LGQ: Learning Discretization Geometry for Scalable and Stable Image Tokenization

Discrete image tokenization is a key bottleneck for scalable visual generation: a tokenizer must remain compact for efficient latent-space priors while preserving semantic structure and using discrete capacity effectively. Existing quantizers face a trade-off: vector-quantized tokenizers learn flexible geometries but often suffer from biased straight-through optimization, codebook under-utilization, and representation collapse at large vocabularies. Structured scalar or implicit tokenizers ensure stable, near-complete utilization by design, yet rely on fixed discretization geometries that may allocate capacity inefficiently under heterogeneous latent statistics. We introduce Learnable Geometric Quantization (LGQ), a discrete image tokenizer that learns discretization geometry end-to-end. LGQ replaces hard nearest-neighbor lookup with temperature-controlled soft assignments, enabling fully differentiable training while recovering hard assignments at inference. The assignments correspond to posterior responsibilities of an isotropic Gaussian mixture and minimize a variational free-energy objective, provably converging to nearest-neighbor quantization in the low-temperature limit. LGQ combines a token-level peakedness regularizer with a global usage regularizer to encourage confident yet balanced code utilization without imposing rigid grids. Under a controlled VQGAN-style backbone on ImageNet across multiple vocabulary sizes, LGQ achieves stable optimization and balanced utilization. At 16K codebook size, LGQ improves rFID by 11.88% over FSQ while using 49.96% fewer active codes, and improves rFID by 6.06% over SimVQ with 49.45% lower effective representation rate, achieving comparable fidelity with substantially fewer active entries. Our GitHub repository is available at: https://github.com/KurbanIntelligenceLab/LGQ

Temporal Realism Evaluation of Generated Videos Using Compressed-Domain Motion Vectors

Temporal realism remains a central weakness of current generative video models, as most evaluation metrics prioritize spatial appearance and offer limited sensitivity to motion. We introduce a scalable, model-agnostic framework that assesses temporal behavior using motion vectors (MVs) extracted directly from compressed video streams. Codec-generated MVs from standards such as H.264 and HEVC provide lightweight, resolution-consistent descriptors of motion dynamics. We quantify realism by computing Kullback-Leibler, Jensen-Shannon, and Wasserstein divergences between MV statistics of real and generated videos. Experiments on the GenVidBench dataset containing videos from eight state-of-the-art generators reveal systematic discrepancies from real motion: entropy-based divergences rank Pika and SVD as closest to real videos, MV-sum statistics favor VC2 and Text2Video-Zero, and CogVideo shows the largest deviations across both measures. Visualizations of MV fields and class-conditional motion heatmaps further reveal center bias, sparse and piecewise constant flows, and grid-like artifacts that frame-level metrics do not capture. Beyond evaluation, we investigate MV-RGB fusion through channel concatenation, cross-attention, joint embedding, and a motion-aware fusion module. Incorporating MVs improves downstream classification across ResNet, I3D, and TSN backbones, with ResNet-18 and ResNet-34 reaching up to 97.4% accuracy and I3D achieving 99.0% accuracy on real-versus-generated discrimination. These findings demonstrate that compressed-domain MVs provide an effective temporal signal for diagnosing motion defects in generative videos and for strengthening temporal reasoning in discriminative models. The implementation is available at: https://github.com/KurbanIntelligenceLab/Motion-Vector-Learning

Geometric-k-means: A Bound Free Approach to Fast and Eco-Friendly k-means

This paper introduces Geometric-k-means (or Gk-means for short), a novel approach that significantly enhances the efficiency and energy economy of the widely utilized k-means algorithm, which, despite its inception over five decades ago, remains a cornerstone in machine learning applications. The essence of Gk-means lies in its active utilization of geometric principles, specifically scalar projection, to significantly accelerate the algorithm without sacrificing solution quality. This geometric strategy enables a more discerning focus on data points that are most likely to influence cluster updates, which we call as high expressive data (HE). In contrast, low expressive data (LE), does not impact clustering outcome, is effectively bypassed, leading to considerable reductions in computational overhead. Experiments spanning synthetic, real-world and high-dimensional datasets, demonstrate Gk-means is significantly better than traditional and state of the art (SOTA) k-means variants in runtime and distance computations (DC). Moreover, Gk-means exhibits better resource efficiency, as evidenced by its reduced energy footprint, placing it as more sustainable alternative.

Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecasting

Time series forecasting remains a challenging task for foundation models due to temporal heterogeneity, high dimensionality, and the lack of inherent symbolic structure. In this work, we propose DRAGON (Discrete Representation and Augmented Graph encoding Over deBruijN Graphs), a novel encoder that introduces Multivariate de Bruijn Graphs (MdBGs) to bridge the gap between symbolic representations and neural modeling. DRAGON discretizes continuous input sequences and maps them onto a fixed graph structure, enabling dynamic context recovery via graph-based attention. Integrated as an auxiliary module within a dual-branch architecture, DRAGON augments conventional CNN-based encoders with symbolic, structure-aware representations. All code developed for this study is available at: https://github.com/KurbanIntelligenceLab/MultdBG-Time-Series-Library