More Like this

1. Option Tracing: Beyond Correctness Analysis in Knowledge Tracing

   https://doi.org/10.1007/978-3-030-78292-4_12  

   Ghosh, A; Raspat, J; Lan, A. (June 2021, International Conference on Artificial Intelligence in Education)

   Roll, I; McNamara, D; Sosnovsky, S; Luckin, R; Dimitrova, V. (Ed.)

   Knowledge tracing refers to a family of methods that estimate each student’s knowledge component/skill mastery level from their past responses to questions. One key limitation of most existing knowledge tracing methods is that they can only estimate an overall knowledge level of a student per knowledge component/skill since they analyze only the (usually binary-valued) correctness of student responses. Therefore, it is hard to use them to diagnose specific student errors. In this paper, we extend existing knowledge tracing methods beyond correctness prediction to the task of predicting the exact option students select in multiple choice questions. We quantitatively evaluate the performance of our option tracing methods on two large-scale student response datasets. We also qualitatively evaluate their ability in identifying common student errors in the form of clusters of incorrect options across different questions that correspond to the same error. 

   more » « less
2. Deep Hierarchical Knowledge Tracing

   Wang, T.; Ma, F.; Gao, J. (January 2019, Proceedings of the 12th International Conference on Educational Data Mining)

   Knowledge tracing is an essential and challenging task in intelligent tutoring systems, whose goal is to estimate students’ knowledge state based on their responses to questions. Although many models for knowledge tracing task are developed, most of them depend on either concepts or items as input and ignore the hierarchical structure of items, which provides valuable information for the prediction of student learning results. In this paper, we propose a novel deep hierarchical knowledge tracing (DHKT) model exploiting the hierarchical structure of items. In the proposed DHKT model, the hierarchical relations between concepts and items are modeled by the hinge loss on the inner product between the learned concept embeddings and item embeddings. Then the learned embeddings are fed into a neural network to model the learning process of students, which is used to make predictions. The prediction loss and the hinge loss are minimized simultaneously during training process. 

   more » « less
3. Adjoint nonlinear ray tracing

   Teh, Arjun; O'Toole, Matthew; Gkioulekas, Ioannis (July 2022, ACM Transactions on Graphics)

   Reconstructing and designing media with continuously-varying refractive index fields remains a challenging problem in computer graphics. A core difficulty in trying to tackle this inverse problem is that light travels inside such media along curves, rather than straight lines. Existing techniques for this problem make strong assumptions on the shape of the ray inside the medium, and thus limit themselves to media where the ray deflection is relatively small. More recently, differentiable rendering techniques have relaxed this limitation, by making it possible to differentiably simulate curved light paths. However, the automatic differentiation algorithms underlying these techniques use large amounts of memory, restricting existing differentiable rendering techniques to relatively small media and low spatial resolutions. We present a method for optimizing refractive index fields that both accounts for curved light paths and has a small, constant memory footprint. We use the adjoint state method to derive a set of equations for computing derivatives with respect to the refractive index field of optimization objectives that are subject to nonlinear ray tracing constraints. We additionally introduce discretization schemes to numerically evaluate these equations, without the need to store nonlinear ray trajectories in memory, significantly reducing the memory requirements of our algorithm. We use our technique to optimize high-resolution refractive index fields for a variety of applications, including creating different types of displays (multiview, lightfield, caustic), designing gradient-index optics, and reconstructing gas flows. 

   more » « less
4. Ray Tracing Harmonic Functions

   https://doi.org/10.1145/3658201  

   Gillespie, Mark; Yang, Denise; Botsch, Mario; Crane, Keenan (July 2024, ACM Transactions on Graphics)

   Sphere tracingis a fast and high-quality method for visualizing surfaces encoded by signed distance functions (SDFs). We introduce a similar method for a completely different class of surfaces encoded byharmonic functions, opening up rich new possibilities for visual computing. Our starting point is similar in spirit to sphere tracing: using conservativeHarnack boundson the growth of harmonic functions, we develop aHarnack tracingalgorithm for visualizing level sets of harmonic functions, including those that are angle-valued and exhibit singularities. The method takes much larger steps than naïve ray marching, avoids numerical issues common to generic root finding methods and, like sphere tracing, needs only perform pointwise evaluation of the function at each step. For many use cases, the method is fast enough to run real time in a shader program. We use it to visualize smooth surfaces directly from point clouds (via Poisson surface reconstruction) or polygon soup (via generalized winding numbers) without linear solves or mesh extraction. We also use it to visualize nonplanar polygons (possibly with holes), surfaces from architectural geometry, mesh exoskeletons, and key mathematical objects including knots, links, spherical harmonics, and Riemann surfaces. Finally we show that, at least in theory, Harnack tracing provides an alternative mechanism for visualizing arbitrary implicit surfaces. 

   more » « less
5. Adjoint nonlinear ray tracing

   https://doi.org/10.1145/3528223.3530077  

   Teh, Arjun; O'Toole, Matthew; Gkioulekas, Ioannis (July 2022, ACM Transactions on Graphics)

   Reconstructing and designing media with continuously-varying refractive index fields remains a challenging problem in computer graphics. A core difficulty in trying to tackle this inverse problem is that light travels inside such media along curves, rather than straight lines. Existing techniques for this problem make strong assumptions on the shape of the ray inside the medium, and thus limit themselves to media where the ray deflection is relatively small. More recently, differentiable rendering techniques have relaxed this limitation, by making it possible to differentiably simulate curved light paths. However, the automatic differentiation algorithms underlying these techniques use large amounts of memory, restricting existing differentiable rendering techniques to relatively small media and low spatial resolutions. We present a method for optimizing refractive index fields that both accounts for curved light paths and has a small, constant memory footprint. We use the adjoint state method to derive a set of equations for computing derivatives with respect to the refractive index field of optimization objectives that are subject to nonlinear ray tracing constraints. We additionally introduce discretization schemes to numerically evaluate these equations, without the need to store nonlinear ray trajectories in memory, significantly reducing the memory requirements of our algorithm. We use our technique to optimize high-resolution refractive index fields for a variety of applications, including creating different types of displays (multiview, lightfield, caustic), designing gradient-index optics, and reconstructing gas flows. 

   more » « less