Jerry Liu

Owen Dugan, Roberto Garcia, Ronny Junkins et al.

The success of large language models (LLMs) can be attributed in part to their ability to efficiently store factual knowledge as key-value mappings within their MLP parameters. Recent work has proposed explicit weight constructions to build such fact-storing MLPs, providing an improved understanding of LLM fact storage mechanisms. In this paper, we introduce an MLP construction framework that improves over previous constructions in three areas: it 1) works for all but a measure-zero set of feasible input-output pairs, 2) achieves asymptotically optimal parameter efficiency matching information-theoretic bounds for some embeddings, and 3) maintains usability within Transformers for factual recall. Through our improvements, we 1) discover a metric on value embeddings that characterizes facts-per-parameter scaling for both constructed and gradient-descent-trained MLPs, 2) identify a simple encoder-decoder mechanism that empirically matches gradient-descent MLP facts-per-parameter asymptotics across all the inputs and outputs we test, and 3) uncover a fundamental tradeoff between an MLP's fact-storage capacity and its usability within Transformers. Finally, we demonstrate a proof-of-concept application of fact-storing MLPs: modular fact editing on one-layer Transformers by \textit{replacing entire MLPs at once}.

Jerry Liu, Yasa Baig, Denise Hui Jean Lee et al.

Physics-informed neural networks (PINNs) offer a flexible way to solve partial differential equations (PDEs) with machine learning, yet they still fall well short of the machine-precision accuracy many scientific tasks demand. In this work, we investigate whether the precision ceiling comes from the ill-conditioning of the PDEs or from the typical multi-layer perceptron (MLP) architecture. We introduce the Barycentric Weight Layer (BWLer), which models the PDE solution through barycentric polynomial interpolation. A BWLer can be added on top of an existing MLP (a BWLer-hat) or replace it completely (explicit BWLer), cleanly separating how we represent the solution from how we take derivatives for the PDE loss. Using BWLer, we identify fundamental precision limitations within the MLP: on a simple 1-D interpolation task, even MLPs with O(1e5) parameters stall around 1e-8 RMSE -- about eight orders above float64 machine precision -- before any PDE terms are added. In PDE learning, adding a BWLer lifts this ceiling and exposes a tradeoff between achievable accuracy and the conditioning of the PDE loss. For linear PDEs we fully characterize this tradeoff with an explicit error decomposition and navigate it during training with spectral derivatives and preconditioning. Across five benchmark PDEs, adding a BWLer on top of an MLP improves RMSE by up to 30x for convection, 10x for reaction, and 1800x for wave equations while remaining compatible with first-order optimizers. Replacing the MLP entirely lets an explicit BWLer reach near-machine-precision on convection, reaction, and wave problems (up to 10 billion times better than prior results) and match the performance of standard PINNs on stiff Burgers' and irregular-geometry Poisson problems. Together, these findings point to a practical path for combining the flexibility of PINNs with the precision of classical spectral solvers.

Jerry Liu, Wenyuan Zeng, Raquel Urtasun et al.

An intelligent agent operating in the real-world must balance achieving its goal with maintaining the safety and comfort of not only itself, but also other participants within the surrounding scene. This requires jointly reasoning about the behavior of other actors while deciding its own actions as these two processes are inherently intertwined - a vehicle will yield to us if we decide to proceed first at the intersection but will proceed first if we decide to yield. However, this is not captured in most self-driving pipelines, where planning follows prediction. In this paper we propose a novel data-driven, reactive planning objective which allows a self-driving vehicle to jointly reason about its own plans as well as how other actors will react to them. We formulate the problem as an energy-based deep structured model that is learned from observational data and encodes both the planning and prediction problems. Through simulations based on both real-world driving and synthetically generated dense traffic, we demonstrate that our reactive model outperforms a non-reactive variant in successfully completing highly complex maneuvers (lane merges/turns in traffic) faster, without trading off collision rate.

Jerry Liu, Shenlong Wang, Wei-Chiu Ma et al.

We propose a very simple and efficient video compression framework that only focuses on modeling the conditional entropy between frames. Unlike prior learning-based approaches, we reduce complexity by not performing any form of explicit transformations between frames and assume each frame is encoded with an independent state-of-the-art deep image compressor. We first show that a simple architecture modeling the entropy between the image latent codes is as competitive as other neural video compression works and video codecs while being much faster and easier to implement. We then propose a novel internal learning extension on top of this architecture that brings an additional 10% bitrate savings without trading off decoding speed. Importantly, we show that our approach outperforms H.265 and other deep learning baselines in MS-SSIM on higher bitrate UVG video, and against all video codecs on lower framerates, while being thousands of times faster in decoding than deep models utilizing an autoregressive entropy model.

Jerry Liu, Fisher Yu, Thomas Funkhouser

This paper proposes the idea of using a generative adversarial network (GAN) to assist a novice user in designing real-world shapes with a simple interface. The user edits a voxel grid with a painting interface (like Minecraft). Yet, at any time, he/she can execute a SNAP command, which projects the current voxel grid onto a latent shape manifold with a learned projection operator and then generates a similar, but more realistic, shape using a learned generator network. Then the user can edit the resulting shape and snap again until he/she is satisfied with the result. The main advantage of this approach is that the projection and generation operators assist novice users to create 3D models characteristic of a background distribution of object shapes, but without having to specify all the details. The core new research idea is to use a GAN to support this application. 3D GANs have previously been used for shape generation, interpolation, and completion, but never for interactive modeling. The new challenge for this application is to learn a projection operator that takes an arbitrary 3D voxel model and produces a latent vector on the shape manifold from which a similar and realistic shape can be generated. We develop algorithms for this and other steps of the SNAP processing pipeline and integrate them into a simple modeling tool. Experiments with these algorithms and tool suggest that GANs provide a promising approach to computer-assisted interactive modeling.