Conditional Velocity

Robotic piano playing has emerged as a standard benchmark for dexterous bimanual manipulation, yet progress on it has been measured almost entirely by note accuracy -- which keys are pressed (pitch) and when (onset) -- leaving the musical dynamics essential for expressive performance neither rewarded nor evaluated. We propose CANTABILE, a dynamics-aware framework for robotic piano performance that (i) closes the score-to-contact loop by conditioning the policy on upcoming velocity goals and mapping each key's angular velocity at onset back to MIDI velocity, (ii) couples a velocity-fidelity reward with an onset-coverage reward, so that dynamics cannot be improved by omitting difficult notes, and (iii) refines a frozen dynamics-aware base policy with an alpha-scaled, finger-only residual that localizes strike-intensity adaptation away from nominal note execution. On EXPRESSIVE-51, a dynamics-rich 51-song subset of RoboPianist, CANTABILE raises Velocity F1 -- jointly measuring pitch, onset, and intensity within a +/-8 MIDI-velocity tolerance -- from 0.06 to 0.34 over the RoboPianist baseline, improves all 51 songs, more than halves matched-note velocity error, and reduces log-mel distance to reference audio by 8%. Intensity-randomized training further enables runtime control of performance intensity without retraining.

Velocity-aware pitch control is standard, but under a broadcast viewport half the players are off screen and on-screen velocities come from a drifting calibration. We ask at which layer of broadcast off-ball analysis velocity changes the answer. Inheriting our off-screen imputation protocol (three Metrica matches, 44 m viewport, block-bootstrap CIs), we score four velocity regimes -- none, viewport-legal observed, true-for-visible, true-for-all -- against a velocity-aware ground truth at three layers: imputation, the control surface, and team verdicts. Velocity is nearly useless for imputation (-0.2 pp against a 12--14 pp velocity-free surface MAE), first-order for the surface (-1.5 to -1.8 pp, 11--15% of that MAE), and ten times smaller for verdicts (-0.12 to -0.19 pp). The velocity that matters is the visible channel: perfect occluded-player velocity adds 2--6% of the visible gain, and no last-seen decay policy we tested exceeds that. Omitting velocity blurs the surface (per-frame |e| 2.2--2.6 pp) with small time-averaged bias (per cell <=0.4 pp), whereas imputation error is a structured bias against the defending team's deep zone (5--9 pp). At a fixed velocity window, a noise ladder of eleven jitter settings, including sigma_v-matched pairs, is ordered to first order by one velocity-noise axis sigma_v with break-even ~1 m/s; eleven SoccerNet-GSR clips from one match through our pipeline measure sigma_v=1.65 m/s yet recover 24--36% of the benefit: 43% of the variance is frame-common, which the surface tolerates, and the residual is heavy-tailed and clustered, which Gaussian controls matched on component RMS do not reproduce (+0.03 vs. +0.36). The share of velocity-free error that velocity removes grows with viewport width (7% at 36 m, 21% at 60 m): fix imputation on tight shots, velocity on wide ones. Code and logs are released.

Inertial odometry (IO) is critical for aerial robots, where aggressive maneuvers and poor lighting degrade visual sensors. Recent learning-based IO methods improve traditional integration-based approaches by learning motion priors from IMU and platform-specific sensors, then fusing the predictions within an extended Kalman filter. However, learning velocity through regression is difficult, while jointly estimating uncertainty with a separate decoder and negative log-likelihood (NLL) loss further complicates training and can lead to over-confident estimates. We introduce VeloBins, which reformulates velocity regression as classification over discretized velocity bins. We decode both the velocity from the bin distribution's expectation and the uncertainty from its variance, removing the need for a separate uncertainty decoder. We further supervise the uncertainty explicitly using an error-conditioned Gaussian label centered at the ground-truth velocity, with a standard deviation set to the velocity error. We evaluate VeloBins on four aerial datasets, ranging from free-form aggressive flights and a 27 g nano-quadrotor to drone racing at over 21~m/s. VeloBins achieves the lowest average errors on all four datasets, reducing velocity, relative trajectory, and absolute trajectory errors by 3-27%, 8-40%, and 6-53%, respectively, compared with the strongest baseline. Notably, the proposed supervision achieves the lowest NLL and best filter consistency despite never optimizing an NLL loss. The code will be available upon acceptance.

Existing unified 4D reconstruction and point tracking approaches typically rely on heuristic interpolations or just predict at integer timestamps, lacking kinematic coherence and failing to model dynamics at any arbitrary timestamp. In this paper, we propose Uni4R, a framework that unifies these tasks by learning continuous velocity fields through the synergy of Optimal Transport (OT) and Ordinary Differential Equation (ODE). Importantly, this continuous velocity field acts as a kinematic prior that mutually benefits both 4D reconstruction and point tracking. Specifically, we propose the Flow Matching Guided Decoder (FMGD). A global velocity branch first extracts anchor features that capture the global dynamic state of the sequence. Then, FMGD leverages Flow Matching (FM) theory to formulate a probability path defined by OT on the anchor feature manifold, instantiating it as FM-guided velocity features for velocity prediction. This establishes a robust kinematic inductive bias. Meanwhile, a point reconstruction branch provides geometric features. The local velocity prediction module then joint above features and time embeddings, to decode velocities at arbitrary timestamps. To overcome the absence of high-quality ground-truth velocities in fractional frames, we propose an integral-consistency training strategy. This strategy uses an ODE solver to integrate velocities to recover target pointmaps, enabling the model to be supervised end-to-end directly from integer timestamps. Experimental results demonstrate that Uni4R achieves SOTA performance in both 4D reconstruction and point tracking, and achieves SOTA in our new kinematics-aware benchmark at continuous time.

Vision-language-action (VLA) policies fine-tuned from a fixed scene camera can fail when the camera is moved, even when the task, objects, language, and robot state are unchanged. We study scene-camera viewpoint robustness using only a scene RGB image, language, and proprioception, without camera labels, extrinsics, depth, or point-cloud inputs. The wrist stream is masked throughout to prevent an unperturbed visual shortcut from confounding attribution to scene-camera variation. For flow-based VLAs, we propose to regularize the action-flow velocity field, the quantity directly integrated to generate continuous action chunks. We construct action-equivalent view pairs by resetting original LIBERO demonstrations to the same MuJoCo state and rendering nominal and perturbed scene-camera views. Both views are supervised by flow matching, while a cross-view loss encourages their predicted action-flow velocities to agree at the same sampled flow coordinates. On the LIBERO-Plus camera-perturbation track, our method reaches 87.2$\pm$0.4% (4,797 rollouts per seed across 3 training seeds), +7.4pp over flow-matching-only training on the same paired data (79.8$\pm$0.8%, also 3 seeds) and +12.5pp over naive mixed-camera SFT, while maintaining nominal-camera ID performance (95.0$\pm$0.8%; same-data FM-only: 95.0$\pm$4.3%). A shuffled-pair control collapses to 25.8%, showing that the gain depends on action-equivalent pairing. On a real robot, we evaluate three tabletop tasks with 10 rollouts per task and camera placement; held-out-camera success improves from 53.3% to 74.4% under the same single-scene-RGB inference interface.

Text-to-music language models begin with a choice usually made by default: how to tokenize music. Normally entangled with backbone, data, and recipe, its effect has never been measured in isolation. We fix pretrained Qwen3.5 (0.8B-27B), data, budget, and decoding, and swap only the representation across seven tokenizations, anchoring texture metrics to each representation's model-free ceiling. The ordering is clean and surprising: representation, not model size, is the binding variable for distributional fidelity. Scaling the backbone 34x barely moves Frechet Music Distance (FMD), whereas switching representation halves it. PMT, a performance-resolution stream we release (10 ms timing, per-note velocity, multi-track texture; 609 symbols), reaches FMD 159 at 0.8B against 272-286 for beat grids (1.7-1.8x lower, up to 2.8x elsewhere; non-overlapping bootstrap CIs), so a 0.8B performance-resolution model beats a 27B beat grid. It reappears on a 26M from-scratch backbone and a second performance-resolution tokenizer: a property of the class, not one lucky vocabulary. Nor is it a finer-lattice artifact: snapping PMT's onsets to the beat grids' resolution still leaves it 67-129 FMD ahead of both (n=500). The effect is distributional; whether it is audible is a separate question, left open by our probe, with a human study pre-registered. Native caption adherence is weak but separable: a lightweight decode-time constraint doubles instrument-F1 (.28 to .60) and Correct-Key (.16 to .35) at no distributional cost. We release the harness, 25+ checkpoints, two corpora (86.6k aligned across caption/MIDI/ABC/audio; 6.25M captioned, the largest for music), and an imprinting diagnostic: published text-to-MIDI systems reproduce their training distribution near-invariant to the caption (72% vs. 71% chord-time on disjoint domains). The field's next representation claim can now be measured, not asserted.

Audio-based piano transcription performs well on onset, pitch, and velocity, but the sustain pedal lets sound persist long after key release, so audio systems predict pedal-extended offsets rather than physical key release. Yet existing Visual Piano Transcription (VPT) systems focus on onset detection from short video windows, offset accuracy lags onset by a wide margin, and note-level velocity has not been reported. To address these gaps, we present V2N (Video to Notes), the first complete VPT system: a shared temporal backbone feeds task-specific heads for onset, offset, key hold, and velocity, jointly trained with per-frame supervision rather than only at the window center. Ablations show that multi-task supervision enables offset and velocity prediction while improving onset accuracy; longer temporal context yields further improvements. V2N sets new state-of-the-art results on PianoVAM and R3.

Sensing ego-velocity estimation is fundamental to state estimation in visually degraded environments, where camera- and LiDAR-based pipelines can become unreliable. Millimetre-wave radar is well suited to these conditions because it provides direct Doppler velocity sensing and remains robust to poor illumination, textureless scenes, and airborne particulates. However, conventional radar ego-velocity pipelines typically apply constant false alarm rate (CFAR) thresholding to convert dense radar spectra into sparse point clouds, prematurely discarding sub-threshold returns that may still retain useful Doppler motion cues. We present Dense Soft Weighting, an analytic radar front-end that maps every range-Doppler cell to a continuous confidence metric rather than enforcing a binary detection threshold. Ego-velocity is then estimated using a deterministic robust weighted least-squares formulation, while the same weighted measurements provide a closed-form, measurement-derived velocity covariance for integration with a shared inertial back-end. The method requires no platform-specific training data or learning-based uncertainty model, supporting transfer across single-chip radar configurations. Across two public datasets and one self-collected dataset, Dense Soft Weighting reduces mean absolute pose error by 31-45% relative to the strongest CFAR point-cloud baseline under an identical inertial back-end, while running in real time on embedded hardware.

Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone-constrained linear response and a scalar non-associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non-associated coupling explicitly, and an inner solve for a strongly convex cone-constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid-body benchmarks with stick-slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.

This application paper presents DebrisTracer, a framework for the reliable tracking of debris in hypervelocity impact fast imaging. These noisy and highly specific datasets capture the ejection of a large number of debris fragments after the impact of a projectile launched at hypervelocity into a target material. The reliable estimation of debris mass and speed distributions is of major importance in aerospace applications. We document how to extend an off-the-shelf topology tracking framework based on critical point extraction and matching, in order to incorporate domain knowledge and physical assumptions. Our approach automatically produces an accurate and reliable debris tracking, enabling an interpretable visual analysis of this complex space-time phenomenon. Extensive experiments demonstrate the accuracy improvements provided by our approach over established tools used by domain experts in terms of physical validation, specifically via the prediction of the experimental ejected mass and crater depth profiles. We illustrate the utility of our approach across several use cases (with varying impact angles and physics). We show that our statistical summaries enable the visual identification of distinct regimes within the debris population, corroborating and refining prior expectations of domain experts. Our database and our C++ implementation are available at this address: https://github.com/tloloum/DebrisTracer.

Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations~(NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout the trajectory. We relax this choice and introduce Velocity Scheduled Flow Matching~(VSFM), which replaces the conditional target $x_1 - x_0$ with $v(t)(x_1 - x_0)$ for any nonnegative profile $v:[0,1]\to\mathbb{R}_{\geq 0}$ satisfying $\int_0^1 v\,dt = 1$. We study six polynomial profiles drawn from motion planning. The first use of VSFM is at inference time: a pretrained linear flow-matching model can be sampled under any admissible profile by integrating its ODE on a non-uniform $τ$-schedule, with no retraining and no additional computation; on CIFAR-10 this lowers FID by up to $19.8\%$. Training from scratch under a braking profile gives a further reduction of $17.4\%$ at $4$~NFE. Both gains follow from the local truncation error of the Euler integrator on the induced grid.

Modern video games are becoming more complex day by day. Most of these modern games are multiplayer first-person shooter (FPS) games. The rising popularity of FPS games emphasizes the need to combat cheating for fair and enjoyable gaming. As the number of players using cheating techniques like aimbots, wallhacks, and speed hacks is also increasing, we need a way to detect players who are using cheating tools to gain an unfair advantage over regular players. In this system, we focus exclusively on detecting aimbot cheats. Players who use aimbot cheats generally do not prioritize other aspects of the game. To distinguish between regular and cheating players, we identify specific features encompassing time-series data such as aim velocity, number of shots, distance to target, and more, along with behavioral data such as utility usage, player movement, and other gameplay patterns. Utilizing these features, we construct a server-side aimbot detection classifier named 'YAACS'. YAACS comprises a parser, a deep learning model, and intermediary connection utilities designed for integration with the game server. The proposed system achieves a classification accuracy of 88.6% with a false positive rate of 0.97% using a Stacked LSTM with Dense layers trained on sequences of 128 ticks (Tick Delta Negative=56, Tick Delta Positive=24), outperforming the Decision Tree baseline which achieves a higher accuracy of 96.2% but at a false positive rate of 2.68%, 2.76x worse than the best LSTM configuration. These results demonstrate that incorporating temporal context through sequence modelling is critical for minimising false accusations in FPS cheat detection.

Rolling-shutter cameras introduce characteristic distortions when imaging fast moving objects, and these effects are typically treated as artifacts to be corrected. In this work, we instead leverage rolling-shutter distortions as a valuable source of temporal information to estimate the 3D translational and angular velocities of rapidly moving spherical objects from a single rolling-shutter frame. We design a robust and easily detectable spherical pattern and propose a correspondence-free formulation that recovers motion by enforcing geometric consistency in a back-projection framework. By exploiting the geometry of the sphere, translational and rotational motions are decoupled and estimated through a two-stage optimization process, enabling reliable velocity recovery even for textureless objects. Extensive experiments on both synthetic and real datasets demonstrate accurate and robust estimation of motion parameters under challenging high-speed conditions.

Agent interoperability protocols (MCP, A2A, ACP, ANP, and ERC-8004) have rapidly matured to enable identity, capability discovery, tool access, and message exchange between autonomous agents. However, as enterprises deploy heterogeneous agent fleets that must make collective decisions under governance constraints, a question arises: can these protocols support governed agent communities, or only task-oriented coordination? We present a systematic gap analysis applying a six-dimension governance requirements taxonomy (membership, deliberation, voting, dissent preservation, human escalation, and audit/replay) derived from organizational theory, multi-agent systems literature, and enterprise governance standards. We analyze each protocol's specification against this taxonomy, classifying capabilities as Supported, Partial, or Absent. The resulting gap matrix reveals that voting and dissent preservation are universally absent across all five protocols, deliberation is absent or at most partial, and no protocol encodes the full set of primitives required for governed agent communities. We distinguish extensible gaps (addressable through protocol extension mechanisms) from structural gaps (requiring a new architectural layer) and assess time-sensitivity based on observed protocol evolution velocity. The analysis establishes that agent community governance constitutes a missing architectural layer above current interoperability standards, not a missing feature within them.

Reinforcement learning (RL) post-training improves the reward alignment of flow-based generators, but often degrades perceptual quality in ways that are not captured by the reward proxy. We identify a simple structural signature of this drift: across three post-training methods (NFT, AWM, DPO), RL fine-tuning inflates the per-step velocity norm $\|v_θ\|$ by $5\%$ to $15\%$ relative to the reference. A form of norm inflation has been studied in classifier-free guidance (CFG), where rescaling the velocity back to a reference norm at inference time can mitigate the resulting artifacts. However, this inference-time correction does not transfer cleanly to RL: rescaling $v_θ$ to match $\|v_{\text{ref}}\|$ at inference time neither improves reward nor fixes the quality degradation, because the inflation is co-adapted into the model weights. Furthermore, an adjoint sensitivity analysis shows that velocity magnitude rescaling carries no coherent first-order reward signal at the batch level, indicating that suppressing norm inflation is unlikely to remove a consistently reward-carrying component. Since inference-time renormalization fails while norm suppression carries no reward cost, training-time intervention is the appropriate strategy. Together, these findings motivate NormGuard, a hinge penalty that activates only when $\|v_θ\|$ exceeds $\|v_{\text{ref}}\|$ and composes additively with any velocity-local base loss. Across two base models, three post-training methods, and two reward proxies, NormGuard consistently improves MLLM-judged image quality and forensic realism while preserving reward, with gains that amplify under few-step inference and are not explained by early stopping.

Concept Bottleneck Models (CBMs) promise transparent reasoning by predicting through human-interpretable concepts, yet their effectiveness fundamentally depends on how well visual and textual representations are aligned or matched. Existing vision-language CBMs often rely on pre-aligned encoders or global cosine similarity, which obscures fine-grained concept localization and fails to reflect true semantic geometry. In this work, we rethink concept alignment as a dynamic cross-modal transport process instead of static projection and propose the Optimal Transport Flow Concept Bottleneck Model (OTF-CBM). It first learns a data-driven semantic cost via Inverse Optimal Transport to measure cross-modal distances, and then performs unbalanced optimal-transport-based flow matching to model semantic transitions between visual patches and textual concepts. With velocity-based concept activation, OTF-CBM captures interpretable geometric relations without ODE integration. Experiments further show that OTF-CBM achieves superior classification accuracy and concept faithfulness, offering a new geometric and dynamical perspective for interpretable cross-modal reasoning.

This paper focuses on the hardware specifications required for a table tennis robot to beat professional players. After analyzing the motions of elite players, we defined target specifications for the workspace, payload, external-force resistance, physical performance, serve capability, and end-effector accuracy. Based on these specifications, we developed "Ace", a custom 8-DoF robot. The mechanical structure was improved through topology optimization to minimize mass while preserving stiffness. Motor and gearbox selection was optimized using an inverse-dynamics torque model. Low-order per-joint dynamics models with delay compensation were identified and integrated into simulation to enable the use of an RL control policy. Experiments demonstrated repeated full-stroke swings with a cycle time of 0.8 s and a peak racket-center velocity of 22 m/s. The robot successfully defeated multiple professional players.

Even when Dirac-Frenkel dynamics determine a well-defined evolution in function space, the corresponding parameter dynamics can be non-unique or ill-conditioned for redundant nonlinear parametrizations such as neural networks or mixture models. We propose to add inertia to the Dirac-Frenkel dynamics and show that this allows useful parameter velocity information to persist from the past trajectory in directions that are weakly informed, while well-informed parameter velocity directions continue to follow the Dirac-Frenkel dynamics. We prove that the inertial formulation yields well-posed parameter dynamics and provide a posteriori error bounds. After time discretization, the method requires the solution of the same type of regularized linear least-squares problem as standard Dirac-Frenkel dynamics, but with the previous velocity appearing as an anchor. Numerical experiments demonstrate the increased robustness obtained with inertia.

This paper introduces a novel tactile sensor for in-hand manipulation with slip-aware control that integrates velocity, force/torque, and pressure map sensing into a single device with a deformable contact pad. To the best of our knowledge, this is the first sensor to combine these sensing modalities within a single compliant structure. The sensor features a deformable contact surface and can robustly track both flat and curved surfaces across a wide range of materials. Its performance is evaluated through a comprehensive set of experiments that highlight both its capabilities and limitations. The sensor is designed for rapid and low-cost fabrication using a combination of standard PCB manufacturing and rapid prototyping techniques.

Post-training via Group Relative Policy Optimization (GRPO) has emerged as a powerful paradigm for aligning flow-based generative models with human preferences. However, the iterative denoising nature of flow models incurs substantial costs when generating group rollouts for policy-gradient updates, compelling existing methods to train with extremely few denoising steps. This temporal sparsity severely restricts preference optimization: reward feedback can only reach a handful of stages per trajectory, leaving the vast majority of intermediate denoising steps without direct supervision and thus compromising alignment granularity. To address this, we propose Pave-GRPO, which reformulates the GRPO objective through Principled average velocity decomposition. Rather than generating expensive high-step rollouts, we maintain efficient few-step group sampling but decompose each coarse transition into an equivalent ensemble of finer sub-trajectories spanning multiple intermediate timesteps. This propagates reward feedback to a denser set of temporal stages for more comprehensive preference alignment without additional generation cost. This design offers two benefits: (i) zero-cost horizon expansion: through the direct reuse of piece-wise group samples and their associated rewards, Pave-GRPO significantly broadens the effective optimization scope under fixed sampling budgets; and (ii) comprehensive temporal supervision: by equivalently decomposing an instantaneous velocity target into a multi-timestep ensemble, it distributes reward signals across more intermediate stages of the denoising process, enabling finer-grained and more thorough preference optimization. Extensive experiments validate that Pave-GRPO effectively advances preference alignment across different reward settings, offering comprehensive performance enhancement.

Accurate and reliable navigation is essential for autonomous ground vehicle operations. Standard INS/GNSS fusion relies on GNSS position updates, which provide limited observability of orientation and inertial sensor error states, particularly during low-dynamic motion. In this work, we propose utilizing past GNSS measurements alongside a motion model to extract meaningful vehicle acceleration information. This acceleration measurement is then integrated into the INS/GNSS filter to improve its robustness and accuracy. The proposed approach is evaluated on two real-world unmanned ground vehicle datasets collected from different mobile platforms and inertial sensor grades. Results demonstrate consistent positioning accuracy improvements relative to the standard position-aided filter, with mean position root mean square error improvements of 11.40 % and 20.74 % on the two datasets, respectively.

We analyze finite-particle drifting models for one-step generative modeling. For a conservative velocity given by the difference of the kernel-smoothed data and model scores, a joint-entropy identity yields continuous-time bounds for the smoothed Fisher discrepancy and the squared particle velocity. The finite-particle correction involves reciprocal kernel density estimates. We give local-occupancy conditions and exact expectation bounds, and show that these expectations diverge for full-support initial densities in a shrinking-bandwidth regime. Keeping the bandwidth dependence of the quadrature constants explicit yields a conditional root residual-velocity rate of $N^{-1/(d+4)}$ under uniform regularity, with a corresponding rate under weaker quadrature growth conditions. We also analyze the original displacement field with the exact Laplace kernel. A companion kernel gives a weighted coercivity estimate that accommodates the unbounded empirical scale and the kernel's nondifferentiability. Localization controls the particle velocity, while relative scale alignment absorbs the mismatch into dissipation. Both analyses quantify the size of an additional drift correction under explicit regularity and stability assumptions.

Diffusion and rectified flow (RF) models generate high-fidelity images and videos, but their iterative velocity-field evaluations are computationally expensive. Existing caching methods accelerate sampling by skipping timesteps, yet their coarse approximations introduce accumulated errors over long skip intervals and degrade quality under aggressive acceleration. We propose TACache (Trajectory-Aware Cache), a training-free acceleration framework following a skip-then-compensate paradigm. TACache performs an orthogonal decomposition of discrete velocity acceleration along the RF trajectory into a parallel component and an orthogonal residual, isolating the magnitude and directional sources of per-step approximation error. The framework operates in two stages: offline, cumulative variation thresholds on the magnitude and direction indicators yield the skip schedule and bound how far each skip interval may extend; online, at each skipped step the offline statistics are combined with the sample's historical orthogonal direction to reconstruct the skipped velocity without additional model evaluations. Experiments on BAGEL, FLUX.1-dev, and Wan2.1-1.3B show that TACache achieves up to 4.14 speedup on text-to-image generation and 2.11 speedup on text-to-video generation, with consistent improvements over prior cache-based methods on all reference-based fidelity metrics. Code will be released soon.

Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D velocity field as a Fourier-feature neural network, replacing the grid-based slowness vector with a continuous, infinitely differentiable function. Prior neural-field tomography has staircased smooth fields under total-variation (TV) priors or oscillated near interfaces under $L^2$ Laplacian smoothing. We adopt second-order total generalized variation (TGV$^2$) and parametrize its auxiliary vector field as a second neural network jointly optimized with the velocity field, eliminating the inner Chambolle-Pock primal-dual loop that classically dominates TGV computation. On three synthetic benchmarks (Gaussian, horizontally layered, curved-fault inspired by OpenFWI) using cross-well acquisition, 5% travel-time noise, and five seeds, MIMIR-TGV$^2$ ties a classical FMM-LSMR baseline with auto-tuned hyperparameters on the Gaussian ($p=0.134$, paired $t$-test) and significantly outperforms it on layered ($p<0.0001$, 44% RMSE reduction) and curved-fault ($p=0.0002$, 33% reduction). Replacing TGV$^2$ with TV degrades performance on Gaussian ($p=0.004$) and layered ($p=0.003$); curriculum-annealed TV improves Gaussian RMSE by only 5.4%, confirming that TV's staircase bias is intrinsic to the regularizer rather than a scheduling artifact. The results empirically validate the Bredies-Kunisch-Pock prediction that piecewise-affine priors are better suited to subsurface velocity recovery than piecewise-constant TV priors. We argue that the central design choice in physics-informed neural-field inversion is not the network architecture but the regularizer. The full pipeline reproduces in under one hour on consumer hardware.

Reconstructing 3D fluid velocity fields from sparse 2D video observations is a highly ill-posed inverse problem, demanding both transport consistency with observed motion and physical validity under fluid laws. Existing methods typically impose these constraints through soft penalties, often leading to compromised accuracy and convergence issues. We introduce a reconstruction framework that structurally enforces both constraints. Specifically, we parameterize the reconstructed velocity using a continuous Divergence-Free Kernel representation, driving the advection of a Lagrangian 3D Gaussian Splatting representation. This formulation intrinsically guarantees both flow incompressibility and long-range transport coherence by construction. To enable the efficient optimization of such a constrained system, we introduce a novel Sliding Window scheme that propagates gradients over meaningful temporal horizons while maintaining tractable training costs. Experiments on synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art baselines in both transport consistency and physical accuracy, enabling applications such as high-quality re-simulation and flow analysis.

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on $\mathbb S^{d-1}$ to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on $(\mathbb S^{d-1})^L$ both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.