From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation. Our survey unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems.

Iterated Schrödinger bridge approximation to Wasserstein Gradient Flows

We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the backward/Jordan-Kinderlehrer-Otto (JKO) approximations. The proposed scheme has two advantages: one, it avoids the use of the score function, and, two, it is amenable to particle-based approximations using the Sinkhorn algorithm. Our proof hinges upon showing that relative entropy between the Schr\"{o}dinger bridge with the same marginals at temperature $\epsilon$ and the joint distribution of a stationary Langevin diffusion at times zero and $\epsilon$ is of the order $o(\epsilon^2)$ with an explicit dependence given by Fisher information. Owing to this inequality, we can show, using a triangular approximation argument, that the interpolated iterated application of the Schr\"{o}dinger bridge approximation converge to the Wasserstein gradient flow, for a class of gradient flows, including the heat flow. The results also provide a probabilistic and rigorous framework for the convergence of the self-attention mechanisms in transformer networks to the solutions of heat flows, first observed in the inspiring work SABP22 in machine learning research.

A Primal-Dual Algorithm for Faster Distributionally Robust Optimization

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses the $f$-DRO, Wasserstein-DRO, and spectral/$L$-risk formulations used in practice. We present Drago, a stochastic primal-dual algorithm that achieves a state-of-the-art linear convergence rate on strongly convex-strongly concave DRO problems. The method combines both randomized and cyclic components with mini-batching, which effectively handles the unique asymmetric nature of the primal and dual problems in DRO. We support our theoretical results with numerical benchmarks in classification and regression.

JAMDEC: Unsupervised Authorship Obfuscation using Constrained Decoding over Small Language Models

The permanence of online content combined with the enhanced authorship identification techniques calls for stronger computational methods to protect the identity and privacy of online authorship when needed, e.g., blind reviews for scientific papers, anonymous online reviews, or anonymous interactions in the mental health forums. In this paper, we propose an unsupervised inference-time approach to authorship obfuscation to address the unique challenges of authorship obfuscation: lack of supervision data for diverse authorship and domains, and the need for a sufficient level of revision beyond simple paraphrasing to obfuscate the authorship, all the while preserving the original content and fluency. We introduce JAMDEC, a user-controlled, inference-time algorithm for authorship obfuscation that can be in principle applied to any text and authorship. Our approach builds on small language models such as GPT2-XL in order to help avoid disclosing the original content to proprietary LLM's APIs, while also reducing the performance gap between small and large language models via algorithmic enhancement. The key idea behind our approach is to boost the creative power of smaller language models through constrained decoding, while also allowing for user-specified controls and flexibility. Experimental results demonstrate that our approach based on GPT2-XL outperforms previous state-of-the-art methods based on comparably small models, while performing competitively against GPT3.5 175B, a propriety model that is two orders of magnitudes larger.

Distributionally Robust Optimization with Bias and Variance Reduction

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and $f$-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition value-at-risk (CVaR) and average top-$k$ loss. We present Prospect, a stochastic gradient-based algorithm that only requires tuning a single learning rate hyperparameter, and prove that it enjoys linear convergence for smooth regularized losses. This contrasts with previous algorithms that either require tuning multiple hyperparameters or potentially fail to converge due to biased gradient estimates or inadequate regularization. Empirically, we show that Prospect can converge 2-3$\times$ faster than baselines such as stochastic gradient and stochastic saddle-point methods on distribution shift and fairness benchmarks spanning tabular, vision, and language domains.

FiLM: Fill-in Language Models for Any-Order Generation

Language models have become the backbone of today's AI systems. However, their predominant left-to-right generation limits the use of bidirectional context, which is essential for tasks that involve filling text in the middle. We propose the Fill-in Language Model (FiLM), a new language modeling approach that allows for flexible generation at any position without adhering to a specific generation order. Its training extends the masked language modeling objective by adopting varying mask probabilities sampled from the Beta distribution to enhance the generative capabilities of FiLM. During inference, FiLM can seamlessly insert missing phrases, sentences, or paragraphs, ensuring that the outputs are fluent and are coherent with the surrounding context. In both automatic and human evaluations, FiLM outperforms existing infilling methods that rely on left-to-right language models trained on rearranged text segments. FiLM is easy to implement and can be either trained from scratch or fine-tuned from a left-to-right language model. Notably, as the model size grows, FiLM's perplexity approaches that of strong left-to-right language models of similar sizes, indicating FiLM's scalability and potential as a large language model.

Faith and Fate: Limits of Transformers on Compositionality

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations? In an attempt to demystify Transformers, we investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that Transformers solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how Transformers' performance will rapidly decay with increased task complexity.

Modified Gauss-Newton Algorithms under Noise

Gauss-Newton methods and their stochastic version have been widely used in machine learning and signal processing. Their nonsmooth counterparts, modified Gauss-Newton or prox-linear algorithms, can lead to contrasting outcomes when compared to gradient descent in large-scale statistical settings. We explore the contrasting performance of these two classes of algorithms in theory on a stylized statistical example, and experimentally on learning problems including structured prediction. In theory, we delineate the regime where the quadratic convergence of the modified Gauss-Newton method is active under statistical noise. In the experiments, we underline the versatility of stochastic (sub)-gradient descent to minimize nonsmooth composite objectives.

Confidence Sets under Generalized Self-Concordance

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its asymptotic behavior in a non-asymptotic fashion. An important feature of our bound is that its dimension dependency is captured by the effective dimension $\unicode{x2013}$ the trace of the limiting sandwich covariance $\unicode{x2013}$ which can be much smaller than the parameter dimension in some regimes. We then illustrate how the bound can be used to obtain a confidence set whose shape is adapted to the optimization landscape induced by the loss function. Unlike previous works that rely heavily on the strong convexity of the loss function, we only assume the Hessian is lower bounded at optimum and allow it to gradually becomes degenerate. This property is formalized by the notion of generalized self-concordance which originated from convex optimization. Moreover, we demonstrate how the effective dimension can be estimated from data and characterize its estimation accuracy. We apply our results to maximum likelihood estimation with generalized linear models, score matching with exponential families, and hypothesis testing with Rao's score test.

MAUVE Scores for Generative Models: Theory and Practice

Generative AI has matured to a point where large-scale models can generate text that seems indistinguishable from human-written text and remarkably photorealistic images. Automatically measuring how close the distribution of generated data is to the target real data distribution is a key step in diagnosing existing models and developing better models. We present MAUVE, a family of comparison measures between pairs of distributions such as those encountered in the generative modeling of text or images. These scores are statistical summaries of divergence frontiers capturing two types of errors in generative modeling. We explore four approaches to statistically estimate these scores: vector quantization, non-parametric estimation, classifier-based estimation, and parametric Gaussian approximations. We provide statistical bounds for the vector quantization approach. Empirically, we find that the proposed scores paired with a range of $f$-divergences and statistical estimation methods can quantify the gaps between the distributions of human-written text and those of modern neural language models by correlating with human judgments and identifying known properties of the generated texts. We conclude the paper by demonstrating its applications to other AI domains and discussing practical recommendations.