Existing long-tailed recognition methods, aiming totrain class-balanced models from long-tailed data, generally assume the models would be evaluated on the uniform test class distribution.

We show results on CIFAR-100 LT with an imbalance factor (β)of100and200.

The main observation behind our approach is that separation does not require optimization butcan besolvedinclosed-form prior totraining and plugged into a network.

We deploy a diffusion model trained from scratch on only the long-tailed dataset to create this proxy and verify the effectiveness of the data produced.

We generate a set of diverse expert models via hypernetworks to cover all possible distribution scenarios, and optimize the model ensemble to adapt to any test distribution. Crucially, in any distribution scenario, we can flexibly output a dedicated model solution that matches the user's preference.

Long-tailed visual recognition is challenging not only due to class imbalance but also because of varying classification difficulty across categories. Simply reweighting classes by frequency often overlooks those that are intrinsically hard to learn. To address this, we propose \textbf{DQRoute}, a modular framework that combines difficulty-aware optimization with dynamic expert collaboration. DQRoute first estimates class-wise difficulty based on prediction uncertainty and historical performance, and uses this signal to guide training with adaptive loss weighting. On the architectural side, DQRoute employs a mixture-of-experts design, where each expert specializes in a different region of the class distribution. At inference time, expert predictions are weighted by confidence scores derived from expert-specific OOD detectors, enabling input-adaptive routing without the need for a centralized router. All components are trained jointly in an end-to-end manner. Experiments on standard long-tailed benchmarks demonstrate that DQRoute significantly improves performance, particularly on rare and difficult classes, highlighting the benefit of integrating difficulty modeling with decentralized expert routing.

Abstract--Despite the fast progress of deep learning, one standing challenge is the gap of the observed training samples and the underlying true distribution. There are multiple reasons for the causing of this gap e.g. In the era of foundation models, we show that when leveraging the off-the-shelf (vision) foundation models (e.g., CLIP, DINOv2) for feature extraction, the geometric shapes of the resulting feature distributions exhibit remarkable transferability across domains and datasets. T o verify its practical usefulness, we embody our geometric knowledge-guided distribution calibration framework in two popular and challenging settings: federated learning and long-tailed recognition. In the federated setting, we devise a technique of acquiring the global geometric shape under privacy constraints, then leverage this knowledge to generate new samples for clients, in the aim of bridging the gap between local and global observations. In long-tailed learning, it utilizes the geometric knowledge transferred from sample-rich categories to recover the true distribution for sample-scarce tail classes. Comprehensive experiments show that our proposed geometric knowledge-guided distribution calibration effectively overcomes information deficits caused by data heterogeneity and sample imbalance, with boosted performance across benchmarks. It is often the case that the training data relied upon by models is often only a local [6], sparse [7], and biased observation [8] of the underlying ideal global data distribution. This distribution missing phenomenon manifests in various forms: in federated learning, it appears as label skew and domain skew due to data silos among clients [9], [10], [11], causing a severe misalignment between local data distributions and the global ideal distribution, thereby leading to divergent or even conflicting local optimization directions [12], [13], [14]. In long-tailed recognition, it is characterized by the extreme scarcity of samples in tail classes, preventing the model from capturing the true and complete shape of their distributions [15], [16]. Despite the differing scenarios, the essence is highly unified--models learn from incomplete information, lacking a comprehensive understanding of the overall structure of the real world. Conventional solutions, such as weighting loss functions [7], [17], [18], designing complex regularization terms [9], [14], [19], or aggregation strategies [20], [21], [22], primarily focus on post-hoc compensation at the optimization level. Y anbiao Ma and Zhiwu Lu are with the Gaoling School of Artificial Intelligence, Renmin University of China. Bowen Liu is with T singhua University.