Learning Filters with Certainty

Hash-based data structures such as Bloom filters are widely used in network systems for tasks including caching, anomaly detection, and machine learning pipelines. They typically provide binary indications of whether an element belongs to a set of interest, e.g., the contents of a cache. When uncertainty arises due to hash collisions, a positive indication is returned to avoid false negatives. We argue that the certainty associated with such indications can itself be useful information. This work focuses on Counting Bloom Filters (CBFs), a Bloom-filter variant that maintains counters rather than bits. Besides supporting insertions and deletions, these counters provide additional information that can be used to estimate the certainty of positive membership indications. We show how this certainty signal can be exploited in architectures that combine Bloom Filters with machine learning (ML) models.

GSVD for Geometry-Grounded Dataset Comparison: An Alignment Angle Is All You Need

Geometry-grounded learning asks models to respect structure in the problem domain rather than treating observations as arbitrary vectors. Motivated by this view, we revisit a classical but underused primitive for comparing datasets: linear relations between two data matrices, expressed via the co-span constraint $Ax = By = z$ in a shared ambient space. To operationalize this comparison, we use the generalized singular value decomposition (GSVD) as a joint coordinate system for two subspaces. In particular, we exploit the GSVD form $A = HCU$, $B = HSV$ with $C^{\top}C + S^{\top}S = I$, which separates shared versus dataset-specific directions through the diagonal structure of $(C, S)$. From these factors we derive an interpretable *angle score* $θ(z) \in [0, π/2]$ for a sample $z$, quantifying whether z is explained relatively more by $A$, more by $B$, or comparably by both. The primary role of $θ(z)$ is as a *per-sample geometric diagnostic*. We illustrate the behavior of the score on MNIST through angle distributions and representative GSVD directions. A binary classifier derived from $θ(z)$ is presented as an illustrative application of the score as an interpretable diagnostic tool.

From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game

Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.