KAIROS: Zero-Shot Non-Autoregressive Forecasting

• KAIROS is a non-autoregressive time series forecasting framework that explicitly models segment-level multi-peak distributions for zero-shot and real-time applications.
• It employs adaptive patch embeddings and a parallel segment-wise decoder with specialized modules (SAGE, LEV, SCRN) to maintain forecast fidelity and speed.
• Evaluated on multiple benchmarks, KAIROS achieves state-of-the-art zero-shot accuracy while reducing inference cost compared to autoregressive models.

KAIROS is a non-autoregressive time series forecasting framework for universal, zero-shot forecasting that directly models segment-level multi-peak distributions, with an emphasis on Web-scale applications requiring fast responsiveness for real-time decision making (Ding et al., 2 Oct 2025). It is designed to avoid the slow inference, exposure bias, and error accumulation associated with autoregressive decoders, while also addressing the over-smoothed predictions and mode collapse that have limited earlier non-autoregressive approaches. In the reported formulation, KAIROS combines adaptive granularity patch embeddings with a parallel segment-wise decoder, and is trained end-to-end on a large-scale corpus to achieve forecasting performance comparable to state-of-the-art foundation models of similar scale at a fraction of their inference cost (Ding et al., 2 Oct 2025).

1. Problem Setting and Motivation

Time series forecasting for Web applications is presented as a setting in which forward-looking signals drive resource planning, cache placement, and anomaly response, and in which faster responsiveness is especially important because user behavior and content distributions evolve continuously (Ding et al., 2 Oct 2025). Within this setting, the central modeling problem is not only point prediction but the representation of segment-level multi-peak distributions: for some forecast intervals, multiple plausible futures can follow from similar historical context because relevant exogenous factors are latent or unobserved (Ding et al., 2 Oct 2025).

KAIROS is motivated by two complementary limitations in prior forecasting paradigms. Autoregressive models are described as having strong modeling capacity, but their sequential decoding causes latency that grows linearly with the forecast horizon, and their train–test mismatch induces exposure bias and error accumulation (Ding et al., 2 Oct 2025). Earlier non-autoregressive models predict all future steps in parallel and therefore are efficient, yet they are reported to suffer from over-smoothed forecasts under point-estimation losses such as MSE and from an inability to represent multimodal futures at the segment level (Ding et al., 2 Oct 2025).

The framework is therefore positioned around a dual requirement: speed through parallel inference and fidelity through explicit modeling of multimodal forecast structure (Ding et al., 2 Oct 2025). This suggests that KAIROS treats non-autoregressive design not merely as a systems optimization, but as a modeling choice intended to preserve uncertainty structure that would otherwise collapse into averaged trajectories.

2. Architectural Design

KAIROS consists of an encoder and a decoder (Ding et al., 2 Oct 2025). The encoder uses adaptive granularity patch embeddings, which are intended to represent past context more flexibly than fixed-size windows. The decoder is a non-autoregressive segment-wise forecasting module that predicts forecast segments in parallel rather than generating future steps sequentially (Ding et al., 2 Oct 2025).

Three architectural components are identified as the framework’s core innovations: Scenario-Aware Generative Experts (SAGE), Learnable Exogenous Vectors (LEV), and Segment Causal Residual Noise (SCRN) (Ding et al., 2 Oct 2025).

SAGE provides a segment-level mixture-of-experts head. For each segment in the prediction horizon, multiple experts specialize in distinct plausible scenarios, and a gating network dynamically routes input to a subset of the $E$ experts using top-$K$ selection, producing an ensemble prediction (Ding et al., 2 Oct 2025). This design is intended to expose multiple plausible futures directly at the segment level rather than forcing them into a single averaged output.

LEV introduces a learnable vector for each forecast segment that acts as a proxy for unobserved exogenous influences such as sudden market changes or environmental factors (Ding et al., 2 Oct 2025). The encoder output for a segment is concatenated with these vectors, which are optimized jointly with the forecasting objective. In the authors’ description, LEV injects scenario variability and additional “noise” into the segment head (Ding et al., 2 Oct 2025).

SCRN is a lightweight mechanism for temporal coherence across adjacent segments. It injects residual noise into each segment using only the previous segment’s output, thereby preserving causal ordering without reintroducing autoregressive generation (Ding et al., 2 Oct 2025). The reported formulation is

$$\mathbf{n}^{(s)} = \mathbf{y}^{(s-1)} \odot \mathbf{e}^{(s)}$$

$$\tilde{\mathbf{y}}^{(s)} = \mathbf{y}^{(s)} + \alpha \mathbf{n}^{(s)}$$

where $\odot$ denotes elementwise multiplication, $\mathbf{e}^{(s)}$ is a learnable vector, and $\alpha$ is a small learnable scalar (Ding et al., 2 Oct 2025). Within the framework, SCRN is intended to reduce output discontinuities between segments while remaining compatible with parallel decoding.

3. Segment-Level Multi-Peak Modeling

The paper formalizes the forecasting target as a multimodal conditional distribution

$$p(\mathbf{Y}\mid \mathbf{X}) = \sum_{m=1}^{M} \pi_m(\mathbf{X})\, p_m(\mathbf{Y}\mid \mathbf{X})$$

and contrasts this with standard non-autoregressive training under MSE, which approximates the conditional mean

$$\hat{\mathbf{Y}} \approx \mathbb{E}_{p(\mathbf{Y}\mid \mathbf{X})}[\mathbf{Y}]$$

thereby producing over-smoothed forecasts when several modes coexist (Ding et al., 2 Oct 2025). KAIROS addresses this with the SAGE head and LEV.

For encoder feature $\mathbf{z}_n$, the routing distribution is defined as

$K$0

and each expert $K$1 predicts a segment as

$K$2

The combined segment prediction is

$K$3

where the second term is a shared pathway added to the expert mixture (Ding et al., 2 Oct 2025). An auxiliary balancing term is also introduced:

$K$4

with $K$5 and $K$6 denoting average routing and selection frequencies (Ding et al., 2 Oct 2025). This term is used to stabilize expert utilization.

In this formulation, the principal representational claim is that segment-level mixture-of-experts routing makes multimodality explicit rather than implicit. LEV complements this by providing learned low-dimensional exogenous tokens that help represent hidden influences (Ding et al., 2 Oct 2025). A plausible implication is that KAIROS distributes uncertainty across both expert specialization and latent exogenous variation, rather than relying on a single stochastic bottleneck.

4. Training Objective and Optimization

KAIROS is trained as a joint encoder–decoder framework with all components optimized end-to-end (Ding et al., 2 Oct 2025). The overall objective combines forecast loss, expert-balancing regularization, and patch-budget regularization:

$K$7

The prediction term is reported as

$K$8

with $K$9 instantiated as MSE or MAE across forecast segments and horizon (Ding et al., 2 Oct 2025). LEV and SCRN are trained implicitly through the main objective rather than through separate auxiliary supervision (Ding et al., 2 Oct 2025).

The architecture is paired with a non-autoregressive decoding procedure in which all forecast segments are generated in parallel (Ding et al., 2 Oct 2025). This means inference time remains nearly constant as forecast length increases, in contrast to autoregressive decoders whose latency grows linearly with prediction length (Ding et al., 2 Oct 2025). The paper explicitly frames this “just-in-time inference” property as a practical advantage for long-horizon and real-time settings.

5. Empirical Evaluation

The reported evaluation emphasizes zero-shot generalization (Ding et al., 2 Oct 2025). Pre-training is conducted on BLAST, described as a massive and diverse time series corpus with 321B observations, and evaluation data are explicitly excluded from pre-training to ensure fairness (Ding et al., 2 Oct 2025). KAIROS is tested on six widely used benchmarks—ETTh1, ETTh2, ETTm1, ETTm2, Weather, and GlobalTemp—each under forecast horizons 96, 192, 336, and 720 (Ding et al., 2 Oct 2025).

The comparison set includes large autoregressive models Sundial, Time-MoE, Timer-XL, Chronos, MOIRAI, TimesFM, and Moment (Ding et al., 2 Oct 2025). The central empirical finding is that KAIROS achieves state-of-the-art or highly competitive zero-shot forecasting accuracy, matching or outperforming leading autoregressive and non-autoregressive time series foundation models of similar or larger size across diverse domains and long horizons (Ding et al., 2 Oct 2025). The abstract further states that KAIROS delivers performance comparable to state-of-the-art foundation models with similar scale at a fraction of their inference cost (Ding et al., 2 Oct 2025).

The evaluation also highlights efficiency. Because KAIROS decodes all forecast segments in parallel, its inference time remains nearly constant as horizon length grows, whereas autoregressive models become bottlenecked by sequential generation (Ding et al., 2 Oct 2025). Even systems such as Sundial, described as having system-level speed optimizations, are said only to approach non-autoregressive efficiency for short horizons and not to match its scalability (Ding et al., 2 Oct 2025).

Ablation studies attribute most of the performance gain to the SAGE mixture-of-experts head (Ding et al., 2 Oct 2025). By contrast, SCRN and LEV provide marginal or mixed utility and may sometimes introduce extra noise, although the paper notes that they are lightweight and preserve the framework’s speed advantage (Ding et al., 2 Oct 2025). The framework is also reported to be robust to segment length and exogenous vector size, with moderate values favored in practice (Ding et al., 2 Oct 2025).

6. Position within Time Series Foundation Modeling

KAIROS is described as the first universal non-autoregressive time series foundation model to explicitly solve segment-level multi-peak prediction (Ding et al., 2 Oct 2025). Within that positioning, its main conceptual claim is that segment-wise mixture-of-experts decoding is necessary to avoid mode collapse while retaining the computational advantages of parallel generation (Ding et al., 2 Oct 2025).

This places the model within a broader debate in time series foundation modeling between autoregressive and non-autoregressive design. The paper does not reject autoregressive models’ modeling power; rather, it argues that their sequential nature imposes structural limitations for real-time, large-scale applications (Ding et al., 2 Oct 2025). Conversely, earlier non-autoregressive systems are characterized as efficient but insufficiently expressive because they tend toward conditional averaging (Ding et al., 2 Oct 2025). KAIROS is presented as an attempt to combine the fidelity typically associated with strong generative modeling and the latency profile associated with parallel decoding.

The paper’s broader implication is that non-autoregressive forecasting can function as a scalable paradigm for universal time series foundation models when multimodality is handled explicitly at the segment level (Ding et al., 2 Oct 2025). This suggests a reframing of forecasting architecture design: the main obstacle to non-autoregressive performance may be less the absence of sequential dependence itself than the failure to represent alternative plausible futures.

7. Limitations, Interpretation, and Future Directions

The reported ablations indicate that not all auxiliary mechanisms contribute equally. SAGE is identified as the dominant source of performance improvement, whereas LEV and SCRN yield marginal or mixed benefits (Ding et al., 2 Oct 2025). This is important because it narrows the paper’s strongest claim to the segment-level mixture-of-experts design rather than to every component of the architecture.

The paper also identifies open directions. Improving the modeling of exogenous variability and localized refinement, along with developing more efficient and generalizable segment-linking mechanisms, is explicitly presented as future work (Ding et al., 2 Oct 2025). This suggests that while KAIROS addresses multimodal segment forecasting, the representation of latent drivers and inter-segment coherence remains only partially resolved.

At a methodological level, KAIROS advances a specific interpretation of universal forecasting: a foundation model should be able to generalize zero-shot across heterogeneous domains while maintaining operationally viable latency under long horizons (Ding et al., 2 Oct 2025). In that sense, its contribution is simultaneously architectural and systems-oriented. The model argues, through both its design and its evaluation, that foundation-scale forecasting in time series may require parallel generation not as a compromise, but as a primary design principle for deployment-sensitive settings (Ding et al., 2 Oct 2025).