pareto-optimal (pareto optimal, pareto optimality, pareto-optimality)

A wide range of machine learning applications such as privacy-preserving learning, algorithmic fairness, and domain adaptation/generalization among others, involve learning invariant representations of the data that aim to achieve two competing goals: (a) maximize information or accuracy with respect to a target response, and (b) maximize invariance or independence with respect to a set of protected features (e.g. for fairness, privacy, etc). Despite their wide applicability, theoretical understanding of the optimal tradeoffs — with respect to accuracy, and invariance — achievable by invariant representations is still severely lacking. In this paper, we provide an information theoretic analysis of such tradeoffs under both classification and regression settings. More precisely, we provide a geometric characterization of the accuracy and invariance achievable by any representation of the data; we term this feasible region the information plane. We provide an inner bound for this feasible region for the classification case, and an exact characterization for the regression case, which allows us to either bound or exactly characterize the Pareto optimal frontier between accuracy and invariance. Although our contributions are mainly theoretical, a key practical application of our results is in certifying the potential sub-optimality of any given representation learning algorithm for either classification or regression tasks. Our results shed new light on the fundamental interplay between accuracy and invariance, and may be useful in guiding the design of future representation learning algorithms.

Multi-objective optimization (MOO) and multi-task learning (MTL) have gained much popularity with prevalent use cases such as production model development of regression / classification / ranking models with MOO, and training deep learning models with MTL. Despite the long history of research in MOO, its application to machine learning requires development of solution strategy, and algorithms have recently been developed to solve specific problems such as discovery of any Pareto optimal (PO) solution, and that with a particular form of preference. In this paper, we develop a novel and generic framework to discover a PO solution with multiple forms of preferences. It allows us to formulate a generic MOO / MTL problem to express a preference, which is solved to achieve both alignment with the preference and PO, at the same time. Specifically, we apply the framework to solve the weighted Chebyshev problem and an extension of that. The former is known as a method to discover the Pareto front, the latter helps to find a model that outperforms an existing model with only one run. Experimental results demonstrate not only the method achieves competitive performance with existing methods, but also it allows us to achieve the performance from different forms of preferences.

The emergence of accurate open large language models (LLMs) has led to a race towards performant quantization techniques which can enable their execution on end-user devices. In this paper, we revisit the problem of “extreme” LLM compression—defined as targeting extremely low bit counts, such as 2 to 3 bits per parameter—from the point of view of classic methods in Multi-Codebook Quantization (MCQ). Our algorithm, called AQLM, generalizes the classic Additive Quantization (AQ) approach for information retrieval to advance the state-of-the-art in LLM compression, via two innovations: 1) learned additive quantization of weight matrices in input-adaptive fashion, and 2) joint optimization of codebook parameters across each transformer blocks. Broadly, AQLM is the first scheme that is Pareto optimal in terms of accuracy-vs-model-size when compressing to less than 3 bits per parameter, and significantly improves upon all known schemes in the extreme compression (2bit) regime. In addition, AQLM is practical: we provide fast GPU and CPU implementations of AQLM for token generation, which enable us to match or outperform optimized FP16 implementations for speed, while executing in a much smaller memory footprint.

Since 2005, processor designers have increased core counts to exploit Moore’s Law scaling, rather than focusing on single-core performance. The failure of Dennard scaling, to which the shift to multicore parts is partially a response, may soon limit multicore scaling just as single-core scaling has been curtailed. This paper models multicore scaling limits by combining device scaling, single-core scaling, and multicore scaling to measure the speedup potential for a set of parallel workloads for the next five technology generations. For device scaling, we use both the ITRS projections and a set of more conservative device scaling parameters. To model single-core scaling, we combine measurements from over 150 processors to derive Pareto-optimal frontiers for area/performance and power/performance. Finally, to model multicore scaling, we build a detailed performance model of upper-bound performance and lower-bound core power. The multicore designs we study include single-threaded CPU-like and massively threaded GPU-like multicore chip organizations with symmetric, asymmetric, dynamic, and composed topologies. The study shows that regardless of chip organization and topology, multicore scaling is power limited to a degree not widely appreciated by the computing community. Even at 22 nm (just one year from now), 21% of a fixed-size chip must be powered off, and at 8 nm, this number grows to more than 50%. Through 2024, only 7.9× average speedup is possible across commonly used parallel workloads, leaving a nearly 24-fold gap from a target of doubled performance per generation.