Computing Direct Shadows Cast by Convex Polyhedra

International audienceWe present an exact method to compute the boundaries between umbra, penumbra and full-light regions cast on a plane by a set of disjoint convex polyhedra, some of which are light sources. This method builds on a recent characterization of topological visual event surfaces presented in a companion paper

SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models

Large language models (LLMs) show excellent performance but are compute- and memory-intensive. Quantization can reduce memory and accelerate inference. However, for LLMs beyond 100 billion parameters, existing methods cannot maintain accuracy or do not run efficiently on hardware. We propose SmoothQuant, a training-free, accuracy-preserving, and general-purpose post-training quantization (PTQ) solution to enable 8-bit weight, 8-bit activation (W8A8) quantization for LLMs that can be implemented efficiently. We observe that systematic outliers appear at fixed activation channels. Based on the fact that weights are easy to quantize while activations are not, SmoothQuant smooths the activation outliers by offline migrating the quantization difficulty from activations to weights with a mathematically equivalent transformation. SmoothQuant enables an INT8 quantization of both weights and activations for all the GEMMs in LLMs, including OPT-175B, BLOOM-176B, and GLM-130B. SmoothQuant has better hardware efficiency than existing techniques using mixed-precision activation quantization or weight-only quantization. We demonstrate up to 1.56x speedup and 2x memory reduction for LLMs with negligible loss in accuracy. Thanks to the hardware-friendly design, we integrate SmoothQuant into FasterTransformer, a state-of-the-art LLM serving framework, and achieve faster inference speed with half the number of GPUs compared to FP16. Our work offers a turn-key solution that reduces hardware costs and democratizes LLMs. Code is available at: https://github.com/mit-han-lab/smoothquant.Comment: The first two authors contributed equally to this wor

Between umbra and penumbra

International audienceComputing shadow boundaries is a difficult problem in the case of non-point light sources. A point is in the umbra if it does not see any part of any light source; it is in full light if it sees entirely all the light sources; otherwise, it is in the penumbra. While the common boundary of the penumbra and the full light is well understood, less is known about the boundary of the umbra. In this paper we prove various bounds on the complexity of the umbra and the penumbra cast by a segment or polygonal light source on a plane in the presence of polygon or polytope obstacles. In particular, we show that a single segment light source may cast on a plane, in the presence of two triangles, four connected components of umbra and that two fat convex obstacles of total complexity n can engender Omega(n) connected components of umbra. In a scene consisting of a segment light source and k disjoint polytopes of total complexity n, we prove an Omega(nk^2+k^4) lower bound on the maximum number of connected components of the umbra and a O(nk^3) upper bound on its complexity. We also prove that, in the presence of k disjoint polytopes of total complexity n, some of which being light sources, the umbra cast on a plane may have Omega(n^2k^3 + nk^5) connected components and has complexity O(n^3k^3). These are the first bounds on the size of the umbra in terms of both k and n. These results prove that the umbra, which is bounded by arcs of conics, is intrinsically much more intricate than the full light/penumbra boundary which is bounded by line segments and whose worst-case complexity is in Omega(n alpha(k) +km +k^2) and O(n alpha(k) +km alpha(k) +k^2), where m is the complexity of the polygonal light source

Événements visuels de convexes et limites d'ombres

To compute shadows in computer graphics, it is common to be interested in the view of a geometric scene by an observer. Particularly, it is important to characterize the structural changes, called visual events, taking place in the view when the observer moves. Based on the combinatorial definition of view introduced by Gigus and Malik and the associated classification of visual events, many studies suffer from time and space complexity problems. For example, it is the case of discontinuity meshing. Thus, we suggest a new approach which relies on a questionning about this notion of view. For a set of pairwise disjoint convex objects, we propose a topological definition of view emphasizing the visible silhouettes of objects in the scene and we geometrically characterize the locus where those visual events take place. We use this characterization to propose a method to extract boundaries between full light and penumbra and between penumbra and umbra in a scene lit by area light sources. We manage to strongly reduce the size of intermediate objects in use to build the limits between those regions.Furthermore, we prove the first non trivial theoretical bounds on the complexity of the limits between full-light and penumbra and between penumbra and umbra.Pour le calcul d'ombres en informatique graphique, il est courant de s'intéresser à la vue qu'un observateur a d'une scène géométrique. En particulier, il est important de caractériser les changements structurels, appelés événements visuels, qui se produisent dans cette vue lorsque l'observateur se déplace. En se basant sur la définition combinatoire de la vue proposée par Gigus et Malik et la classification des événements visuels qui en découle, de nombreux travaux se heurtent à des problèmes de complexité en temps et en espace. C'est notamment le cas de la méthode du maillage de discontinuités. Nous suggérons donc une approche nouvelle qui repose sur la remise en cause de cette notion de vue.Pour un ensemble d'objets convexes disjoints, nous proposons une définition topologique de la vue qui fait la part belle aux silhouettes visibles des objets de la scène et nous caractérisons géométriquement les lieux où se produisent les événements visuels. Nous utilisons cette caractérisation pour proposer une méthode qui permet d'extraire les limites entre lumière et pénombre et entre ombre et pénombre dans une scène éclairée par des sources surfaciques. Nous arrivons ainsi à réduire considérablement la taille des objets intermédiaires utilisés pour la construction des limites entre les régions.De plus, nous démontrons les premières bornes théoriques non triviales sur la complexité des limites entre lumière et pénombre ainsi qu'entre ombre et pénombre

Computing Direct Shadows Cast by Convex Polyhedra

We present an exact method to compute the boundaries between umbra, penumbra and full-light regions cast on a plane by a set of disjoint convex polyhedra, some of which are light sources. This method builds on a recent characterization of topological visual event surfaces presented in a companion paper.

Parallel Fast Möbius (Reed-Muller) Transform and its Implementation with CUDA on GPUs

One of the most important cryptographic characteristics of the Boolean and vector Boolean functions is the algebraic degree which is connected with the Algebraic Normal Form. In this paper, we present an algorithm for computing the Algebraic Normal Form of a Boolean function using binary Fast Möbius (Reed-Muller) Transform implemented in CUDA for parallel execution on GPU. In the end, we give some experimental results