Patchify: Partitioning Signals for Deep Learning

Updated 16 December 2025

Patchify is a technique that partitions high-dimensional data into small, structured patches that serve as atomic tokens for embedding in deep learning models.
It incorporates multi-scale, non-square, frequency domain, and dynamic strategies to adapt the patchification process for diverse modalities like images, video, and time series.
Empirical studies show that patchify improves computational efficiency and localization accuracy in vision transformers, capsule networks, instance retrieval systems, and diffusion-based visual generation.

Patchify refers to the systematic partitioning of raw signals, images, or high-dimensional feature maps into a collection of small, structured "patches." Each patch typically provides a localized view of the original data, serving as the atomic unit for downstream embedding, modeling, classification, or retrieval. Originating in vision transformers, patchify has been widely generalized across domains including time series modeling, video, capsule networks, visual generation, and instance-level retrieval, each adapting the core methodology to their task and inductive biases.

1. Patchify: Formalization and General Variants

Patchify in its canonical form transforms a high-dimensional signal—most commonly an image $X \in \mathbb{R}^{H \times W \times C}$ —into a sequence of $N$ non-overlapping patches. For square patches of size $P \times P$ , $N = (H/P) \cdot (W/P)$ . Each patch is flattened ( $P^2C$ -dimensional), linearly projected into $d$ -dimensional patch embeddings, and optionally augmented by learnable positional encodings. This sequence of patch embeddings serves as input tokens to models such as transformers (Wu et al., 30 Nov 2024).

Patchify schemes have evolved to accommodate:

Multi-scale grid partitioning (retrieval, capsule nets): grid levels of varying patch sizes (e.g., $1\times1$ , $2\times2$ , up to $4\times4$ ) (Choi et al., 14 Dec 2025, Hu et al., 23 Aug 2025).
Non-square patching: vertical or horizontal stripes, to exploit anisotropy in the data (e.g., width-level patchify for egocentric vision) (Zhao et al., 18 Apr 2024).
Frequency domain patching: partitioning the FFT spectrum of time series into frequency bands ("frequency patching") (Wu et al., 16 Oct 2024).
Dynamic or pyramidal patchification: variable patch sizes within a model (e.g., adaptively using coarser or finer patches as a function of diffusion timestep) (Li et al., 30 Jun 2025).
Time series patchify: segmenting $T$ -length multivariate signals into temporal windows of size $L$ (stride $S$ ) (Lee et al., 2023).

These formulations extend patchify beyond the original ViT square-patch paradigm, supporting a wider set of inductive biases and computational trade-offs.

2. Methodological Implementations and Architectural Use

Patchify is a critical architectural primitive in a range of neural representations:

Vision Transformers (ViT): Patchify is usually implemented by a stride- $P$ $P \times P$ convolution with $C$ input and $d$ output channels. The tensor is partitioned, flattened, projected, and fed into transformer layers. Empirical work shows that alternative stems (e.g., stacks of stride-2 $3\times3$ convolutions) enhance optimizability and early feature learning (Xiao et al., 2021).
Capsule Networks: In the MSPCaps model, PatchifyCaps applies average pooling and $1\times1$ convolutions to multi-scale feature maps, assigns one primary capsule per patch at each scale, and adds positional encoding before layer normalization. This enables localized, multi-scale part-whole modeling and reduces capsule count compared to previous dense or concatenation-based capsule constructions (Hu et al., 23 Aug 2025).
Instance Retrieval: Patchify divides each image into overlapping or non-overlapping grid patches (at multiple scales), computes descriptors for each patch with a frozen encoder, and enables retrieval by maximum similarity between a global query descriptor and any patch descriptor in a database image. This improves spatial localization (LocScore) and recall compared to global descriptors (Choi et al., 14 Dec 2025).
Visual Generation via Diffusion Transformers: Patchify forms the backbone of the DiT class of models, where latent activations are divided into patches. The Pyramidal Patchification Flow (PPFlow) further reduces computational cost by using coarser patches in high-noise steps and finer ones in low-noise steps, with learned projection matrices for each patch scale (Li et al., 30 Jun 2025).
Time Series Modeling: Patchify splits temporal signals into patches for self-supervised learning. Some recent work advocates for independent patch embedding (e.g., via a patch-wise MLP) rather than modeling patch interdependencies as in Masked Autoencoding, citing improved efficiency and performance (Lee et al., 2023). In the frequency-domain, patchify is used to carve the FFT spectrum into overlapping frequency bands, which are processed for fine-grained anomaly detection (Wu et al., 16 Oct 2024).

3. Computation, Embedding, and Complexity Trade-offs

The computational profile of patchify-based models is heavily affected by:

Patch size $P$ : Larger patches yield fewer tokens $N$ , reducing the quadratic self-attention cost $O(N^2d)$ in transformers but potentially losing fine spatial details.
Embedding dimension: Linear projection from patch to embedding space adds $O(N \cdot P^2C \cdot d)$ operations.
Masking strategies: Random masking of up to 75% of patches prior to transformer input (as in federated ViT settings) reduces both local computation and privacy risk, with minimal performance loss observed up to practical thresholds (Wu et al., 30 Nov 2024).

Width-level or stripe-level patchify, as used in SFTIK for egocentric terrain images, trades increased per-token embedding cost (longer flattened vectors) for a massive reduction in total tokens, thus reducing quadratic complexity by an order of magnitude (Zhao et al., 18 Apr 2024).

Dynamic or pyramidal patchify (PPFlow) enables further savings by varying $P$ across inference, allocating coarse patches to computationally intensive early-stage computations, while restoring fine-grained patching at critical steps (Li et al., 30 Jun 2025).

4. Applications Across Modalities

Visual Recognition

Patchify as grid partitioning underlies SOTA feature extractors in visual transformers, capsule networks, and convolutional hybrids. MSPCaps demonstrates that multi-scale PatchifyCaps, each assigning a capsule per patch of a different feature map, can elevate classification accuracy beyond single-scale or globally pooled capsule networks (Hu et al., 23 Aug 2025).

Instance-level Retrieval

Patchify enables local-to-global matching: database images store only grid-patch descriptors, while queries are processed globally. Maximum patch similarity determines both retrieval and the localizing region, and memory is minimized by capping patches at $\leq$ 30 per image. Product Quantization can be optimized by clustering semantically-informative (GT-aligned) patch descriptors instead of global or arbitrary ones (Choi et al., 14 Dec 2025).

Visual Generation

Diffusion models using patchify (DiT, PPFlow) operate on vectors associated with patches of latent feature maps, adjusting patch size during inference for compute-quality trade-offs (Li et al., 30 Jun 2025).

Video and Time Series

Temporal patchify divides sequences for task-agnostic representation learning (e.g., masked patch modeling, contrastive learning), with variants for channel-wise or independent embeddings. Frequency domain patchify, via band partition of FFT spectra, enables fine-grained detection of subsequence anomalies and localized cross-channel correlations in multivariate series (Wu et al., 16 Oct 2024).

Federated and Low-Resource Training

Patchify with masking is a cornerstone of models for edge-device federated learning; randomly omitting patches reduces per-client compute while privacy is enhanced by obfuscating local patch distributions. Accuracy and convergence speed are often maintained or improved (Wu et al., 30 Nov 2024).

5. Empirical Outcomes, Metrics, and Design Trade-offs

Empirical studies consistently emphasize:

Accuracy gains with patchify over global-pooling, especially for fine-grained recognition and localization (Choi et al., 14 Dec 2025, Hu et al., 23 Aug 2025).
- In retrieval, grid-patch methods outperform global descriptors by 10–20 mAP (INSTRE: mAP 57.7→72.54 with DINOv2 backbone) and LocScore (Choi et al., 14 Dec 2025).
- For multi-scale capsule modeling, aggregating coarse and fine PatchifyCaps raises accuracy to 88.71% on CIFAR-10 (versus single-scale models at 74–87%) (Hu et al., 23 Aug 2025).
Efficiency gains from optimized patchification:
- Width-level patchify reduces image-encoder FLOPs by >10× (from 8.37G to 0.63G) with negligible performance loss (Zhao et al., 18 Apr 2024).
- Pyramidal patchify achieves 1.6–2.0× speedup in diffusion transformers at matched or better FID/Inception/Precision scores (Li et al., 30 Jun 2025).
- Patch masking lowers federated ViT training FLOPs by 2.0–2.8× and training time by up to 4.4× (Wu et al., 30 Nov 2024).
Interpretability and localization enhancements: Patch-wise representations map naturally to spatial localizations (e.g., retrieval bounding-boxes); the LocScore metric combines rank and IoU to assess spatial correctness (Choi et al., 14 Dec 2025).

6. Limitations, Challenges, and Future Directions

Despite broad utility, patchify presents several limitations:

Fixed granularity in grid-patch designs constrains localization; small/irregular objects may not align with any patch and thus remain undetected. Sliding-window or region-proposal patching can partially mitigate this at cost of higher compute and storage (Choi et al., 14 Dec 2025).
Information redundancy and aliasing can arise with large, non-overlapping patches. Convolutional stems or overlapping conv-based patchification can alleviate these defects, improving representational power and optimizability in transformers (Xiao et al., 2021).
Hyperparameter selection (patch size, stride, embedding dimension) requires cross-validation; too small $P$ increases token count and overfitting, while too large $P$ reduces local detail (Hu et al., 23 Aug 2025).
Product Quantization training is sensitive to the feature selection; clustering on semantically meaningful patch descriptors yields higher retrieval mAP (Choi et al., 14 Dec 2025).
Masking threshold: Excessively high patch masking ( $>75\%$ ) in federated settings may degrade accuracy (Wu et al., 30 Nov 2024).

A plausible implication is that further advances may result from adaptive, token-aware patchification, learned region proposals, or hybrid CNN-transformer frontends optimized for both computability and fine-grained localization.

7. Summary Table: Patchify Strategies by Application

Domain/Task	Patch Type	Representative Model/Paper
Image Classification	Square grid, multi-scale	PatchifyCaps, ViT, MSPCaps (Hu et al., 23 Aug 2025, Wu et al., 30 Nov 2024, Xiao et al., 2021)
Instance Retrieval	Multi-scale grid	Patch-wise Retrieval (Choi et al., 14 Dec 2025)
Vision Transformers	Square grid (conv stem alt.)	ViT (Xiao et al., 2021)
Visual Generation	Dynamic/pyramidal	PPFlow (Li et al., 30 Jun 2025)
Egocentric Vision	Width-level stripes	SFTIK (Zhao et al., 18 Apr 2024)
Time Series	Temporal window, frequency bands	PITS (Lee et al., 2023), CATCH (Wu et al., 16 Oct 2024)
Federated Learning	Square patch + masking	EFTViT (Wu et al., 30 Nov 2024)

Patchify thus constitutes a foundational abstraction for tokenizing continuous, high-dimensional signals, supporting nearly all modern neural models where local structure, efficiency, or spatial interpretability is demanded. The evolution of patchify mechanisms continues to shape and expand the applications of token-based deep learning architectures across modalities.