Training Crossroads for Recurrent Vision Transformers: Recurrence, Neural ODEs, and Deep Supervision

Vision Transformers (ViTs) achieve strong image-recognition performance, but their parameter count grows linearly with depth when each block is independently parameterized. Single-block recurrent ViTs (bViT) remove this growth by repeatedly applying one shared block. Rather than proposing a new architecture, we fix a bViT and provide a controlled empirical characterization of three training and inference regimes under a common CIFAR-100 protocol, asking: (i)~when does recurrence beat independently parameterized depth---at matched FLOPs or at matched parameter memory? (ii)~when a residual recurrent block is trained through an ODE solver, does solver order act as numerical refinement or as an architectural bias? and (iii)~what does robustness beyond the training horizon cost in nominal accuracy? We find that standard ViTs remain preferable when FLOPs are the primary constraint, whereas recurrent ViTs offer a better accuracy--parameter trade-off under memory constraints. Consistent with the standard view of residual networks as Euler discretizations of ODEs, the continuous-time analogue of a residual recurrent block is the state-subtracted vector field $\dot{z}=F_θ(z)-z$; although known in principle, this distinction is easy to violate when the block is wrapped as a black-box vector field, and we qualify the cost at few accuracy points. Because the vector field is learned jointly with the solver, higher-order solvers act as a solver-induced architectural bias rather than a numerical-accuracy improvement, and their gains are not uniform. Finally, stage-wise deep supervision traces an accuracy--robustness frontier: it does not improve nominal accuracy, but degrades gracefully far beyond the training horizon, where naive recurrence collapses to near-random performance.

Enhancing Oracle Bone Inscription Recognition via Multi-Scale Layer Attention

Oracle Bone Inscriptions (OBIs) recognition plays a crucial role in understanding ancient Chinese culture. However, accurately recognizing OBIs remains highly challenging due to their complex, irregular, and often degraded shapes. Traditional methods rely on expert knowledge and manual analysis, which are time-consuming and error-prone. Although deep learning has greatly advanced general image recognition, existing methods struggle to capture the fine-grained details and subtle variations inherent in OBIs, resulting in limited performance. Even most recent and effective layer attention techniques are designed to capture fine-grained dependencies through enhanced inter-layer interactions, yet they still exhibit only marginal improvements in OBIs recognition. To address these limitations, we propose Multi-Scale Layer Attention (MSLA), a novel paradigm that explicitly models both multi-scale and cross-layer feature interactions. By enriching the representation with fine-grained details across multiple spatial scales, MSLA enables more accurate and robust OBIs recognition. Extensive experiments on large-scale OBIs datasets demonstrate that MSLA consistently outperforms existing attention mechanisms while maintaining computational efficiency.

Enhancing Layer Interaction Using Key-Correlated Layer Attention

Recent advances in network architecture design have introduced layer attention to enhance inter-layer interactions. In such frameworks, each layer queries all preceding layers to establish cross-layer connections. However, layer attention results in quadratic computational complexity with respect to network depth. To mitigate this issue, prior works have proposed Recurrent Layer Attention (RLA) and linear attention mechanisms, which suffer from static information updates and limited long-range cross-layer dependency modeling. To overcome these limitations, we propose Key-Correlated Layer Attention (KCLA), inspired by our observation that Key representations in layer attention exhibit high cosine similarity. KCLA achieves linear computational complexity while preserving dynamic information updates, directly derived from the foundational definition of layer attention. Furthermore, KCLA maintains long-range cross-layer connections and features a fixed spatial complexity, independent of network depth. Empirical evaluations demonstrate that KCLA delivers good performance across diverse tasks, including image recognition, object detection, and medical image segmentation. The code is publicly available at https://github.com/bgx666/KCLA.

Winfree Oscillatory Neural Network

Oscillations and synchronization are widely believed to play a fundamental role in representation and computation. However, existing machine learning approaches based on synchronization dynamics have largely been confined to specialized settings such as object discovery, with limited evidence of scalability to standard vision benchmarks or logic reasoning tasks. We propose the Winfree Oscillatory Neural Network (WONN), a dynamical neural architecture based on generalized Winfree dynamics. WONN evolves representations on the torus $(S^1)^d$ through structured oscillatory interactions, combining phase-based inductive biases with flexible and hierarchical interaction mechanisms instantiated as either fixed trigonometric mappings or learnable neural networks. We evaluate WONN on image recognition and complex reasoning tasks, including CIFAR, ImageNet, Maze-hard, and Sudoku. Across these domains, WONN achieves competitive or superior performance with strong parameter efficiency. In particular, WONN is, to our knowledge, the first synchronization-based oscillatory architecture to scale competitively to ImageNet-1K. Furthermore, on Maze-hard, WONN achieves 80.1% accuracy using only 1% of the parameters of prior state-of-the-art models. These results suggest that structured oscillatory dynamics provide a scalable and parameter-efficient alternative to conventional neural architectures.

Learning to Reason: Targeted Knowledge Discovery and Fuzzy Logic Update for Robust Image Recognition

Integrating domain knowledge into deep neural networks is a promising way to improve generalization. Existing methods either encode prior knowledge in the loss function or apply post-processing modules, but both depend on identifying useful symbolic knowledge to integrate. Since such rules are often unavailable in real-world vision tasks, we propose a method for targeted knowledge discovery. We propose a Differentiable Knowledge Unit (DKU) that enables modulating the classifier logits, yielding refined class probabilities. The DKU uses implication rules to represent relationships between task classes and implicit concepts learned entirely from the main task supervision, without requiring concept labels. Concepts are identified by dedicated classifiers, whose probabilities are passed to DKU alongside the primary class probabilities. DKU computes a logic-based adjustment vector via fuzzy inference, which modulates the primary class logits to yield refined class probabilities. When concept classifiers represent concepts that do not support the logical rule structure, the resulting adjustments to the class probabilities do not directly minimize the supervision loss. Consequently, optimizing the supervision loss on these adjusted class probabilities implicitly trains the concept classifiers. We construct the rule base so that bidirectional logical relations connect concepts and classes. We enforce the concepts to be distinct from each other and with respect to the classes. This design enforces a clean supervision signal for concept learning. We evaluate our methods on the PASCAL-VOC, COCO, and MedMNIST datasets. We demonstrate improvement through our knowledge integration across these datasets. We conduct domain generalization and hard-sample ablation studies and find that our implicit knowledge discovery and integration outperforms the baseline.