Novel view synthesis from monocular videos of dynamic scenes with unknown While camera recent poses remains advances a in fundamental 3D representations challenge such in computer as Neural vision Radiance and graphics. Fields (NeRF) scenes, and they 3D struggle Gaussian with Splatting dynamic (3DGS) content ha and ve sho typically wn promising rely on results pre-computed for static camera poses. We present 4D3R, a pose-free dynamic neural rendering framework that Our method decouples first static leverages and dynamic 3D foundational components models through for initial a tw pose o-stage and approach.

Dynamic scene reconstruction poses a persistent challenge in 3D vision. Deformable 3DGaussian Splatting has emerged as an effective method for this task, offering real-time rendering and high visual fidelity.

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, LoRA-Curve yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

In this section we prove the theoretical results around the dual curriculum game and use these results to show approximation bounds for our methods, given that they have reached a Nash equilibrium (NE). The first theorem is the main result that allows us to analyze dual curriculum games. The high-level result says that the NE of a dual curriculum game are approximate NE of the base game from the perspective of any of the individual players, or from the perspective of the joint strategy. Let Bbe the maximum difference between U1t and U2t, and let (π,θ1,θ2) be a NE for G. Then (π,pθ1 + (1 p)θ2) is an approximate NE for the base game with either teacher or for a teacher optimizing their joint objective. More precisely, it is a 2Bp(1 p)-approximate NE when Ut = pU1t + (1 p)U2t, a 2B(1 p)-approximate NE when Ut = U1t, and a 2Bp-approximate NE when Ut = U2t. At a high level, this is true because, for low values of p, the best-response strategies for the individual players can be thought of as approximate-best response strategies for the joint-player, and vis-versa. Since the Nash Equilibrium consists of each of the players playing their own best response, they must be playing an approximate best response for the joint-player. We provide a formal proof below: Proof. Let B be the maximum difference between U1t and U2t, and let (π,θ1,θ2) be a Nash Equilibrium for G. Then consider pθ1 + (1 p)θ2 as a strategy in the base game for the joint player pU1t + (1 p)U2t.

Additionally, we introduce a Bézier-boundary gradient approximation strategy within our framework to keep the "differentiability"

In this paper, we present DiffSketcher, an innovative algorithm that creates vectorized free-hand sketches using natural language input.