Deep Supervision

Looped Transformers extend inference-time computation through repeated latent-state updates, but final-depth training does not directly encourage useful intermediate alternatives. We introduce Best-of-Depth (BoD), which trains a recurrent trajectory as a candidate set by minimizing prediction loss across depths. Different valid targets can be matched at different depths without architectural changes or depth-specific labels. An exact-match analysis connects this objective to solution coverage. On N-Queens completion and graph coloring, BoD improves coverage over final-depth and intermediate-supervision objectives. N-Queens coverage reaches 91.03%, versus 45.75% for final-depth training. Further experiments show discovery beyond the training depth and recovery of solutions withheld from teacher pools on familiar inputs. Fine-tuning a pretrained looped language model with BoD yields higher pooled code-generation success than final-depth training when programs are generated separately at evaluated fixed depths. These results support training recurrent computation for solution discovery along its trajectory.

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.

Vision-Language Models (VLMs) perform well on commonsense reasoning tasks but struggle with visual spatial reasoning. Most existing solutions introduce extra 3D prior inputs or external spatial encoders, which increase complexity and degrade the underlying VLMs' general-purpose capabilities after spatial fine-tuning. To this end, we propose a parameter-efficient Spatio-vision Language Models (SpatioLM), that enhances spatial intelligence without extra 3D prior inputs or third-party spatial encoders. Concretely, we design a plug-and-play and non-invasive spatio-vision module that elicits the spatial knowledge inherent in VLMs. Furthermore, we innovatively leverage pseudo depth and camera information as supervision to guide the model in learning physically coherent representations. Extensive experiments show that SpatioLM achieves significant improvements in diverse tasks, including spatial perception and understanding while effectively limiting the degradation of general capabilities. Notably, the model achieves an impressive score of 71.6 on the VSI-Bench (the first model to surpass 70). In addition, it attains competitive performance when transferred to embodied manipulation tasks. Code is available at \faGithub~spatio-lm.

End-to-end autonomous driving (E2E AD) systems integrate perception, prediction, and planning into a single differentiable architecture. While these models show great promise, their standard training often relies on output-only supervision, which can lead to weak gradients for the hidden layers of increasingly complex models. Recent works have integrated vision-language model (VLM) supervision for latent features to address this, yielding substantial empirical gains, yet leaving the underlying theoretical mechanisms poorly understood. Our investigation into this methodology reveals that the resulting performance gains stem not from VLM reasoning capabilities, as previously assumed, but rather from the latent connections forged between the E2E AD model and ground-truth (GT) data during training. Building on this insight, we propose a probabilistic deep supervision framework that regularizes intermediate latent representations directly from GT data. By treating model latents as reparameterizable distributions, we optimize the architecture via the Evidence Lower Bound (ELBO). Our evaluations conducted on the nuScenes dataset demonstrate that supervising trajectory-related latents with future GT paths consistently improves planning performance. Using identical training data and E2E architectures, our method achieves an 8% reduction in planning L2 error and a 3% decrease in collision rates compared to competitive vectorized baselines, all while incurring negligible computational overhead.

Mamba-based models have emerged as a promising alternative for salient object detection (SOD), offering significant advantages in modeling long sequences. However, existing models often fail to explore contextual information and the depth of the entire architecture. This paper introduces U$^2$Mamba, a powerful and innovative U-structured network for salient object detection. We propose multiscale Mamba U-blocks (MMUBs) that enhance the model depth to improve local feature extraction capabilities. Our newly developed nested U-structure, incorporating MMUBs, enables the network to integrate various receptive fields from shallow and deep layers, thereby collecting richer contextual information and longer-range data without being constrained by resolution. Instead of using the traditional deep supervision scheme and top-level supervised training, we propose a hierarchical training supervision method where the loss is computed at each level during the training process. Extensive experiments demonstrate that U$^2$Mamba achieves highly competitive performance against state-of-the-art methods. The source code is available at https://github.com/JL021/U2Mamba.

Looped language models turn hidden states into runtime state: each state is decoded for prediction and fed back into future computation. This creates a basic supervision question: which state variables does cross-entropy actually control? We show that dense per-loop cross-entropy controls the variables exposed by the readout, not every variable active in the recurrent transition. Hidden-state scale gives a concrete failure mode. Scale-invariant readouts such as RMSNorm and LayerNorm hide radial scale from the immediate cross-entropy loss, while pre-norm residual recurrence continues to carry and update that same scale. Thus per-loop loss can make early exits usable without controlling recurrent scale. In 44M and 129M looped transformers without inter-loop normalization, per-loop cross-entropy through RMSNorm readouts still drives final hidden-state norms into the thousands or tens of thousands. Scale-visible readouts and explicit norm penalties keep norms in the tens, and scale-removing recurrence is the complementary architectural fix. The resulting design rule is simple: dense supervision trains exits; recurrent scale control requires either making scale visible to a loss or removing it from the loop. Consistent with this rule, scale-controlled variants achieve lower perplexity at matched inference-depth operating points in our variable-depth benchmarks.

Traffic sign recognition is crucial for intelligent transportation and autonomous driving, as it can improve driving efficiency and ensure road safety. However, traditional recognition methods are based on large datasets and intensive computation, which limits their real-time applicability. Spiking Neural Networks (SNNs) offer a biologically inspired, energy-efficient alternative due to their spatiotemporal processing capabilities, but suffer from information loss and vanishing gradients during training. To overcome these limitations, this study proposes a Quantum Deep-supervised Spiking Neural Network (QDS-SNN) that integrates Quantum Neural Networks (QNNs) for efficient, low-power deep supervision. Using quantum superposition and entanglement, QNNs enable expressive representations and parallel computation, thereby enhancing performance without compromising energy efficiency. The proposed QDS-SNN incorporates a temporally and spatially adaptive LIF (TSA-LIF) neuron and a quantum-assisted classifier module (QACM) to mitigate gradient issues and improve training effectiveness. This study conducts experiments on the PennyLane quantum simulation platform, and the results show that QDS-SNN achieves 99.72% accuracy on the GTSRB dataset in only 6 time steps -- outperforming the MS-ResNet baseline by 1.32% while reducing energy consumption by 55.77%. In the TSRD dataset, it achieves 97.90% accuracy while reducing energy use to 52.68% of the baseline. These results demonstrate that QDS-SNN offers a high-performance, energy-efficient solution for traffic sign recognition in intelligent transportation systems.

Deep learning has achieved remarkable success in medical image segmentation, often reaching expert-level accuracy in delineating tumors and tissues. However, most existing approaches remain task-specific, showing strong performance on individual datasets but limited generalization across diverse imaging modalities. Moreover, many methods focus primarily on the encoder, relying on large pretrained backbones that increase computational complexity. In this paper, we propose a decoder-centric approach for generalized 2D medical image segmentation. The proposed Deco-Mamba follows a U-Net-like structure with a Transformer-CNN-Mamba design. The encoder combines a CNN block and Transformer backbone for efficient feature extraction, while the decoder integrates our novel Co-Attention Gate (CAG), Vision State Space Module (VSSM), and deformable convolutional refinement block to enhance multi-scale contextual representation. Additionally, a windowed distribution-aware KL-divergence loss is introduced for deep supervision across multiple decoding stages. Extensive experiments on diverse medical image segmentation benchmarks yield state-of-the-art performance and strong generalization capability while maintaining moderate model complexity. The source code will be released upon acceptance.