BDNet: Fast-slow thinking is all you need

Modern object detectors are static, fixed-depth networks optimized for a single operating point, requiring separate models for different deployment scenarios. We present an any-depth detection framework that enables a single network to span a continuous range of accuracy--efficiency trade-offs by controlling depth at inference time without retraining. Each backbone and neck stage is divided into an essential path, which always executes, and a skippable refinement path; this decomposition preserves the full multi-scale feature hierarchy at every depth configuration, unlike conventional early exiting that discards entire stages. To train such a network, jointly optimizing many sub-networks of varying depth introduces conflicting gradient signals. We address this via self-distillation between only the two extremes, with prediction-level and feature-level alignment losses that enforce stage-wise modularity, ensuring the outputs of each stage remain compatible regardless of the paths taken. Instantiated on RT-DETR and YOLOv12, our full-depth configurations match or surpass their respective SOTA baselines with negligible parameter overhead, while the most efficient configurations achieve up to $1.82\times$ speedup at a cost of only 2.0 AP, all from a single set of weights.

Fine-grained visual classification benefits from high-resolution inputs to resolve subtle, localized cues, but at the cost of large compute and memory budgets. Inspired by human saccadic vision, we propose a lightweight extension that turns any pretrained backbone with spatial feature maps into a saccadic classifier through glimpse-induced inference. The only architectural additions are a small priority head and a single cross-attention fusion block. The same weight-tied encoder encodes a downsampled peripheral glance, exposes the spatial feature map from which the priority head predicts a glimpse-priority distribution and re-encodes high-resolution glimpse crops sampled from that distribution in parallel. A sequential sampler with non-maximum suppression draws a runtime-configurable number of glimpses. A residual multi-head cross-attention block then fuses the glance against the glimpses. To improve the quality of the priority maps, we train the priority head by a per-glimpse information-gain target from a lightweight per-image memory bank. This requires no reinforcement learning. Complexity is linear in the number of glimpses and peak memory is decoupled from input resolution. Across nine benchmarks our framework improves consistently over its backbones.

We present Green-ELM, a non-iterative neural architecture that replaces gradient-based optimization of the output layer with a closed-form analytic solution over a fixed, high-dimensional random feature representation. By projecting input manifolds into a high-dimensional, random feature space ($d \gg 784$), our results show that complex class boundaries can be effectively untangled without the computational overhead of backpropagation. Utilizing the Moore-Penrose pseudoinverse, LU and Cholesky decomposition to solve for the output layer in a single analytic step, Green-ELM achieves a classification accuracy of 98.10% on MNIST ($d=4000$) and 86.63% on Fashion-MNIST. Furthermore, we experiment with a pre-trained ``frozen-backbone'' based on ResNet-18 to extract high-quality features and show that these one-shot solvers are effective beyond simple datasets. Notably, our baseline CPU configuration on MNIST ($d=2000$) achieves 97.15% accuracy in 1.5s, representing a 11.6$\times$ reduction in reported training time over an SGD baseline while maintaining comparable performance. We observe a near-logarithmic scaling behavior between dimensionality and accuracy, where the accuracy increases approximately logarithmically with hidden dimensionality over the tested range, suggesting that feature-space expansion contributes substantially to performance in these experiments. . This one-shot linear matrix solver approach offers a viable alternative for real-time Edge AI, where the traditional training phase is bypassed in favor of non-iterative manifold representation and readout. Finally, we propose an Empirical Scaling Hypothesis, a framework that models accuracy bounds as a function of high dimensionality and intrinsic dataset complexity.