Understanding is Compression

We have previously shown all understanding or learning are compression, under reasonable assumptions. In principle, better understanding of data should improve data compression. Traditional compression methodologies focus on encoding frequencies or some other computable properties of data. Large language models approximate the uncomputable Solomonoff distribution, opening up a whole new avenue to justify our theory. Under the new uncomputable paradigm, we present LMCompress based on the understanding of data using large models. LMCompress has significantly better lossless compression ratios than all other lossless data compression methods, doubling the compression ratios of JPEG-XL for images, FLAC for audios and H264 for videos, and tripling or quadrupling the compression ratio of bz2 for texts. The better a large model understands the data, the better LMCompress compresses.

A Circuit Complexity Formulation of Algorithmic Information Theory

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There is one universal definition for Boolean circuits involving an universal operation such as nand with simple conversions to alternative definitions such as and, or, and not. Second, there is no analogue of the halting problem. The output value of a circuit can be calculated recursively by computer in time proportional to the number of gates, while a short program may run for a very long time. Our prior assumes that a Boolean function, or equivalently, Boolean string of fixed length, is generated by some Bayesian mixture of circuits. This model is appropriate for learning Boolean functions from partial information, a problem often encountered within machine learning as "binary classification." We argue that an inductive bias towards simple explanations as measured by circuit complexity is appropriate for this problem.

Robust Group Synchronization via Quadratic Programming

We propose a novel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem. Our objective function exploits the cycle consistency of the group and we thus refer to our method as detection and estimation of structural consistency (DESC). This general framework can be extended to other algebraic and geometric structures. Our formulation has the following advantages: it can tolerate corruption as high as the information-theoretic bound, it does not require a good initialization for the estimates of group elements, it has a simple interpretation, and under some mild conditions the global minimum of our objective function exactly recovers the corruption levels. We demonstrate the competitive accuracy of our approach on both synthetic and real data experiments of rotation averaging.

Semantically-Aware Strategies for Stereo-Visual Robotic Obstacle Avoidance

Mobile robots in unstructured, mapless environments must rely on an obstacle avoidance module to navigate safely. The standard avoidance techniques estimate the locations of obstacles with respect to the robot but are unaware of the obstacles' identities. Consequently, the robot cannot take advantage of semantic information about obstacles when making decisions about how to navigate. We propose an obstacle avoidance module that combines visual instance segmentation with a depth map to classify and localize objects in the scene. The system avoids obstacles differentially, based on the identity of the objects: for example, the system is more cautious in response to unpredictable objects such as humans. The system can also navigate closer to harmless obstacles and ignore obstacles that pose no collision danger, enabling it to navigate more efficiently. We validate our approach in two simulated environments: one terrestrial and one underwater. Results indicate that our approach is feasible and can enable more efficient navigation strategies.