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Hold-One-Shot-Out (HOSO) in Few-Shot Learning

Updated 5 July 2026
  • HOSO is a mechanism that holds out a one-shot example to prevent overfitting, leakage, and improper reuse of limited supervision.
  • It enables precise calibration by excluding the self-induced predictor, ensuring unbiased aggregation in conformal prediction or hyperparameter tuning scenarios.
  • HOSO is applied in distinct settings, including leave-one-out calibration in CAOS and validation-free optimization in CLIP adapters for few-shot tasks.

Searching arXiv for the cited HOSO-related papers to ground the article in current arXiv records. Hold-One-Shot-Out (HOSO) is a context-dependent hold-out mechanism for one-shot or few-shot learning in which a single labeled example, or the predictor induced by that example, is excluded from part of the training or calibration pipeline to control overfitting, leakage, or invalid reuse of scarce supervision. In the arXiv literature represented here, the term has two distinct technical realizations. In "CAOS: Conformal Aggregation of One-Shot Predictors" (Waldron, 8 Jan 2026), the underlying idea appears as leave-one-out calibration for one-shot conformal prediction: each calibration example is scored after removing the one-shot predictor induced by that same example. In "Hold-One-Shot-Out (HOSO) for Validation-Free Few-Shot CLIP Adapters" (Vorster et al., 4 Mar 2026), HOSO denotes a validation-free procedure that holds out exactly one labeled image per class from the few-shot support to learn a CLIP-adapter blending ratio. By contrast, "NAS-Bench-1Shot1: Benchmarking and Dissecting One-shot Neural Architecture Search" (Zela et al., 2020) does not define or use HOSO.

1. Terminological scope and conceptual core

The shared conceptual core of HOSO is selective exclusion under severe label scarcity. A one-shot element is held out so that the remaining data can be used for model fitting, aggregation, or calibration, while the held-out element provides an unbiased or less biased signal for a secondary objective. The exact object being held out differs by setting.

In CAOS, what is held out is the one-shot predictor induced by the calibration example itself. The paper does not use the name “HOSO”; it uses “leave-one-out calibration.” The provided formulation identifies HOSO with that leave-one-out calibration idea specialized to one-shot predictors: for each labeled example, the calibration score is computed after removing that example’s own induced predictor from the aggregation pool (Waldron, 8 Jan 2026).

In the CLIP-adapter setting, HOSO is the explicit name of a protocol in which exactly one labeled image per class is removed from the few-shot support and used as a micro-validation cache to optimize the blending ratio α\alpha, while the adapter is trained on the remaining support examples (Vorster et al., 4 Mar 2026).

These two usages are analogous in spirit but not identical in mechanics. One addresses conformal uncertainty quantification with finite-sample coverage guarantees; the other addresses hyperparameter learning under a strict validation-free few-shot protocol. This suggests that “HOSO” is best treated not as a single algorithm, but as a family resemblance among one-shot hold-out constructions.

2. HOSO as leave-one-out calibration in CAOS

In CAOS, the problem setting is one-shot prediction with foundation models under a small labeled dataset D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n. Each labeled example induces its own one-shot predictor through a fixed mechanism π\pi:

πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).

Each predictor has an associated nonconformity score sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R} (Waldron, 8 Jan 2026).

The paper gives two concrete instantiations. For landmark transfer in vision via patch similarity,

sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),

with point prediction

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).

For one-shot text classification with LLMs via in-context learning,

sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),

again with

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).

The motivation is that split conformal is inefficient in the one-shot regime because it requires disjoint reference and calibration splits and equips each one-shot predictor independently. The baseline for a fixed ii uses calibration scores

D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n0

threshold

D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n1

and prediction set

D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n2

with

D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n3

CAOS replaces this with adaptive aggregation across multiple one-shot predictors. For any reference set D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n4 and target D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n5, it defines the score multiset

D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n6

and the D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n7-min sum operator

D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n8

where D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n9 are the ordered values in π\pi0.

The test-time aggregated nonconformity score is

π\pi1

HOSO enters through the leave-one-out calibration statistic. For each π\pi2, define

π\pi3

and compute

π\pi4

The calibration quantile is

π\pi5

and the final prediction set is

π\pi6

Operationally, HOSO here means that when calibrating on π\pi7, the unique one-shot predictor generated from π\pi8 is excluded. This prevents a “self-score” advantage, avoids self-score leakage, and allows all π\pi9 labeled examples to participate in calibration without data splitting (Waldron, 8 Jan 2026).

3. Algorithmic structure and theory of CAOS-HOSO

The CAOS construction proceeds in three stages. First, multiple one-shot predictors are built by instantiating πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).0 and πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).1 for each labeled example. Second, HOSO or leave-one-out calibration scores πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).2 are computed using πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).3, followed by the quantile πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).4. Third, for each candidate πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).5 at test time, the aggregated score πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).6 is computed over the full labeled pool πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).7, and πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).8 is returned (Waldron, 8 Jan 2026).

The aggregation rule is the πi(x):=π(x;(Xi,Yi)).\pi_i(\cdot \mid x) := \pi(\cdot \mid x;\,(X_i,Y_i)).9-min-sum operator, averaged by sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}0. The paper states that this selects the sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}1 most supportive one-shot predictors for a given sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}2, avoiding dilution by weak or irrelevant references. In experiments, sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}3 is used throughout. The operator is described as permutation-invariant and monotone in the reference set.

The finite-sample coverage theorem is stated under exchangeability and a self-score condition. The required assumption is

sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}4

Under exchangeability of the labeled data sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}5 and the test example sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}6, and under this self-score optimality assumption, the CAOS prediction set satisfies

sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}7

The proof route is not classical exchangeability of the score sequence, because adaptive aggregation and leave-one-out calibration violate the usual form. Instead, the paper introduces a full CAOS construction with a hypothetical test label sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}8:

sπi(x,y)Rs_{\pi_i}(x,y) \in \mathbb{R}9

For each calibration index sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),0, the full CAOS score is

sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),1

The corresponding threshold is

sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),2

and the full conformal set is

sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),3

The key lemmas are: symmetry of the full CAOS score, monotonicity of the CAOS score with respect to enlarging the reference set, and a comparison lemma asserting

sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),4

The argument then yields sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),5 together with test-score equivalence under self-score optimality, giving

sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),6

and hence the CAOS coverage guarantee. The significance of this construction is that CAOS attains exact marginal coverage without adding extra slack, despite score-level non-exchangeability (Waldron, 8 Jan 2026).

A plausible implication is that HOSO in this sense is not merely a data-efficiency heuristic; it is part of a formally justified conformal design whose validity depends on monotonicity, permutation symmetry, exchangeability of examples, and self-score optimality.

4. HOSO for validation-free few-shot CLIP adapters

In the CLIP-adapter literature, HOSO denotes a distinct procedure aimed at learning the blending ratio sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),7 without a labeled validation set. The setting begins with frozen CLIP encoders: an image encoder sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),8 and text encoder sπi(x,y)=1sim ⁣(ex(y),eXi(Yi)),s_{\pi_i}(x,y) = 1 - \mathrm{sim}\!\bigl(e_x(y), e_{X_i}(Y_i)\bigr),9, both producing y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).0-normalized embeddings. For class y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).1, the class prototype is

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).2

For image y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).3, y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).4 with y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).5, and zero-shot probabilities are

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).6

CLIP-Adapter introduces an adapter y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).7, a bottleneck MLP, with adapted feature

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).8

The blended representation is

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).9

followed by sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),0 normalization and classification using the same text prototypes and temperature sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),1:

sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),2

Here sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),3 is the blending ratio, sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),4 are adapter parameters, and the protocol is explicitly validation-free (Vorster et al., 4 Mar 2026).

The HOSO step is to hold out exactly one labeled image per class from the few-shot support sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),5 to form a tiny cache sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),6 of size sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),7 images. Those examples are removed from the adapter’s training set, leaving sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),8. The held-out shot is selected randomly per class once at the start and kept fixed. The blending ratio is a single global scalar per dataset, not per-class and not per-layer.

To constrain the optimization, HOSO parameterizes sπi(x,y)=AvgNLL ⁣(yprompt(Xi,Yi,x)),s_{\pi_i}(x,y) = \mathrm{AvgNLL}\!\bigl(y \mid prompt(X_i,Y_i,x)\bigr),9 by a logit:

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).0

so that y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).1. The stated purpose is to stabilize optimization and avoid degenerate solutions that fully discard either CLIP or the adapter.

Optimization is decoupled. On y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).2, the adapter is trained with

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).3

updating only adapter parameters y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).4 while keeping y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).5 fixed during that step. On the cache y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).6, HOSO updates only y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).7 via

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).8

equivalently

y^i=arg minyYsπi(x,y).\hat y_i = \argmin_{y \in \mathcal{Y}} s_{\pi_i}(x,y).9

in single-example notation. The paper uses two separate SGD optimizers, initializes ii0 to ii1 via ii2, and updates the ratio each epoch using the hold-out cache (Vorster et al., 4 Mar 2026).

This HOSO formulation differs sharply from CAOS-HOSO. The hold-out object is no longer a one-shot predictor within a conformal pipeline, but a one-shot-per-class micro-validation set for learning a hyperparameter under strict few-shot constraints.

5. Empirical results and comparative behavior

The empirical evidence for CAOS-HOSO is reported on one-shot facial landmarking and RAFT text classification. In the facial landmarking setup with 478 landmarks and ii3 patches, the reported results are as follows.

Setting Coverage / size
ii4, SCOS Avg. ii5 / ii6
ii7, SCOS Best ii8 / ii9
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n00, CAOS D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n01 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n02
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n03, Oracle D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n04 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n05
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n06, SCOS Avg. D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n07 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n08
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n09, SCOS Best D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n10 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n11
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n12, CAOS D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n13 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n14
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n15, Oracle D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n16 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n17
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n18, SCOS Avg. D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n19 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n20
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n21, SCOS Best D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n22 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n23
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n24, CAOS D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n25 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n26
D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n27, Oracle D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n28 / D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n29

The paper summarizes this as CAOS consistently attaining target coverage while reducing set sizes relative to split conformal baselines and approaching oracle efficiency in many landmarks. For RAFT one-shot text classification with Llama2-7B at D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n30, CAOS produces smaller prediction sets in D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n31 tasks; in coverage terms, D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n32 tasks are hit by both CAOS and SCOS, D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n33 only by CAOS, and D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n34 are missed by both, with the note that small test-set size leads to noisy coverage estimates (Waldron, 8 Jan 2026).

For HOSO-Adapter, the validation-free few-shot protocol uses D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n35 shots per class in the main experiments and evaluates on 11 standard few-shot classification datasets: ImageNet, Caltech101, OxfordPets, StanfordCars, Flowers102, Food101, FGVCAircraft, SUN397, DTD, EuroSAT, and UCF101. The paper states that HOSO-Adapter outperforms the CLIP-Adapter baseline by more than 4 percentage points on average across 11 standard few-shot datasets, and that in the 8- and 16-shot settings it outperforms CLIP-Adapter even with the optimal blending ratio selected on the test set (Vorster et al., 4 Mar 2026).

Ablations on RN50, 16-shot, reported as averages, are:

Variant Average accuracy
Full HOSO-Adapter 76.43%
Without decoupled training 73.02%
Keep cache samples in adapter training set 73.35%
Use 2 shots per class in cache 76.04%
Use 8 shots per class in cache 73.68%

The RN50 16-shot snapshot, averaged over 3 runs, gives HOSO-Adapter at 75.25%, CLIP-Adapter (validation-free reimplementation) at 73.35%, CLIP zero-shot at 57.71%, TIP-Adapter (training-free) at 64.61%, and PathCLIP (reimplementation) at 73.35%. The ViT-B/16 16-shot snapshot gives HOSO-Adapter at 80.33%, CLIP-Adapter at 75.82%, and CLIP-Adapter “best D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n36” tuned on the test set over D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n37 at 81.07%, which the paper notes is not strictly comparable. Reported per-dataset improvements versus validation-free CLIP-Adapter include DTD D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n38, FGVCAircraft D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n39, and EuroSAT D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n40 points (Vorster et al., 4 Mar 2026).

The paper also reports across-shot averages. RN50 HOSO-Adapter averages are 63.03 for 2-shot, 65.13 for 4-shot, 71.78 for 8-shot, and 75.25 for 16-shot. ViT-B/16 HOSO-Adapter averages are 69.76, 71.61, 77.43, and 80.33, respectively. It further reports that jointly learning D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n41 on the support set without hold-out causes D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n42 to increase monotonically during training and overfit, whereas HOSO’s D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n43 stays conservative and drops when overfitting is detected, reducing train–test gaps across datasets (Vorster et al., 4 Mar 2026).

6. Practical conditions, limitations, and relation to adjacent literature

The practical guidance for CAOS-HOSO is to use all available labeled examples to instantiate one-shot predictors, compute each calibration score D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n44 with D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n45, and choose a small D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n46, with D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n47 used throughout the experiments. The score functions should be comparable across references, and the aggregation should remain symmetric to reference permutations, monotone in the reference set, and compatible with the self-score optimality assumption. The paper identifies possible failure modes: violating self-score optimality can break the set-inclusion step in the proof; retraining-dependent scores or aggregation that depends on model parameters fitted on augmented data may violate the required assumptions. Computationally, per test input and candidate D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n48, computing D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n49 is D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n50; finding the D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n51 smallest can be done in D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n52 with selection or D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n53 with a heap; overall complexity is D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n54 per test input, with D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n55 preprocessing for calibration (Waldron, 8 Jan 2026).

The practical guidance for HOSO-Adapter is correspondingly specific: hold out exactly one random sample per class, train the adapter on D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n56, optimize D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n57 on the cache D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n58, use decoupled optimization with two optimizers, and keep D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n59 in D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n60 with initialization near D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n61. The reported defaults are an adapter bottleneck MLP with reduction factor 4 and ReLU, 200 epochs, batch size 32, SGD with momentum 0.9, weight decay 0.0005, cosine learning-rate schedule, initial learning rate 0.002 for the adapter, and a separate ratio optimizer with learning rate 0.1. The paper warns against jointly optimizing D={(Xi,Yi)}i=1nD = \{(X_i,Y_i)\}_{i=1}^n62 and the adapter on the same few-shot data, keeping the held-out samples in the adapter training set, or using large cache sizes; it reports that one-shot per class is best on average (Vorster et al., 4 Mar 2026).

The literature boundary is also explicit. "NAS-Bench-1Shot1: Benchmarking and Dissecting One-shot Neural Architecture Search" does not introduce, name, or evaluate a Hold-One-Shot-Out protocol. Its one-shot supernet is trained on the full one-shot search space; architectures are not held out from supernet training; and the only hold-outs described are standard train/validation data splits for updating weights and architectural parameters, plus use of NAS-Bench-101 validation data for BOHB objective computation during hyperparameter tuning (Zela et al., 2020).

Taken together, these sources support a precise but non-unified view of HOSO. In one strand, HOSO is a leave-one-out conformal calibration device for aggregating one-shot predictors with exact finite-sample marginal coverage under exchangeability and self-score optimality. In another, HOSO is a one-shot-per-class micro-validation mechanism for learning a CLIP-adapter blending ratio under a strict validation-free few-shot protocol. A plausible implication is that the label “HOSO” now denotes a broader methodological pattern: using minimal, explicitly excluded one-shot supervision to estimate a secondary quantity—such as a calibration threshold or blending ratio—without sacrificing the structural constraints of the underlying low-data regime.

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