Computing with Residue Numbers in High-Dimensional Representation.

We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional vectors in a manner that allows algebraic operations to be performed with component-wise, parallelizable operations on the vector elements. The resulting framework, when combined with an efficient method for factorizing high-dimensional vectors, can represent and operate on numerical values over a large dynamic range using vastly fewer resources than previous methods, and it exhibits impressive robustness to noise. We demonstrate the potential for this framework to solve computationally difficult problems in visual perception and combinatorial optimization, showing improvement over baseline methods. More broadly, the framework provides a possible account for the computational operations of grid cells in the brain, and it suggests new machine learning architectures for representing and manipulating numerical data.

Efficient optimization with higher-order ising machines.

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean k-satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines.

Efficient Decoding of Compositional Structure in Holistic Representations.

We investigate the task of retrieving information from compositional distributed representations formed by hyperdimensional computing/vector symbolic architectures and present novel techniques that achieve new information rate bounds. First, we provide an overview of the decoding techniques that can be used to approach the retrieval task. The techniques are categorized into four groups. We then evaluate the considered techniques in several settings that involve, for example, inclusion of external noise and storage elements with reduced precision. In particular, we find that the decoding techniques from the sparse coding and compressed sensing literature (rarely used for hyperdimensional computing/vector symbolic architectures) are also well suited for decoding information from the compositional distributed representations. Combining these decoding techniques with interference cancellation ideas from communications improves previously reported bounds (Hersche et al., 2021) of the information rate of the distributed representations from 1.20 to 1.40 bits per dimension for smaller codebooks and from 0.60 to 1.26 bits per dimension for larger codebooks.

Nifedipine nanoparticle agglomeration as a dry powder aerosol formulation strategy.

Efficient administration of drugs represents a leading challenge in pulmonary medicine. Dry powder aerosols are of great interest compared to traditional aerosolized liquid formulations in that they may offer improved stability, ease of administration, and simple device design. Particles 1-5microm in size typically facilitate lung deposition. Nanoparticles may be exhaled as a result of their small size; however, they are desired to enhance the dissolution rate of poorly soluble drugs. Nanoparticles of the hypertension drug nifedipine were co-precipitated with stearic acid to form a colloid exhibiting negative surface charge. Nifedipine nanoparticle colloids were destabilized by using sodium chloride to disrupt the electrostatic repulsion between particles as a means to achieve the agglomerated nanoparticles of a controlled size. The aerodynamic performance of agglomerated nanoparticles was determined by cascade impaction. The powders were found to be well suited for pulmonary delivery. In addition, nanoparticle agglomerates revealed enhanced dissolution of the drug species suggesting the value of this formulation approach for poorly water-soluble pulmonary medicines. Ultimately, nifedipine powders are envisioned as an approach to treat pulmonary hypertension.