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In offline reinforcement learning (RL), updating the value function with the discrete-time Bellman Equation often encounters challenges due to the limited scope of available data. This limitation stems from the Bellman Equation, which cannot accurately predict the value of unvisited states. To address this issue, we have introduced an innovative solution that bridges the continuousand discrete-time RL methods, capitalizing on their advantages. Our method uses a discrete-time RL algorithm to derive the value function from a dataset while ensuring that the function’s first derivative aligns with the local characteristics of states and actions, as defined by the HamiltonJacobi-Bellman equation in continuous RL. We provide practical algorithms for both deterministic policy gradient methods and stochastic policy gradient methods. Experiments on the D4RL dataset show that incorporating the first-order information significantly improves policy performance for offline RL problems. 

Computations in physical simulation, computer graphics, and probabilistic inference often require the differentiation of discontinuous processes due to contact, occlusion, and changes at a point in time. Popular differentiable programming languages, such as PyTorch and JAX, ignore discontinuities during differentiation. This is incorrect forparametric discontinuities—conditionals containing at least one real-valued parameter and at least one variable of integration. We introduce Potto, the first differentiable first-order programming language to soundly differentiate parametric discontinuities. We present a denotational semantics for programs and program derivatives and show the two accord. We describe the implementation of Potto, which enables separate compilation of programs. Our prototype implementation overcomes previous compile-time bottlenecks achieving an 88.1x and 441.2x speed up in compile time and a 2.5x and 7.9x speed up in runtime, respectively, on two increasingly large image stylization benchmarks. We showcase Potto by implementing a prototype differentiable renderer with separately compiled shaders. 

Neural image representations offer the possibility of high fidelity, compact storage, and resolution-independent accuracy, providing an attractive alternative to traditional pixel- and grid-based representations. However, coordinate neural networks fail to capture discontinuities present in the image and tend to blur across them; we aim to address this challenge. In many cases, such as rendered images, vector graphics, diffusion curves, or solutions to partial differential equations, the locations of the discontinuities are known. We take those locations as input, represented as linear, quadratic, or cubic Bézier curves, and construct a feature field that is discontinuous across these locations and smooth everywhere else. Finally, we use a shallow multi-layer perceptron to decode the features into the signal value. To construct the feature field, we develop a new data structure based on a curved triangular mesh, with features stored on the vertices and on a subset of the edges that are marked as discontinuous. We show that our method can be used to compress a 100, 000²-pixel rendered image into a 25MB file; can be used as a new diffusion-curve solver by combining with Monte-Carlo-based methods or directly supervised by the diffusion-curve energy; or can be used for compressing 2D physics simulation data. 

We introduce SLANG.D, an extension to the Slang shading language that incorporates first-class automatic differentiation support. The new shading language allows us to transform a Direct3D-based path tracer to be fully differentiable with minor modifications to existing code. SLANG.D enables a shared ecosystem between machine learning frameworks and pre-existing graphics hardware API-based rendering systems, promoting the interchange of components and ideas across these two domains. Our contributions include a differentiable type system designed to ensure type safety and semantic clarity in codebases that blend differentiable and non-differentiable code, language primitives that automatically generate both forward and reverse gradient propagation methods, and a compiler architecture that generates efficient derivative propagation shader code for graphics pipelines. Our compiler supports differentiating code that involves arbitrary control-flow, dynamic dispatch, generics and higher-order differentiation, while providing developers flexible control of checkpointing and gradient aggregation strategies for best performance. Our system allows us to differentiate an existing real-time path tracer, Falcor, with minimal change to its shader code. We show that the compiler-generated derivative kernels perform as efficiently as handwritten ones. In several benchmarks, the SLANG.D code achieves significant speedup when compared to prior automatic differentiation systems. 

We address the problem of synthesizing physical animations that can loop seamlessly. We formulate a variational approach by deriving a physical law in a periodic time domain. The trajectory of the animation is represented as a parametric closed curve, and the physical law corresponds to minimizing the bending energy of the curve. Compared to traditional keyframe animation approaches, our formulation is constraint-free, which allows us to apply a standard Gauss--Newton solver. We further propose a fast projection method to efficiently generate an initial guess close to the desired animation. Our method can handle a variety of physical cyclic animations, including clothes, soft bodies with collisions, and N-body systems. 

Great storytellers know how to take us on a journey. They direct characters to act—not necessarily in the most rational way—but rather in a way that leads to interesting situations, and ultimately creates an impactful experience for audience members looking on. If audience experience is what matters most, then can we help artists and animators directly craft such experiences, independent of the concrete character actions needed to evoke those experiences? In this paper, we offer a novel computational framework for such tools. Our key idea is to optimize animations with respect to simulated audience members’ experiences. To simulate the audience, we borrow an established principle from cognitive science: that human social intuition can be modeled as “inverse planning,” the task of inferring an agent’s (hidden) goals from its (observed) actions. Building on this model, we treat storytelling as “inverse inverse planning,” the task of choosing actions to manipulate an inverse planner’s inferences. Our framework is grounded in literary theory, naturally capturing many storytelling elements from first principles. We give a series of examples to demonstrate this, with supporting evidence from human subject studies.