# Density Estimation

Discrete diffusion models have lacked the statistical theory that continuous diffusion enjoys, and it was unclear whether they can exploit sparse structure in the data distribution. This analysis casts masked-diffusion score estimation as a per-context label-smoothed classifier and shows the smoothing is equivalent to regularizing with the score loss of the uniform distribution. On sparse distributions where at most k sequences have positive probability, the terminal laws of both masked and uniform noising attain the sparse minimax rate, and the smoothing level can be chosen adaptively from the number of distinct training sequences without knowing the sparsity parameter.

Discrete diffusion models have lacked the statistical theory that continuous diffusion enjoys, and it was unclear whether they can exploit sparse structure in the data distribution. This analysis casts masked-diffusion score estimation as a per-context label-smoothed classifier and shows the smoothing is equivalent to regularizing with the score loss of the uniform distribution. On sparse distributions where at most k sequences have positive probability, the terminal laws of both masked and uniform noising attain the sparse minimax rate, and the smoothing level can be chosen adaptively from the number of distinct training sequences without knowing the sparsity parameter.

The paper argues that unsupervised learning, including self-supervised learning, has no single goal or single maximized objective function, and proposes four distinct goals that are partly orthogonal or even conflicting: estimating the distribution, generating new data points, extracting features for downstream tasks, and understanding the data; for each goal it gives a problem statement, representative methods, and validation approaches, noting that understanding depends on identifiability while validation is often the hardest part.

The paper argues that unsupervised learning, including self-supervised learning, has no single goal or single maximized objective function, and proposes four distinct goals that are partly orthogonal or even conflicting: estimating the distribution, generating new data points, extracting features for downstream tasks, and understanding the data; for each goal it gives a problem statement, representative methods, and validation approaches, noting that understanding depends on identifiability while validation is often the hardest part.

Using newly released 1 µm/px BigBrain sections of the right hippocampus, this work presents CALHippo, a Cellular Annotation Library for the Hippocampus: an expert-validated, cell-level annotated dataset spanning all Cornu Ammonis (CA1–CA4) subfields with explicit three-class labels for excitatory neurons, inhibitory interneurons, and glial cells, together with a lower-resolution mesoscale cellular point-cloud map; high-resolution cell instances are obtained through a human-in-the-loop pipeline combining foundation-model-based segmentation, iterative expert correction, and model ensembling, then projected into 20 µm/px low-resolution BigBrain space to produce class-specific supervision maps used to train a UNet-based density estimation model, enabling slice-by-slice inference across the ful

Using newly released 1 µm/px BigBrain sections of the right hippocampus, this work presents CALHippo, a Cellular Annotation Library for the Hippocampus: an expert-validated, cell-level annotated dataset spanning all Cornu Ammonis (CA1–CA4) subfields with explicit three-class labels for excitatory neurons, inhibitory interneurons, and glial cells, together with a lower-resolution mesoscale cellular point-cloud map; high-resolution cell instances are obtained through a human-in-the-loop pipeline combining foundation-model-based segmentation, iterative expert correction, and model ensembling, then projected into 20 µm/px low-resolution BigBrain space to produce class-specific supervision maps used to train a UNet-based density estimation model, enabling slice-by-slice inference across the ful