Xuan Qi

Xuan Qi, Daniele Berardini, Dario Serez et al.

Unsupervised domain adaptation (UDA) aims to learn a target-domain classifier from labeled source data and unlabeled target data under distribution shift. Recent diffusion-based UDA methods approach this problem by synthesizing labeled target-style images and training on the resulting synthetic data. However, their performance depends heavily on the conditioning design: class prompts provide only coarse guidance, while domain adaptation modules mainly control appearance, which may leave target-style synthesis insufficiently specified. We propose VT-DUDA, a visual-token conditioning framework for diffusion-guided UDA. Instead of relying only on text prompts, VT-DUDA uses source images to provide additional instance-level visual context for target-style synthesis. Specifically, VT-DUDA maps each source image to a compact sequence of visual tokens and forms a hybrid conditioning context by concatenating these tokens with the corresponding text embeddings along the cross-attention context dimension of a latent diffusion model. This provides instance-dependent conditioning beyond text alone, while synthesis is performed with the target-domain adapter branch. Because guidance is represented explicitly as a token sequence, the same interface also permits inference-time manipulation of the conditioning signal through token selection and token-strength adjustment. The proposed method preserves the standard diffusion objective and can be integrated into existing adapter-based diffusion frameworks without modifying the backbone. Across Office-31, Office-Home, and VisDA-2017, VT-DUDA improves average target-domain accuracy over strong discriminative and diffusion-based UDA baselines. The results suggest that, in generation-based UDA, a stronger conditioning interface can improve the downstream usefulness of synthetic target-style data.

Xuan Qi, Yi Wei, Fanqi Yu et al.

Piecewise-affine neural networks (e.g., with ReLU or LeakyReLU activations) implement continuous piecewise-affine maps, and the number of affine regions provides a natural proxy for expressive capacity. However, the gap between theoretical region capacity and the affine regions realized after training remains insufficiently understood. We study this gap from two complementary perspectives. First, we give a rigorous, architecture-dependent theorem for affine line-segment probes: for multilayer perceptrons with piecewise-affine activations, the number of affine pieces realized along an affine line-segment probe is upper bounded by an explicit product of layer-wise width terms (and activation breakpoint factors). This yields a neuron-threshold lower bound for representing target functions with prescribed one-dimensional piece complexity, formalizing the minimal region budget required for complex signals. Second, we exactly enumerate affine regions realized within bounded 2D and higher-dimensional domains under controlled task complexity. Under fixed architectures and training protocols, increasing input--label complexity yields trained solutions with markedly fewer realized regions in the evaluation domain, even though worst-case architectural capacity is unchanged; we call this reduced region usage expressivity saturation. Moreover, in the most challenging regimes, 2D visualizations show that region-usage collapse often coincides with degraded decision boundaries. Finally, we visualize the training dynamics of affine-region partitions and decision boundaries, revealing a consistent refinement process during optimization.