Multidimensional Task Learning: A Unified Tensor Framework for Computer Vision Tasks

Vision Transformers have achieved state-of-the-art performance in a wide range of computer vision tasks, but their practical deployment is limited by high computational and memory costs. In this paper, we introduce a novel tensor-based framework for Vision Transformers built upon the Tensor Cosine Product (Cproduct). By exploiting multilinear structures inherent in image data and the orthogonality of cosine transforms, the proposed approach enables efficient attention mechanisms and structured feature representations. We develop the theoretical foundations of the tensor cosine product, analyze its algebraic properties, and integrate it into a new Cproduct-based Vision Transformer architecture (TCP-ViT). Numerical experiments on standard classification and segmentation benchmarks demonstrate that the proposed method achieves a uniform 1/C parameter reduction (where C is the number of channels) while maintaining competitive accuracy.

We present TAPe+ML v3, a compact computer vision system based on TAPe (Theory of Active Perception), a structured representation that encodes relations among perceptual elements before recognition. Instead of operating directly on pixel tensors, the system uses a shared TAPe representation and a modular recognition architecture for image classification, object detection, and instance segmentation. TAPe+ML v3 combines background and contour processing, local object localization, prototype-based classification, and a coordinator for specialized submodels. Across the reported experiments, it uses fewer than 100,000 parameters. On COCO object detection, it obtains 84.7 mAP50 and 65.3 mAP50-95. On COCO instance segmentation, it obtains 80.7 mask mAP50 and 58.4 mask mAP50-95. In classification experiments, it reaches 92 percent validation accuracy on Imagenette under an identical-training comparison with a raw-pixel baseline, and 89.9 percent Top-1 accuracy on ImageNet-Real. We also evaluate compactness in video scene detection and adaptation under distribution shift in an industrial pilot. The results suggest that shifting part of the modeling burden from network parameters to a structured input representation can support compact multi-task vision systems with reduced data, memory, and compute requirements.

Current visual representation learning remains bifurcated: vision-language models (e.g., CLIP) excel at global semantic alignment but lack spatial precision, while self-supervised methods (e.g., MAE, DINO) capture intricate local structures yet struggle with high-level semantic context. We argue that these paradigms are fundamentally complementary and can be integrated into a principled multi-task framework, further enhanced by dense spatial supervision. We introduce MTV, a multi-task visual pretraining framework that jointly optimizes a shared backbone across vision-language contrastive, self-supervised, and dense spatial objectives. To mitigate the need for manual annotations, we leverage high-capacity "expert" models--such as Depth Anything V2 and OWLv2--to synthesize dense, structured pseudo-labels at scale. Beyond the framework, we provide a systematic investigation into the mechanics of multi-task visual learning, analyzing: (i) the individual and marginal gain of each objective, (ii) task synergies versus interference, and (iii) scaling behavior across varying data and model scales. Our results demonstrate that MTV achieves "best-of-both-worlds" performance, significantly enhancing fine-grained spatial reasoning without compromising global semantic understanding. Our findings suggest that multi-task learning, fueled by high-quality pseudo-supervision, is a scalable path toward more general visual encoders.