Zero-shot and few-shot forecasting, classification, imputation, anomaly detection

"They asked me to forecast a vibration channel I had never seen. I read the last 512 samples, thought for one forward pass, and did not retrain a single weight. The maintenance team called it magic. I called it Tuesday."

An Unfazed AI Agent

This section assumes you understand what a foundation model is (Section 19.1) and how patching and value tokenization encode a series (Section 19.2). It also leans on probabilistic forecasting notation and proper scoring rules from the uncertainty primer in Chapter 4, and on the residual-based detectors of Chapter 12. You do not need to have trained a TSFM yourself; every technique here treats the backbone as a fixed function.

The zero-shot to few-shot spectrum

What distinguishes the regimes is how much task-specific weight update you allow. Zero-shot means no gradient touches the model: you supply a context window \(x_{1:L}\) and the network emits its answer in one forward pass, exactly as a large language model answers a prompt it was never fine-tuned on. Few-shot means you have somewhere between a handful and a few hundred labeled windows, too few to train a model from scratch, and you use them to nudge the pretrained representation. The three standard nudges, from cheapest to most expressive, are the linear probe (freeze the backbone, fit a logistic or ridge head on its embeddings), parameter-efficient fine-tuning such as LoRA (inject a few low-rank adapter matrices, train only those), and full fine-tuning (unfreeze everything, viable only when you have thousands of windows).

Why zero-shot works at all is worth stating plainly: pretraining on hundreds of billions of time points across electricity, traffic, weather, finance, and sensor corpora teaches the model the shared grammar of temporal data, trend, seasonality, autocorrelation, level shifts, and heavy tails. A new vibration or glucose channel is rarely grammatically novel even when it is semantically novel. When the new signal violates that grammar (a control loop with a sampling rate the model never saw, a regime with no analogue in pretraining), zero-shot degrades and the few-shot budget earns its keep.

Zero-shot forecasting: the flagship capability

Forecasting is where TSFMs shine hardest because it is the task most of them were pretrained on directly. How it runs: you choose a context length \(L\) (often 512 to 2048 samples), the model consumes the (instance-normalized) window, and it emits a distribution over the next \(H\) steps. Good TSFMs are probabilistic: they return quantiles \(q_\alpha(x_{L+h})\) rather than a single point, so you get calibrated intervals for free. That matters for sensor decisions, where a predictive-maintenance alert needs a confidence band, not just a mean. Evaluate with a quantile loss such as the weighted quantile loss, \(\mathrm{WQL} = \tfrac{2}{\sum_h |x_{L+h}|}\sum_{h,\alpha} \big[\alpha(x - q_\alpha)_+ + (1-\alpha)(q_\alpha - x)_+\big]\), which rewards sharp, calibrated intervals and reduces to mean absolute error at the median.

Two practical knobs dominate zero-shot quality. First, context length: too short and the model cannot see the dominant seasonality; too long and irrelevant ancient history dilutes the prior. Match \(L\) to at least two or three periods of the slowest cycle you care about. Second, instance normalization: nearly all TSFMs standardize each window internally, so a channel measured in \(\mathrm{m/s^2}\) and one in millivolts are treated identically; you rarely need to rescale by hand, but you must ensure the window has enough non-constant signal for the statistics to be meaningful.

Classification, imputation, and anomaly detection from the same prior

Imputation is forecasting turned inward. Sensor streams drop samples: a wearable loses skin contact, a CAN bus drops a frame, a lidar returns nothing off a black surface. A TSFM with a masked-reconstruction objective (MOMENT is the canonical example) fills interior gaps by conditioning on both past and future context, which is strictly more information than a causal forecaster has, so zero-shot imputation is often excellent. Anomaly detection reuses either head: run the model, form the residual \(r_t = x_t - \hat{x}_t\) (forecast residual) or the reconstruction error (imputation residual), and threshold it. The surprise signal is model-agnostic; you are simply asking "how far did reality fall outside what the pretrained prior expected," which connects directly to the residual detectors and change-point tests of Chapter 12. Classification is the one task that needs a new head: extract a pooled embedding \(z = f_\theta(x_{1:L})\) from the frozen backbone and fit a small classifier on top. Section 19.5 develops this embeddings-as-features view in depth; here the point is that even classification rides the same frozen model.

import numpy as np
from chronos import ChronosBoltPipeline   # frozen TSFM, no training

pipe = ChronosBoltPipeline.from_pretrained("amazon/chronos-bolt-base")

def zero_shot_anomaly(series, context=512, horizon=1, k=3.0):
    """Slide a frozen forecaster over a channel; flag samples that fall
    outside its predicted quantile band by more than k robust sigmas."""
    flags = np.zeros(len(series), dtype=bool)
    for t in range(context, len(series) - horizon):
        ctx = series[t - context:t]
        q = pipe.predict_quantiles(ctx, prediction_length=horizon,
                                   quantile_levels=[0.1, 0.5, 0.9])
        lo, mid, hi = q[0, 0], q[1, 0], q[2, 0]      # 10/50/90 percentiles
        band = max(hi - lo, 1e-6)                     # predicted spread
        resid = abs(series[t] - mid)
        flags[t] = resid > k * band                   # surprise exceeds prior
    return flags

Few-shot adaptation: spending a small label budget well

When zero-shot leaves a gap, do not jump to full fine-tuning. The efficient frontier is: linear probe first, then LoRA, then full unfreeze only if data justifies it. A linear probe on frozen embeddings needs only tens of examples per class and cannot overfit the backbone, making it the right first move for a new activity-recognition or arrhythmia-screening task. LoRA adds low-rank matrices \(W + \Delta W\) with \(\Delta W = BA\), \(A \in \mathbb{R}^{r\times d}\), \(B \in \mathbb{R}^{d\times r}\) and small rank \(r\); you train perhaps 0.1 to 1% of the parameters, which shifts the forecasting or reconstruction behavior toward your domain without erasing the pretrained prior. Because you touch so few weights, few-shot fine-tuning is also far less prone to the leakage traps of full retraining, though you still hold out a strictly future validation window, a discipline this book returns to in Section 19.6 and in Chapter 5.

What's Next

In Section 19.5, we go one level deeper on the classification move that appeared here only in passing: using a frozen foundation model purely as a feature extractor, so its embeddings become drop-in inputs for downstream classifiers, regressors, retrieval, and clustering, and we measure when those embeddings beat hand-engineered features.