Poly-Window Contrastive Learning

• Poly-window contrastive learning is a self-supervised method that aggregates information from multiple windows to extend traditional two-view contrastive objectives.
• It employs arithmetic and geometric aggregation schemes to lower-bound one-vs-rest mutual information, thereby improving representation quality and convergence.
• The approach enables efficient multi-positive learning in applications like ECG analysis, image cropping, and long-term forecasting through principled view multiplicity.

Poly-window contrastive learning denotes a family of self-supervised contrastive methods in which each sample contributes more than two windows or views, and the learning objective aggregates agreement across these windows rather than relying on a single positive pair. In the literature, the underlying views may be temporal windows from a time series, multiple crops of an image, or broader multi-view observations; the common thread is view multiplicity and a contrastive objective that exploits relationships among many related views of the same underlying instance (Shidani et al., 2024). In time-series work, the term appears explicitly in ECG representation learning, where multiple temporal windows from the same recording are treated as positives (Yuan et al., 21 Aug 2025). Closely related formulations include full-graph combinatorial pairing for many image crops (Kim et al., 2024) and globally autocorrelation-aware window comparison for long-term forecasting, where multiple windows are related through lag structure over an entire series (Park et al., 2024).

1. Definition, scope, and major formulations

A central formalization is the notion of view multiplicity. In poly-view tasks, the number of views per sample is $M$, and drawing $K$ samples yields $V = M \times K$ views per batch (Shidani et al., 2024). This extends the standard two-view setting of SimCLR-style contrastive learning to $M > 2$, with all views of a sample sharing a common latent generative factor.

In the ECG formulation, poly-window contrastive learning is a direct multi-window extension of InfoNCE. For each time-series instance, $M$ temporal windows are sampled; each anchor window takes all other windows from the same signal as positives, while windows from other signals are negatives. The numerator is aggregated over the positive set using either an arithmetic or geometric mean, rather than selecting a single positive per anchor (Yuan et al., 21 Aug 2025). This makes the method explicitly multi-positive.

In the theoretical poly-view framework, the key objective is One-vs-Rest mutual information,

$I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$

which measures how much information one view contains about the rest of the views from the same sample. Arithmetic PVC, Geometric PVC, and a sufficient-statistics loss are derived as lower bounds on this quantity, and all recover the usual two-view objective when $M=2$ (Shidani et al., 2024).

A distinct but related formulation appears in long-term forecasting. There, multiple windows are not paired because they are augmentations of the same observation, but because they occupy positions in a long series with meaningful global lag structure. Window relations are weighted by a global autocorrelation term computed over the whole training series, and contrastive learning is applied only to the long-term branch of a decomposition model (Park et al., 2024). This suggests that “poly-window” is best understood as an umbrella for many-window contrastive learning rather than a single canonical loss.

Paper	Window/view relation	Defining mechanism
"Poly-View Contrastive Learning" (Shidani et al., 2024)	$M$ related views per sample	One-vs-Rest MI; Arithmetic PVC; Geometric PVC; Sufficient Statistics
"Enhancing Contrastive Learning with Efficient Combinatorial Positive Pairing" (Kim et al., 2024)	$K$ image crops per sample	Full-graph pairing over all ${}_K C_2$ positives
"Learning ECG Representations via Poly-Window Contrastive Learning" (Yuan et al., 21 Aug 2025)	$K$0 temporal windows per recording	Multi-positive InfoNCE with arithmetic or geometric aggregation
"Self-Supervised Contrastive Learning for Long-term Forecasting" (Park et al., 2024)	Windows across a long series	Global autocorrelation-weighted AutoCon

2. Objective functions and information-theoretic interpretation

The poly-view literature generalizes pairwise InfoNCE by replacing a single positive with a set of positives drawn from the same sample. In the ECG setting, a batch of $K$1 sequences with $K$2 windows each produces $K$3 embeddings. After L2 normalization, the scaled similarity matrix is

$K$4

and the conditional probability of selecting window $K$5 as a positive for anchor $K$6 is

$K$7

The geometric aggregation objective is

$K$8

and the arithmetic aggregation objective is

$K$9

When $V = M \times K$0, both reduce to standard two-view InfoNCE (Yuan et al., 21 Aug 2025).

The theoretical poly-view treatment gives a broader interpretation of these losses. Arithmetic PVC and Geometric PVC are derived as lower bounds on One-vs-Rest MI, with per-positive terms of the form

$V = M \times K$1

Arithmetic PVC aggregates $V = M \times K$2 with a log of an arithmetic mean, whereas Geometric PVC averages the log-probabilities. The sufficient-statistics formulation instead pools the rest-set of views and contrasts a single view against this pooled statistic (Shidani et al., 2024).

A central theoretical claim is that increasing the number of related views tightens the MI lower bound. For Arithmetic PVC and Geometric PVC, the MI gap is monotonically non-increasing in $V = M \times K$3, and in a 1D Gaussian setting

$V = M \times K$4

so the rest-set becomes a better proxy for the latent generative factor as multiplicity grows (Shidani et al., 2024). This is the main information-theoretic justification for poly-window learning.

The forecasting formulation uses a different relational prior. If $V = M \times K$5 and $V = M \times K$6 are windows beginning at times $V = M \times K$7 and $V = M \times K$8, their window-level relation is

$V = M \times K$9

where $M > 2$0 is the global autocorrelation of the full training series at lag $M > 2$1. AutoCon then treats each anchor window as participating in many relative positive/negative comparisons against all other windows in the batch, weighted by these autocorrelation-derived similarities (Park et al., 2024).

3. Window construction and the semantics of positives and negatives

Poly-window methods differ most sharply in how windows are generated and in what counts as a positive relationship.

In ECG representation learning, each recording is 10 seconds, sampled at 100 Hz, giving 1000 time points per lead and 12 leads in total. Pre-training uses random temporal crops only; crop sizes tested are $M > 2$2, overlap is chosen from $M > 2$3, and all 12 leads are cropped with the same temporal indices. Windows from the same recording define the positive set, and no additional augmentations such as noise or scaling are used (Yuan et al., 21 Aug 2025). The paper reports that crop size 64, which roughly corresponds to one cardiac cycle, is optimal.

In ECPP for images, each image produces $M > 2$4 views. Two are global, full-resolution views generated with standard SimCLR augmentation; the remaining $M > 2$5 views are small-resolution views, created either with full SimCLR augmentation or with crop-only augmentation. ECPP uses full combinatorial positive pairing: every unordered pair $M > 2$6, $M > 2$7, is a positive pair, giving $M > 2$8 positive pairs per batch for batch size $M > 2$9 (Kim et al., 2024).

ECPP also modifies the negative set. Other views of the same image are treated as false negatives in standard SimCLR-style denominators, so ECPP excludes all same-image views from the negative pool. The corresponding per-pair loss replaces the SimCLR denominator with one that contains only views from other images (Kim et al., 2024). This design principle generalizes directly to many-window learning whenever multiple windows from the same sample are known positives.

The forecasting setting differs because windows need not come from the same local neighborhood. A univariate or multivariate series $M$0 is partitioned into sliding windows $M$1, with

$M$2

The motivating issue is that standard sliding-window objectives ignore outer-window variations: long-period dependencies with lags much larger than the window length. AutoCon addresses this by defining positives and negatives through lag-based global similarity rather than through augmentation or overlap, and no data augmentation is used (Park et al., 2024).

Taken together, these designs show that poly-window contrastive learning does not require a single window generator. The essential requirement is a principled rule that identifies multiple windows as related views of a shared underlying factor, whether that factor is instance identity, physiological state, or seasonal position in a long series.

4. Architectural realizations

The most elaborate architecture among the cited works is the long-term forecasting model built around AutoCon. It is a decomposition-style forecaster with two branches. At the window level, input normalization and output denormalization are performed using the window mean: $M$3 The short-term branch is a purely linear time projection,

$M$4

while the long-term branch uses an encoder

$M$5

and a decoder built from multi-scale moving average and MLP components. The overall prediction is the sum of short-term and long-term components, and the training loss is

$M$6

Contrastive learning is applied only to the long-term branch, whereas the short-term branch is supervised by MSE alone (Park et al., 2024).

In ECG poly-window learning, the encoder is a 1D ResNet-18 adapted to 12-lead input. Each temporal window is processed independently with shared weights. The encoder output is a 512-dimensional representation, followed by a 1-layer linear projection from 512 to 128-dimensional embedding for contrastive pre-training. During evaluation, the projection head is removed, the full 1000-point recording is mapped to a 512-dimensional feature, and a linear layer maps 512 to 5 superclass logits (Yuan et al., 21 Aug 2025). The paper states that the method is model-agnostic in principle because the loss requires only a shared encoder that maps windows into an embedding space.

The theoretical poly-view work emphasizes the loss more than the backbone. It assumes a generic representation map $M$7, and the sufficient-statistics variant defines a pooled rest-set representation

$M$8

This pooled rest-set is then contrasted against individual views, giving a contrastive sufficient-statistics objective that also lower-bounds One-vs-Rest MI (Shidani et al., 2024).

ECPP is primarily a training strategy rather than a new encoder architecture. Its architectural significance lies in making many-view training computationally tractable through small-resolution views while preserving a full-graph positive structure (Kim et al., 2024).

5. Empirical findings, compute trade-offs, and convergence behavior

The empirical case for poly-window learning is strongest when long-range or slowly varying structure matters.

In long-term forecasting, the AutoCon-based model outperforms 14 baseline models over nine long-term benchmarks and ranks 1st in 42 settings. Gains are largest on datasets with strong outer-window autocorrelation. Reported examples include ETTh2 at $M$9, where the model attains MSE 0.198 versus 0.240 for the second-best method; Electricity at $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$0, where it attains 0.380 versus 0.415 for DLinear and 0.536 for TimesNet; and Exchange at $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$1, where it attains 1.067 versus 1.239 for the second-best method (Park et al., 2024). Ablations further show that removing the long-term branch or removing AutoCon degrades long-horizon performance substantially.

In ECG representation learning on PTB-XL, poly-window contrastive learning is reported to consistently outperform conventional two-view methods in multi-label superclass classification, with higher AUROC (0.891 vs. 0.888) and F1 scores (0.680 vs. 0.679) while requiring up to four times fewer pre-training epochs (32 vs. 128) and 14.8% in total wall clock pre-training time reduction (Yuan et al., 21 Aug 2025). The paper also reports that more windows improve convergence speed, with effect size $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$2 for number of windows, while crop size is the most influential hyperparameter with $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$3.

In many-view vision contrastive learning, ECPP reports that the learning speed of $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$4-views can be increased by $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$5 times for small learning rate and early training, reflecting the growth in the number of positive terms. On ImageNet-100 with ResNet-50 linear evaluation, SimCLR$I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$6: 87.0% (800) exceeds the listed Supervised: 86.2%, and on ImageNet-1K SimCLR$I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$7: 71.1% (200) improves markedly over SimCLR (original): 64.3% (200), though it remains below SwAV (72.7%) (Kim et al., 2024). The paper further reports that removing same-image false negatives yields consistent improvements.

The theoretical poly-view study gives the broadest compute argument. It concludes that, with unlimited computation, one should maximize the number of related views, and with a fixed compute budget it is beneficial to decrease the number of unique samples while increasing the number of views of those samples. A specific result is that poly-view contrastive models trained for 128 epochs with batch size 256 outperform SimCLR trained for 1024 epochs at batch size 4096 on ImageNet1k (Shidani et al., 2024). The work also distinguishes its objectives from ordinary Multi-Crop: Multi-Crop reduces variance, but the MI lower bound remains the same as the pairwise two-view bound, whereas PVC improves bound tightness as multiplicity increases.

A plausible implication is that the empirical advantages of poly-window learning come from two interacting effects. First, more windows per sample provide more supervision about the same latent factor. Second, specialized aggregation or weighting rules determine whether this extra supervision merely lowers variance, as in pairwise averaging, or changes the learning target itself by tightening an information-theoretic bound or by injecting a global temporal prior.

6. Misconceptions, limitations, and extensions

One common misconception is that poly-window learning is simply “more positive pairs.” The cited literature draws sharper distinctions. Multi-Crop pairwise averaging increases the number of comparisons and reduces estimator variance, but it does not improve the MI lower bound beyond the two-view setting (Shidani et al., 2024). By contrast, Arithmetic PVC, Geometric PVC, and sufficient-statistics losses are genuine multi-view objectives, and AutoCon is not augmentation-based at all: it defines relations across windows using global autocorrelation rather than proximity or overlap (Park et al., 2024). ECPP adds a separate caution that other windows from the same sample should not be treated as negatives, because they are false negatives by construction (Kim et al., 2024).

The limitations are correspondingly heterogeneous. In forecasting, the authors note the linearity of autocorrelation, the reliance on a fixed window length and single scale, the need for precomputation of autocorrelation, and the assumption of stationary lag-structure over the full training series (Park et al., 2024). In ECG, all experiments are restricted to PTB-XL, performance depends strongly on window size and number of windows, and the method assumes that multiple windows from the same recording reflect the same underlying physiological state; rapid state changes could blur important distinctions (Yuan et al., 21 Aug 2025). In ECPP, the $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$8 speed scaling is stated to be most accurate for small constant learning rate and early training, and larger $I\left(\rvx_\alpha ; \rmX_{1:M}^{\neq \alpha}\right),$9 can require careful epoch tuning to avoid overtraining (Kim et al., 2024). In the theoretical poly-view work, experiments are limited to synthetic Gaussian analysis and ImageNet1k, and multiplicity is explored only up to $M=2$0 (Shidani et al., 2024).

Proposed or implied extensions are notably consistent across papers. They include multiple window lengths, hierarchical segments, multi-resolution autocorrelation, adaptive window selection, correlation-aware pairing, non-linear similarity kernels, cross-series or cross-modal poly-window learning, and application to other biomedical and non-medical temporal data (Park et al., 2024). The ECG work also suggests that the framework is applicable wherever there is temporal redundancy and a sample-level identity that persists across local windows, such as EEG, respiration, speech, or industrial time series (Yuan et al., 21 Aug 2025).

In this sense, poly-window contrastive learning is best regarded as a general design paradigm for self-supervised representation learning on structured sequential or multi-view data. Its defining commitments are view multiplicity, multi-positive reasoning, and the use of window relationships that are richer than the single-pair logic of classical two-view contrastive learning.