled segments. Final output fusion is deliberately simple—top-\(K\) average ensembling rather than learned combination—so some performance may remain unrealized. The evaluation is also for point forecasting rather than probabilistic forecasting; the paper explicitly excludes CRPS because ZooCast targets point forecasts.

Within those constraints, ZooCast represents a shift in the design philosophy of zero-shot forecasting systems. It rejects the premise that one TSFM should dominate every domain and instead makes model diversity operational through a single shared retrieval space. The framework is therefore not itself a forecaster in the narrow sense; it is a selector and ensemble controller that turns a collection of heterogeneous TSFMs into a coherent inference system. The paper’s broader significance lies in that move from “one foundation model fits all” to “one embedding space fits all models and tasks,” with the empirical result that a dynamically selected zoo can approach the efficiency of a single TSFM while improving average robustness across heterogeneous forecasting regimes.

Source: https://www.emergentmind.com/topics/zoocast