A Minimal Mathematical Model for Conducting Patterns

Generating expressive conducting gestures from music is a challenging cross-modal motion synthesis problem: the output must follow long-range musical structure, preserve beat-level synchronization, and remain plausible as a fine-grained 3D human performance. Existing conducting-motion studies are often limited by sparse pose representations, small-scale data, or evaluation protocols that do not directly measure whether music and gesture are mutually aligned. This paper presents TransConductor, a Transformer-based framework for music-driven conducting gesture generation. We introduce ConductorMotion, a SMPL-parameter data construction pipeline that recovers detailed body motion from conducting videos and forms a dataset targeted at professional conducting gestures. Given acoustic descriptors extracted from audio and an initial pose, TransConductor uses a Trans-Temporal Music Encoder and a Trans-Temporal Conducting Gesture Decoder to autoregressively predict SMPL pose parameters. To better assess artistic correspondence, we further build a retrieval-based evaluation model that embeds music and gestures into a shared space and yields FID, modality distance, multi-modality distance, and diversity metrics. Experiments show that TransConductor outperforms dance-generation and conducting-generation baselines, while ablations verify the benefits of the Transformer backbone and the proposed alignment loss.

Under a fixed physical law, the visible geometry of a scene determines how motion must change. We ask how video generators realize this relationship. We fix the law and the initial state and change only the geometry drawn in the first frame, within matched families of tracks and deflectors, and compare each generated trajectory with the simulator prediction for that geometry. Paired interventions change one thing at a time: a local bump, the height of a barrier, the words of the prompt, the length of the clip. Across nine image-to-video models, geometry is preserved and shapes the motion: the speed of the ball follows the drawn undulation of a track. A physical state would carry this response forward, and here the generated motion parts from the law. The mean slope barely accelerates the ball, successive contacts fail to compose through a consistent state, an edit ahead of the ball alters its motion before it arrives, and the ball climbs over barriers higher than its release point. Two global conditions organize the global trajectory: text strongly controls the destination, while clip length strongly controls timing in the open-weight models tested. The pattern persists with photographed first frames. Current video generation thus behaves as geometry-conditioned motion synthesis whose evolution of state differs systematically from that of a fixed physical law.

We introduce modal kinetic typography, which animates a vector glyph to express a semantic concept while keeping it legible. Our key idea is to build motion from the glyph's natural vibration modes. Specifically, a finite-element eigenproblem assembled from the vector outline yields the glyph's softest modes, for the whole letter and for each of its parts, allowing it to bend. The problem's zero-energy solutions, i.e., rigid translations and rotations, are applied in closed form to each part, allowing parts to also move as blocks. To animate the glyph, a frozen video diffusion model supervises only the modes' amplitudes and phases. Our modal approach addresses two weaknesses of prior work. Free-form point optimization under video score distillation (SDS) moves each point and frame independently along noisy gradients, tearing the outline and causing jitter. In contrast, our modes are smooth along the outline and driven by a few whole-cycle harmonics, which restricts these gradients to smooth, seamlessly looping motion. On the other hand, structured alternatives rely on skeletons or keypoints from category-specific priors, whereas our modes come from the glyph itself; the only prior is a list naming each letter's moving parts, generated once for the whole alphabet by a language model. In modal kinetic typography, shape and motion are disentangled by construction: a single base outline is sculpted toward the concept, and the modal drive cannot alter it, so a letter can also be animated without being reshaped. Our method produces more articulated and smoother motion than Dynamic Typography and AniClipart at comparable or better concept alignment, with less glyph tearing than Dynamic Typography, and is preferred by human raters, including in a frozen-shape setting where motion alone must carry the concept. Our results were also preferred over Astra (GPT-6) by human raters.