#01Aug 19, 2026
stat.ML
Learning Random Geometric Graphs Drawn in Probabilistic Metric Spaces
Dalia Chakrabarty, Kangrui Wang, Chuqiao Zhang and 1 more
We present a new data-driven learning of a Random Geometric Graph (RGG) of a multivariate dataset, where the graph is drawn in a probabilistic metric space. This graph learning works for generic datasets, irrespective of the type of the observables; their probability distributions; or size of the data. We identify a metric of the space that the graph is drawn in, as a probability distribution of a random variable that we introduce, namely, a variable that represents the disparity between the connectedness of two vertices of the graph, and the correlation between the two random variables that are attached to the respective vertex. It is the closed-form {\it{cdf}} of this disparity variable that we advance as the distance function of the host space of the learnt RGG, such that the edge exists between any two nodes, if this inter-nodal distance falls short of a chosen cutoff probability. Drawing the RGG in this probabilistic space leads to the graph being an Soft RGG, such that any edge - if it exists - exists with an identified probability. We forward a simple Rejection Sampling-based technique for learning the probability of any edge. The expected degree distribution of a vertex of this RGG is identified as local, and dependent on the inter-observable correlation matrix. If said correlation matrix is not known, it can be learnt given the data, using its closed-form posterior probability density function, that we forward. We illustrate our graph learning method by learning multiple RGGs of highly multivariate real datasets.
#02Aug 19, 2026
cs.CL
Comment-level Topic Drift Analysis in the Reddit Corpus
Steven Morse, Daniel Runfola, Trenton W. Ford
We present a novel application of embedding-based dynamic topic modeling techniques to detect and quantify topic drift at the comment level in a massive corpus. By leveraging pretrained language models to generate contextualized semantic embeddings for short text, we analyzed 12.7 billion Reddit comments spanning 2006 to 2022. Using unsupervised methods on these embeddings, we identify dynamically evolving topic clusters over time. Our primary contribution is a methodology for analysis of semantic drift and discourse evolution in the embedding space itself. We also demonstrate modifications to existing methods that enable this analysis at scale, and we propose and demonstrate a null model comparison test to filter spurious dynamics. Key findings suggest that politically and socially contentious topics exhibit significant directional drift in embedding space, with inter-topic distances changing systematically over time beyond what the null model can explain, whereas domains such as music and sports remain comparatively stable.
#03Aug 19, 2026
cs.SD
Geometric Iterative Retrieval for Neural Audio Codec Resynthesis
Leo Schmidt-Traub, Frédéric Berdoz, Luca A. Lanzendörfer and 1 more
Neural audio codecs based on Residual Vector Quantization (RVQ) have become the dominant discrete representation for token-based general audio generation, yet resynthesizing high-quality audio from coarse codec tokens remains an open problem and bounds the fidelity of every system that generates them. Prior work has framed resynthesis as a choice between discrete token prediction and continuous regression. We argue that this dichotomy is incomplete and introduce geometric iterative retrieval, a paradigm that uses the RVQ layer hierarchy itself as a natural iterative decomposition in continuous codebook space. Rather than classifying over discrete vocabularies or regressing to a single target vector, our method performs contrastive retrieval in the codebook's geometric space. We evaluate our method on codec restoration tasks across speech and music, and show improvements over both single-pass token prediction and one-step regression baselines.
#04Aug 19, 2026
cs.LG
Open-MOPD: Diagnosing and Fixing Capability Imbalance in Multi-Teacher On-Policy Distillation
Huan-ang Gao, Haohan Chi, Yong Yan and 7 more
Multi-teacher on-policy distillation (M-OPD) has emerged as a promising paradigm for consolidating domain-specialized reinforcement learning (RL) experts into a single generalist student via dense, token-level reward supervision. Despite its practical success, the optimization dynamics governing multi-teacher capability integration remain poorly understood, and open, rigorously reproducible recipes are conspicuously lacking. In this work, we establish a controlled M-OPD benchmark on SmolLM3-3B-Base with oracle routing, isolating capability integration from routing ambiguity. Our investigation reveals a pronounced capability integration gap: standard M-OPD captures only 35.6% of the available headroom relative to a domain-routed oracle ensemble, with concise tasks such as instruction following suffering severe degradation and premature stagnation. Crucially, we show that this failure stems not from gradient conflict, but from a severe misallocation of the token-level optimization budget. This pathology is driven by three orthogonal factors: structural sequence-length disparities across domains, dynamic convergence drift due to non-uniform learning rates, and multi-step reward staleness from asynchronous policy updates. To resolve these imbalances, we introduce Open-MOPD, a principled framework incorporating token-share balancing, gap-aware dynamic budget allocation, and student reward refresh. Together, these mechanisms systematically restore cross-domain balance, elevating headroom recovery from 35.6% to 83.4% in a single deployable student. We fully open-source our end-to-end post-training recipe, training trajectories, and evaluation suites on an academically accessible hardware budget.
#05Aug 19, 2026
cs.LG
Discretizing Continuous Time Series for Imputation with Masked Diffusion Training
Dongbin Kim, Seungyun Lee, Geonwoo Shin and 1 more
Time series imputation is a crucial area for reliable time series analysis, yet it remains challenging due to the complex temporal dynamics and noise of real-world data. Existing approaches, however, exhibit two limitations: missing and observed values are embedded within the same representation space without explicit structural separation, and continuous diffusion-based methods are trained to predict added noise rather than the original signal. To address these, we propose the Masked Diffusion Time-series Imputation Model (MDTIM), which leverages the training paradigm of masked diffusion model for imputation tasks. The MASK token is structurally orthogonal to valid observations, and the model directly predicts the original values, naturally aligning both the representation and the learning objective with the imputation task. To bridge the gap between discrete masked diffusion and the continuous, ordinal nature of time series, we further introduce Stochastic Discretization, which maps continuous values to ordinal-aware tokens while preserving continuous dynamics. Our experiments on diverse benchmarks confirm that MDTIM achieves superior robustness and scalability, consistently outperforming state-of-the-art deterministic and generative baselines across various missing scenarios.