Algorithmic Trading

We analyze the capabilities of Transformer language models in learning compositional discrete tasks. To this end, we evaluate training LLaMA models and prompting GPT-4 and Gemini on four tasks demanding to learn a composition of several discrete sub-tasks. In particular, we measure how well these models can reuse primitives observable in the sub-tasks to learn the composition task. Our results indicate that compositional learning in state-of-the-art Transformer language models is highly sample inefficient: LLaMA requires more data samples than relearning all sub-tasks from scratch to learn the compositional task; in-context prompting with few samples is unreliable and fails at executing the sub-tasks or correcting the errors in multi-round code generation. Further, by leveraging complexity theory, we support these findings with a theoretical analysis focused on the sample inefficiency of gradient descent in memorizing feedforward models. We open source our code at https://github.com/IBM/limitations-lm-algorithmic-compositional-learning.

Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To what extent do they depend on the supervisory signal provided to models, and to what extent are they attributable to behavior already present in models at the beginning of training? To investigate these questions, we investigate what functions can be learned by randomly initialized transformers in which only the embedding layers are optimized, so that the only input--output mappings learnable from data are those already implemented (up to a choice of encoding scheme) by the randomly initialized model. We find that these random transformers can perform a wide range of meaningful algorithmic tasks, including modular arithmetic, in-weights and in-context associative recall, decimal addition, parenthesis balancing, and even some aspects of natural language text generation. Our results indicate that some algorithmic capabilities are present in transformers (and accessible via appropriately structured inputs) even before these models are trained.

The recent increasing adoption of autobidding has inspired the growing interest in analyzing the performance of classic mechanism with value-maximizing autobidders both theoretically and empirically. It is known that optimal welfare can be obtained in first-price auctions if autobidders are restricted to uniform bid-scaling and the price of anarchy is $2$ when non-uniform bid-scaling strategies are allowed. In this paper, we provide a fine-grained price of anarchy analysis for non-uniform bid-scaling strategies in first-price auctions, demonstrating the reason why more powerful (individual) non-uniform bid-scaling strategies may lead to worse (aggregated) performance in social welfare. Our theoretical results match recent empirical findings that a higher level of non-uniform bid-scaling leads to lower welfare performance in first-price auctions.

Algorithmic monoculture arises when many decision-makers rely on the same algorithm to evaluate applicants. An emerging body of work investigates possible harms of this kind of homogeneity, but has been limited by the challenge of incorporating market effects in which the preferences and behavior of many applicants and decision-makers jointly interact to determine outcomes. Addressing this challenge, we introduce a tractable theoretical model of algorithmic monoculture in a two-sided matching market with many participants. We use the model to analyze outcomes under monoculture (when decision-makers all evaluate applicants using a common algorithm) and under polyculture (when decision-makers evaluate applicants independently). All else equal, monoculture (1) selects less-preferred applicants when noise is well-behaved, (2) matches more applicants to their top choice, though individual applicants may be worse off depending on their value to decision-makers and risk tolerance, and (3) is more robust to disparities in the number of applications submitted.

We propose a new framework for algorithmic stability in the context of multiclass classification. In practice, classification algorithms often operate by first assigning a continuous score (for instance, an estimated probability) to each possible label, then taking the maximizer---i.e., selecting the class that has the highest score. A drawback of this type of approach is that it is inherently unstable, meaning that it is very sensitive to slight perturbations of the training data, since taking the maximizer is discontinuous. Motivated by this challenge, we propose a pipeline for constructing stable classifiers from data, using bagging (i.e., resampling and averaging) to produce stable continuous scores, and then using a stable relaxation of argmax, which we call the "inflated argmax", to convert these scores to a set of candidate labels. The resulting stability guarantee places no distributional assumptions on the data, does not depend on the number of classes or dimensionality of the covariates, and holds for any base classifier. Using a common benchmark data set, we demonstrate that the inflated argmax provides necessary protection against unstable classifiers, without loss of accuracy.

We investigate the rate at which algorithms for pre-training language models have improved since the advent of deep learning. Using a dataset of over 200 language model evaluations on Wikitext and Penn Treebank spanning 2012-2023, we find that the compute required to reach a set performance threshold has halved approximately every 8 months, with a 90\% confidence interval of around 2 to 22 months, substantially faster than hardware gains per Moore's Law. We estimate augmented scaling laws, which enable us to quantify algorithmic progress and determine the relative contributions of scaling models versus innovations in training algorithms. Despite the rapid pace of algorithmic progress and the development of new architectures such as the transformer, our analysis reveals that the increase in compute made an even larger contribution to overall performance improvements over this time period. Though limited by noisy benchmark data, our analysis quantifies the rapid progress in language modeling, shedding light on the relative contributions from compute and algorithms.