Chaotic CNN for Limited Data Image Classification

Abstract: Convolutional neural networks (CNNs) often exhibit poor generalisation in limited training data scenarios due to overfitting and insufficient feature diversity. In this work, a simple and effective chaos-based feature transformation is proposed to enhance CNN performance without increasing model complexity. The method applies nonlinear transformations using logistic, skew tent, and sine maps to normalised feature vectors before the classification layer, thereby reshaping the feature space and improving class separability. The approach is evaluated on greyscale datasets (MNIST and Fashion-MNIST) and an RGB dataset (CIFAR-10) using CNN architectures of varying depth under limited data conditions. The results show consistent improvement over the standalone (SA) CNN across all datasets. Notably, a maximum performance gain of 5.43% is achieved on MNIST using the skew tent map with a 3-layer CNN at 40 samples per class. A higher gain of 9.11% is observed on Fashion-MNIST using the sine map with a 3-layer CNN at 50 samples per class. Additionally, a strong gain of 7.47% is obtained on CIFAR-10 using the skew tent map at 200 samples per class. The consistent improvements across different chaotic maps indicate that the performance gain is driven by the shared nonlinear and dynamical properties of chaotic systems. The proposed method is computationally efficient, requires no additional trainable parameters, and can be easily integrated into existing CNN architectures, making it a practical solution for data-scarce image classification tasks.

• The paper introduces a training-free transformation using logistic, skew tent, or sine maps on normalized CNN features, adding no trainable parameters or meaningful computational cost.
• The method improves macro F1 over plain CNNs by up to 5.43% on MNIST, 9.11% on Fashion-MNIST, and 7.47% on CIFAR-10 in low-sample settings.
• The results suggest chaotic transforms act as lightweight regularizers, but their advantages are dataset-dependent and require validation against augmentation, dropout, feature noise, and larger modern architectures.

The paper proposes a lightweight, training-free modification to standard CNNs for image classification under limited labeled data: a chaotic feature transformation applied to normalized convolutional features immediately before the fully connected classifier. The central claim is that element-wise application of one-dimensional chaotic maps—the logistic map, the skew tent map, and the sine map—reshapes the feature space in a way that improves class separability without adding trainable parameters or meaningful computational cost (2604.14645). The work positions itself within the neurochaos learning literature, which has previously demonstrated that chaos-based feature extraction benefits low-data and imbalanced classification, but extends it by integrating chaotic dynamics directly into a deep learning pipeline rather than using standalone chaotic architectures.

Motivation and positioning

CNNs overfit when trained on few samples per class, memorizing training instances rather than learning transferable structure. Existing remedies each carry drawbacks: data augmentation may not capture true data variability; dropout and weight decay reduce effective model capacity; semi-supervised methods depend on pseudo-label quality; transfer learning requires suitable pre-trained models and domain similarity. The authors argue that what is needed is a mechanism that enriches feature representation without increasing model complexity—a gap they fill with a deterministic nonlinear transformation.

The choice of chaotic maps is motivated by three shared properties: strong nonlinearity, boundedness on $[0,1]$, and sensitivity to initial conditions. Because these maps operate on bounded inputs, they can be applied directly to min-max normalized CNN features. Prior neurochaos work (ChaosNet, logistic-map-based neurons, stochastic resonance in neurochaos learning) established that such transformations enhance classification in low-data regimes; this paper's contribution is demonstrating the same benefit inside a conventional end-to-end trained CNN.

Methodology

The pipeline is straightforward. An input image passes through convolutional and pooling layers producing a feature vector $f = \Phi(x;\theta_c)$. This vector is normalized to $[0,1]$ ($\tilde{f} = \mathcal{N}(f)$), then transformed element-wise by one of three maps:

• Logistic map: $f^* = r\,\tilde{f}(1-\tilde{f})$ with $r=4$ fixed for maximal chaos.
• Skew tent map: piecewise linear with $p = 0.499$ fixed for maximum entropy.
• Sine map: $f^* = \sin(\pi \tilde{f})$, providing a smooth alternative to the other two.

The transformed vector feeds a fully connected layer followed by softmax, and the entire network is trained end-to-end with categorical cross-entropy and Adam. Crucially, the transformation introduces zero additional trainable parameters and preserves dimensionality.

Experiments use MNIST and Fashion-MNIST (grayscale, 10 classes) with 2-layer and 3-layer CNNs at 40, 50, and 60 samples per class, and CIFAR-10 (RGB) with a 5-layer CNN at 100, 150, and 200 samples per class. Hyperparameters were selected via grid search with 5-fold stratified cross-validation, and performance is reported as macro F1-score.

Results

The headline results are substantial relative gains over the standalone (SA) CNN baseline:

Dataset	Best configuration	Baseline F1	Chaotic F1	Gain
MNIST	Skew tent, 3-conv, 40/class	0.8619	0.9087	5.43%
Fashion-MNIST	Sine, 3-conv, 50/class	0.7210	0.7867	9.11%
CIFAR-10	Skew tent, 200/class	0.4513	0.4850	7.47%

On Fashion-MNIST at 50 samples per class with the 3-layer CNN, the baseline drops to 0.7210 while all three chaotic variants recover to roughly 0.775–0.788—gains of 7.50% to 9.29%. This suggests the transformation acts as a regularizer precisely where the baseline is most unstable. On MNIST, gains are more uniform across configurations (roughly 0.4–5.4%), with the skew tent map strongest for the deeper model and the sine map competitive for the shallower one. On CIFAR-10, absolute F1 scores remain low (0.40–0.49), reflecting the difficulty of the task at these sample budgets, but the relative improvements are consistent: the logistic map leads at 100 samples per class (+7.33%), while the skew tent and sine maps dominate at 150 (+3.60%, +4.07%) and 200 (+7.47%, +5.27%) samples per class.

Two patterns emerge across all datasets. First, the relative gain generally decreases as sample count increases—for example, the logistic map's CIFAR-10 gain falls from +7.33% at 100 samples to −0.16% at 200—consistent with the interpretation that the transformation compensates for insufficient data rather than providing an unconditional improvement. Second, no single map dominates universally: the skew tent map excels on MNIST and CIFAR-10, while the logistic and sine maps are stronger on Fashion-MNIST. The authors attribute the consistency of positive results to the shared dynamical properties of the maps rather than any specific formulation, which implies the method is robust to map selection even if optimal performance is not.

Limitations and open questions

Several caveats bear directly on the strength of the claims. The evaluation covers only three benchmark datasets with balanced classes and small CNNs; behavior on imbalanced data, larger architectures, or modern backbones is not tested. Map parameters are fixed heuristically ($r=4$, $p=0.499$) without ablation over the chaotic regime, so the sensitivity of results to these choices remains unquantified. A small number of configurations show negligible or negative gains (e.g., sine map on MNIST 3-conv at 60 samples, logistic map on CIFAR-10 at 200), indicating the improvement is not guaranteed in every setting. The paper also concedes that the mechanism is not explained: why bounded chaotic perturbation improves separability is asserted through the maps' dynamical properties rather than demonstrated analytically, and the authors explicitly identify explainability of the chaotic CNN as an open question. Finally, the comparison baseline is a plain CNN without augmentation or regularization; whether the chaotic transformation outperforms equally cheap alternatives (e.g., feature-space noise injection or dropout on the penultimate layer) is not established.

Conclusion

This paper demonstrates that inserting a parameter-free chaotic map transformation between CNN feature extraction and classification yields consistent macro F1 improvements in limited-data image classification, with peak gains of 5.43% (MNIST), 9.11% (Fashion-MNIST), and 7.47% (CIFAR-10). The method's appeal lies in its simplicity: negligible cost, no added capacity, and drop-in compatibility with existing architectures. Its main weaknesses are the absence of a mechanistic explanation, fixed hyperparameters without sensitivity analysis, and evaluation restricted to small networks and balanced benchmarks. The specific question left open—whether the observed gains arise from general nonlinear mixing or from genuinely chaotic dynamics, and how to characterize this formally—remains the most important direction for subsequent work.