Both biological and artificial neural networks inherently balance their performance with their operational cost, which balances their computational abilities. Typically, an efficient neuromorphic neural network is one that learns representations that reduce the redundancies and dimensionality of its input. This is for instance achieved in sparse coding, and sparse representations derived from natural images yield representations that are heterogeneous, both in their sampling of input features and in the variance of those features. Here, we investigated the connection between natural images' structure, particularly oriented features, and their corresponding sparse codes. We showed that representations of input features scattered across multiple levels of variance substantially improve the sparseness and resilience of sparse codes, at the cost of reconstruction performance. This echoes the structure of the model's input, allowing to account for the heterogeneously aleatoric structures of natural images. We demonstrate that learning kernel from natural images produces heterogeneity by balancing between approximate and dense representations, which improves all reconstruction metrics. Using a parametrized control of the kernels' heterogeneity used by a convolutional sparse coding algorithm, we show that heterogeneity emphasizes sparseness, while homogeneity improves representation granularity. In a broader context, these encoding strategy can serve as inputs to deep convolutional neural networks. We prove that such variance-encoded sparse image datasets enhance computational efficiency, emphasizing the benefits of kernel heterogeneity to leverage naturalistic and variant input structures and possible applications to improve the throughput of neuromorphic hardware.

翻译：生物神经网络与人工神经网络本质上都在性能与运行成本之间寻求平衡，从而调控其计算能力。典型的高效神经形态神经网络通过学习表征来降低输入数据的冗余性和维度，例如稀疏编码即能实现这一目标。从自然图像中导出的稀疏表征在输入特征的采样方式及特征方差上均呈现异质性。本研究探究了自然图像结构（特别是定向特征）与其对应稀疏编码之间的关联。结果表明，跨多个方差层级分布的输入特征表征能显著提升稀疏编码的稀疏性与鲁棒性，但以重构性能为代价。这一现象呼应了模型输入的结构特性，使我们能够解释自然图像中异质随机性结构的内在规律。我们进一步证实，从自然图像中学习核函数可通过近似表征与密集表征的权衡产生异质性，从而全面改善重构指标。通过参数化控制卷积稀疏编码算法中核的异质性程度，我们发现异质性强化了稀疏性，而同质性则提升了表征粒度。在更广的背景下，此类编码策略可作为深度卷积神经网络的输入。实验证明，这种基于方差编码的稀疏图像数据集能增强计算效率，凸显了核异质性在利用自然化与变异输入结构方面的优势，以及其在提升神经形态硬件吞吐量方面的潜在应用价值。