Large language models (LLMs) are expensive to deploy. Parameter sharing offers a possible path towards reducing their size and cost, but its effectiveness in modern LLMs remains fairly limited. In this work, we revisit "layer tying" as form of parameter sharing in Transformers, and introduce novel methods for converting existing LLMs into smaller "Recursive Transformers" that share parameters across layers, with minimal loss of performance. Here, our Recursive Transformers are efficiently initialized from standard pretrained Transformers, but only use a single block of unique layers that is then repeated multiple times in a loop. We further improve performance by introducing Relaxed Recursive Transformers that add flexibility to the layer tying constraint via depth-wise low-rank adaptation (LoRA) modules, yet still preserve the compactness of the overall model. We show that our recursive models (e.g., recursive Gemma 1B) outperform both similar-sized vanilla pretrained models (such as TinyLlama 1.1B and Pythia 1B) and knowledge distillation baselines---and can even recover most of the performance of the original "full-size" model (e.g., Gemma 2B with no shared parameters). Finally, we propose Continuous Depth-wise Batching, a promising new inference paradigm enabled by the Recursive Transformer when paired with early exiting. In a theoretical analysis, we show that this has the potential to lead to significant (2-3$\times$) gains in inference throughput.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. With the goal of using PRMs to improve a *base* policy via test-time search and reinforcement learning (RL), we ask: ``How should we design process rewards?'' Our key insight is that, to be effective, the process reward for a step should measure *progress*: a change in the likelihood of producing a correct response in the future, before and after taking the step, as measured under a *prover* policy distinct from the base policy. Such progress values can {distinguish} good and bad steps generated by the base policy, even though the base policy itself cannot. Theoretically, we show that even weaker provers can improve the base policy, as long as they distinguish steps without being too misaligned with the base policy. Our results show that process rewards defined as progress under such provers improve the efficiency of exploration during test-time search and online RL. We empirically validate our claims by training **process advantage verifiers (PAVs)** to measure progress under such provers and show that compared to ORM, they are >8% more accurate, and 1.5-5x more compute-efficient. Equipped with these insights, our PAVs enable **one of the first results** showing a 6x gain in sample efficiency for a policy trained using online RL with PRMs vs. ORMs.

Scaling language models unlocks impressive capabilities, but the accompanying computational and memory demands make both training and deployment expensive. Existing efficiency efforts typically target either parameter sharing or adaptive computation, leaving open the question of how to attain both simultaneously. We introduce Mixture-of-Recursions (MoR), a unified framework that combines the two axes of efficiency inside a single Recursive Transformer. MoR reuses a shared stack of layers across recursion steps to achieve parameter efficiency, while lightweight routers enable adaptive token-level thinking by dynamically assigning different recursion depths to individual tokens. This allows MoR to focus quadratic attention computation only among tokens still active at a given recursion depth, further improving memory access efficiency by selectively caching only their key-value pairs. Beyond these core mechanisms, we also propose a KV sharing variant that reuses KV pairs from the first recursion, specifically designed to further decrease memory footprint. Across model scales ranging from 135M to 1.7B parameters, MoR forms a new Pareto frontier: at equal training FLOPs and smaller model sizes, it significantly lowers validation perplexity and improves few-shot accuracy, while delivering higher throughput compared with vanilla and existing recursive baselines.

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an $\mathcal{O}(1/n)$ factor. We also introduce extensions of the idea to distribution shift, quantile risk control, multiple and adversarial risk control, and expectations of U-statistics. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm to bound the false negative rate, graph distance, and token-level F1-score.

In this paper, we propose a novel approach to conformal prediction for language models (LMs) in which we produce prediction sets with performance guarantees. LM responses are typically sampled from a predicted distribution over the large, combinatorial output space of language. Translating this to conformal prediction, we calibrate a stopping rule for sampling LM outputs that get added to a growing set of candidates until we are confident that the set covers at least one acceptable response. Since some samples may be low-quality, we also simultaneously calibrate a rejection rule for removing candidates from the output set to reduce noise. Similar to conformal prediction, we can prove that the final output set obeys certain desirable distribution-free guarantees. Within these sets of candidate responses, we also show that we can also identify subsets of individual components---such as phrases or sentences---that are each independently correct (e.g., that are not ``hallucinations''), again with guarantees. Our method can be applied to any LM API that supports sampling. Furthermore, we empirically demonstrate that we can achieve many desired coverage levels within a limited number of total samples when applying our method to multiple tasks in open-domain question answering, text summarization, and radiology report generation using different LM variants.

Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. PPI achieves this by combining small amounts of human-labeled data with larger amounts of data labeled by a reasonably accurate---but potentially biased---automatic system, in a way that results in tighter confidence intervals for certain parameters of interest (e.g., the mean performance of a language model). In this paper, we propose a method called Stratified Prediction-Powered Inference (StratPPI), in which we show that the basic PPI estimates can be considerably improved by employing simple data stratification strategies. Without making any assumptions on the underlying automatic labeling system or data distribution, we derive an algorithm for computing provably valid confidence intervals for parameters of any dimensionality that is based on stratified sampling. In particular, we show both theoretically and empirically that, with appropriate choices of stratification and sample allocation, our approach can provide substantially tighter confidence intervals than unstratified approaches. Specifically, StratPPI is expected to improve in cases where the performance of the autorater varies across different conditional distributions of the target data.

We introduce the Block Transformer which adopts hierarchical global-to-local modeling to autoregressive transformers to mitigate the inference bottlenecks associated with self-attention. Self-attention requires the key-value (KV) cache of all previous sequences to be retrieved from memory at every decoding step to retrieve context information, leading to two primary bottlenecks during batch inference. First, there is a significant delay in obtaining the first token, as the information of the entire prompt must first be processed to prefill the KV cache. Second, computation of subsequent tokens is bottlenecked by the high memory I/O demand of fetching the entire KV cache, which grows linearly with sequence length, incurring quadratic memory reads overall. We design the Block Transformer to strategically mitigate these costs, by incorporating coarsity and locality into an integrated global-to-local architecture. At the lower layers, we aggregate tokens into fixed size blocks to apply attention across the entire sequence at coarse-grained detail, to capture the global context while minimizing KV cache overhead. At upper layers, we apply attention within each block to decode individual tokens, to model fine-grained details with a lightweight local KV cache. We pretrain vanilla and Block Transformers from scratch and demonstrate that Block Transformers reach 10--20x inference throughput compared to vanilla transformers with equivalent perplexity and zero-shot task performance.

We develop a new approach to multi-label conformal prediction in which we aim to output a precise set of promising prediction candidates with a bounded number of incorrect answers. Standard conformal prediction provides the ability to adapt to model uncertainty by constructing a calibrated candidate set in place of a single prediction, with guarantees that the set contains the correct answer with high probability. In order to obey this coverage property, however, conformal sets can become inundated with noisy candidates—which can render them unhelpful in practice. This is particularly relevant to practical applications where there is a limited budget, and the cost (monetary or otherwise) associated with false positives is non-negligible. We propose to trade coverage for a notion of precision by enforcing that the presence of incorrect candidates in the predicted conformal sets (i.e., the total number of false positives) is bounded according to a user-specified tolerance. Subject to this constraint, our algorithm then optimizes for a generalized notion of set coverage (i.e., the true positive rate) that allows for any number of true answers for a given query (including zero). We demonstrate the effectiveness of this approach across a number of classification tasks in natural language processing, computer vision, and computational chemistry.

Recent advances in Transformer-based large language models (LLMs) have led to significant performance improvements across many tasks. These gains come with a drastic increase in the models' size, potentially leading to slow and costly use at inference time. In practice, however, the series of generations made by LLMs is composed of varying levels of difficulty. While certain predictions truly benefit from the models' full capacity, other continuations are more trivial and can be solved with reduced compute. In this work, we introduce Confident Adaptive Language Modeling (CALM), a framework for dynamically allocating different amounts of compute per input and generation timestep. Early exit decoding involves several challenges that we address here, such as: (1) what confidence measure to use; (2) connecting sequence-level constraints to local per-token exit decisions; and (3) attending back to missing hidden representations due to early exits in previous tokens. Through theoretical analysis and empirical experiments on three diverse text generation tasks, we demonstrate the efficacy of our framework in reducing compute---potential speedup of up to $\times 3$---while provably maintaining high performance.

Tianyu Gao, Adam Fisch, Danqi Chen. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

We develop a novel approach for confidently accelerating inference in the large and expensive multilayer Transformers that are now ubiquitous in natural language processing (NLP).Amortized or approximate computational methods increase efficiency, but can come with unpredictable performance costs.In this work, we present CATs-Confident Adaptive Transformers-in which we simultaneously increase computational efficiency, while guaranteeing a specifiable degree of consistency with the original model with high confidence.Our method trains additional prediction heads on top of intermediate layers, and dynamically decides when to stop allocating computational effort to each input using a meta consistency classifier.To calibrate our early prediction stopping rule, we formulate a unique extension of conformal prediction.We demonstrate the effectiveness of this approach on four classification and regression tasks. 1 * The first two authors contributed equally. 1

We develop a novel approach to conformal prediction when the target task has limited data available for training. Conformal prediction identifies a small set of promising output candidates in place of a single prediction, with guarantees that the set contains the correct answer with high probability. When training data is limited, however, the predicted set can easily become unusably large. In this work, we obtain substantially tighter prediction sets while maintaining desirable marginal guarantees by casting conformal prediction as a meta-learning paradigm over exchangeable collections of auxiliary tasks. Our conformalization algorithm is simple, fast, and agnostic to the choice of underlying model, learning algorithm, or dataset. We demonstrate the effectiveness of this approach across a number of few-shot classification and regression tasks in natural language processing, computer vision, and computational chemistry for drug discovery.

Typical fact verification models use retrieved written evidence to verify claims.Evidence sources, however, often change over time as more information is gathered and revised.In order to adapt, models must be sensitive to subtle differences in supporting evidence.We present VITAMINC, a benchmark infused with challenging cases that require fact verification models to discern and adjust to slight factual changes.We collect over 100,000 Wikipedia revisions that modify an underlying fact, and leverage these revisions, together with additional synthetically constructed ones, to create a total of over 400,000 claim-evidence pairs.Unlike previous resources, the examples in VITAMINC are contrastive, i.e., they contain evidence pairs that are nearly identical in language and content, with the exception that one supports a given claim while the other does not.We show that training using this design increases robustness-improving accuracy by 10% on adversarial fact verification and 6% on adversarial natural language inference (NLI).Moreover, the structure of VITAMINC leads us to define additional tasks for fact-checking resources: tagging relevant words in the evidence for verifying the claim, identifying factual revisions, and providing automatic edits via factually consistent text generation. 1

The traditional image captioning task uses generic reference captions to provide textual information about images.Different user populations, however, will care about different visual aspects of images.In this paper, we propose a new task, Captioning with A Purpose (CAPWAP).Our goal is to develop systems that can be tailored to be useful for the information needs of an intended population, rather than merely provide generic information about an image.In this task, we use questionanswer (QA) pairs-a natural expression of information need-from users, instead of reference captions, for both training and postinference evaluation.We show that it is possible to use reinforcement learning to directly optimize for the intended information need, by rewarding outputs that allow a question answering model to provide correct answers to sampled user questions.We convert several visual question answering datasets into CAP-WAP datasets, and demonstrate that under a variety of scenarios our purposeful captioning system learns to anticipate and fulfill specific information needs better than its generic counterparts, as measured by QA performance on user questions from unseen images, when using the caption alone as context.

Adam Fisch, Jiang Guo, Regina Barzilay. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.

We present StarSpace, a general-purpose neural embedding model that can solve a wide variety of problems: labeling tasks such as text classification,ranking tasks such as information retrieval/web search,collaborative filtering-based or content-based recommendation,embedding of multi-relational graphs, and learning word, sentence or document level embeddings.In each case the model works by embedding those entities comprised of discrete features and comparing them against each other -- learning similarities dependent on the task.Empirical results on a number of tasks show that StarSpace is highly competitive with existing methods, whilst also being generally applicable to new cases where those methods are not.

This paper proposes to tackle open-domain question answering using Wikipedia as the unique knowledge source: the answer to any factoid question is a text span in a Wikipedia article. This task of machine reading at scale combines the challenges of document retrieval (finding the relevant articles) with that of machine comprehension of text (identifying the answer spans from those articles). Our approach combines a search component based on bigram hashing and TF-IDF matching with a multi-layer recurrent neural network model trained to detect answers in Wikipedia paragraphs. Our experiments on multiple existing QA datasets indicate that (1) both modules are highly competitive with respect to existing counterparts and (2) multitask learning using distant supervision on their combination is an effective complete system on this challenging task.

Directly reading documents and being able to answer questions from them is an unsolved challenge.To avoid its inherent difficulty, question answering (QA) has been directed towards using Knowledge Bases (KBs) instead, which has proven effective.Unfortunately KBs often suffer from being too restrictive, as the schema cannot support certain types of answers, and too sparse, e.g.Wikipedia contains much more information than Freebase.In this work we introduce a new method, Key-Value Memory Networks, that makes reading documents more viable by utilizing different encodings in the addressing and output stages of the memory read operation.To compare using KBs, information extraction or Wikipedia documents directly in a single framework we construct an analysis tool, WIKIMOVIES, a QA dataset that contains raw text alongside a preprocessed KB, in the domain of movies.Our method reduces the gap between all three settings.It also achieves state-of-the-art results on the existing WIKIQA benchmark.