Search

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

When developing a clinical prediction model, the sample size of the development dataset is a key consideration. Small sample sizes lead to greater concerns of overfitting, instability, poor performance and lack of fairness. Previous research has outlined minimum sample size calculations to minimise overfitting and precisely estimate the overall risk. However even when meeting these criteria, the uncertainty (instability) in individual-level risk estimates may be considerable. In this article we propose how to examine and calculate the sample size required for developing a model with acceptably precise individual-level risk estimates to inform decisions and improve fairness. We outline a five-step process to be used before data collection or when an existing dataset is available. It requires researchers to specify the overall risk in the target population, the (anticipated) distribution of key predictors in the model, and an assumed 'core model' either specified directly (i.e., a logistic regression equation is provided) or based on specified C-statistic and relative effects of (standardised) predictors. We produce closed-form solutions that decompose the variance of an individual's risk estimate into Fisher's unit information matrix, predictor values and total sample size; this allows researchers to quickly calculate and examine individual-level uncertainty interval widths and classification instability for specified sample sizes. Such information can be presented to key stakeholders (e.g., health professionals, patients, funders) using prediction and classification instability plots to help identify the (target) sample size required to improve trust, reliability and fairness in individual predictions. Our proposal is implemented in software module pmstabilityss. We provide real examples and emphasise the importance of clinical context including any risk thresholds for decision making., Comment: 36 pages, 6 figures, 1 table

Additive manufacturing (AM; 3D printing) in aluminium using laser powder bed fusion provides a new design space for lightweight mirror production. Printing layer-by-layer enables the use of intricate lattices for mass reduction, as well as organic shapes generated by topology optimisation, resulting in mirrors optimised for function as opposed to subtractive machining. However, porosity, a common AM defect, is present in printed aluminium and it is a result of the printing environment being either too hot or too cold, or gas entrapped bubbles within the aluminium powder. When present in an AM mirror substrates, porosity manifests as pits on the reflective surface, which increases micro-roughness and therefore scattered light. There are different strategies to reduce the impact of porosity: elimination during printing, coating the aluminium print in nickel phosphorous, or to apply a heat and pressure treatment to close the pores, commonly known as a hot isostatic press (HIP). This paper explores the application of HIP on printed aluminium substrates intended for mirror production using single point diamond turning (SPDT). The objective of the HIP is to reduce porosity whilst targeting a small grain growth within the aluminium, which is important in allowing the SPDT to generate surfaces with low micro-roughness. For this study, three disks, 50 mm diameter by 5 mm, were printed in AlSi10Mg at 0 deg, 45 deg, and 90 deg with respect to the build plate. X-ray computed tomography (XCT) was conducted before and after the HIP cycle to confirm the effectiveness of HIP to close porosity. The disks were SPDT and the micro-roughness evaluated. Mechanical testing and electron backscatter diffraction (EBSD) was used to quantify the mechanical strength and the grain size after HIP., Comment: 14 pages, 8 figures, submitted to SPIE Astronomical Telescopes & Instrumentation, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation VI (Conference 13100, Paper 141)

This report examines the success of students with lower levels of high school performance who began in transfer-level math as a result of Assembly Bill 705 (Irwin 2017). AB 705 is historic legislation that transformed placement and eventually ended developmental education in California's community colleges. Since community colleges are open access institutions, it is particularly important to monitor the impact of such reforms on students who are perceived to be underprepared--particularly in math, which has historically been a persistent barrier to academic progress for many students. In this report, the authors focus on students in the lowest placement band of the placement rules (i.e., default placement rules), that were developed by the Multiple Measures Assessment Project (MMAP) to support colleges in operationalizing AB 705. The authors compare the predicted versus actual success rates of students in the lowest placement band who were placed into, and began in, transfer-level math courses post-AB 705. If the predictions overestimated the success of these students, California community colleges may have grounds to revisit the efficacy of developmental education as a means for meeting AB 705's mandates.

When evaluating the performance of a model for individualised risk prediction, the sample size needs to be large enough to precisely estimate the performance measures of interest. Current sample size guidance is based on precisely estimating calibration, discrimination, and net benefit, which should be the first stage of calculating the minimum required sample size. However, when a clinically important threshold is used for classification, other performance measures can also be used. We extend the previously published guidance to precisely estimate threshold-based performance measures. We have developed closed-form solutions to estimate the sample size required to target sufficiently precise estimates of accuracy, specificity, sensitivity, PPV, NPV, and F1-score in an external evaluation study of a prediction model with a binary outcome. This approach requires the user to pre-specify the target standard error and the expected value for each performance measure. We describe how the sample size formulae were derived and demonstrate their use in an example. Extension to time-to-event outcomes is also considered. In our examples, the minimum sample size required was lower than that required to precisely estimate the calibration slope, and we expect this would most often be the case. Our formulae, along with corresponding Python code and updated R and Stata commands (pmvalsampsize), enable researchers to calculate the minimum sample size needed to precisely estimate threshold-based performance measures in an external evaluation study. These criteria should be used alongside previously published criteria to precisely estimate the calibration, discrimination, and net-benefit., Comment: 27 pages, 1 figure

Humans rely on strong inductive biases to learn from few examples and abstract useful information from sensory data. Instilling such biases in machine learning models has been shown to improve their performance on various benchmarks including few-shot learning, robustness, and alignment. However, finding effective training procedures to achieve that goal can be challenging as psychologically-rich training data such as human similarity judgments are expensive to scale, and Bayesian models of human inductive biases are often intractable for complex, realistic domains. Here, we address this challenge by introducing a Bayesian notion of generative similarity whereby two datapoints are considered similar if they are likely to have been sampled from the same distribution. This measure can be applied to complex generative processes, including probabilistic programs. We show that generative similarity can be used to define a contrastive learning objective even when its exact form is intractable, enabling learning of spatial embeddings that express specific inductive biases. We demonstrate the utility of our approach by showing how it can be used to capture human inductive biases for geometric shapes, and to better distinguish different abstract drawing styles that are parameterized by probabilistic programs.

For California's community colleges, fall 2019 marked the deadline for implementing the state's historic developmental education legislation, Assembly Bill 705 (Irwin 2017). AB 705 drove transformative changes in community college math and English programs as colleges implemented research-based placement policies designed to maximize students' likelihood of completing transferable college-level courses in those disciplines. The result was a large increase in the proportion of students beginning in transfer-level coursework instead of developmental education. After the pandemic hit in the second semester of AB 705 implementation, throughput gains were maintained despite a 14-percentage point decline in community college enrollments. Despite the well-documented positive student outcomes associated with AB 705 reforms, it is one of several legislative mandates that some believe have had the unintended consequence of reducing California's community college enrollment. Any connection between AB 705 and enrollment is difficult to examine after fall 2019, given the enrollment declines driven by the pandemic. For this reason, this report analyzes enrollment in California's community colleges in the context of AB 705 with a focus on fall 2019, the AB 705 implementation deadline.

Over the past several years, the misidentification of SpaceX Starlink satellites as Unidentified Aerial Phenomena (UAP) by pilots and laypersons has generated unnecessary aviation risk and confusion. The many deployment and orbital evolution strategies, coupled with changing sun specular reflection angles, contribute to this gap in space situational awareness. In this paper we present a case analysis of an incident that generated multiple, corroborating reports of a UAP from five pilots on two commercial airline flights over the Pacific Ocean on August 10th, 2022. This incident included two cell phone photos and a video of an unrecognizable and possibly anomalous phenomenon. We then use supplemental two-line elements (TLEs) for the Starlink train of satellites launched that same day and Automatic Dependent Surveillance Broadcast (ADS-B) data from the flight with the photographs to reconstruct a view of these satellites from the cockpit at the time and place of the sighting. The success of this work demonstrates an approach that could, in principle, warn aviators about satellites that could be visible in unusual or novel illumination configurations, thus increasing space situational awareness and supporting aviation safety. We conclude with recommendations for governments and satellite operators to provide better a-priori data that can be used to create advisories to aviators and the public. The automated simulation of known specular reflection off constellations of satellites could also support researchers investigating sightings of unfamiliar aerial or aerospace objects as likely being from normal versus novel space events., Comment: 35 pages, 10 figures, submitted to the 4th IAA Conference on Space Situational Awareness (ICSSA), May 8-10 2024, Daytona Beach, FL, USA; Abstract number AH-92328

As Large Language Models (LLMs) become more pervasive across various users and scenarios, identifying potential issues when using these models becomes essential. Examples of such issues include: bias, inconsistencies, and hallucination. Although auditing the LLM for these problems is often warranted, such a process is neither easy nor accessible for most. An effective method is to probe the LLM using different versions of the same question. This could expose inconsistencies in its knowledge or operation, indicating potential for bias or hallucination. However, to operationalize this auditing method at scale, we need an approach to create those probes reliably and automatically. In this paper we propose the LLMAuditor framework which is an automatic, and scalable solution, where one uses a different LLM along with human-in-the-loop (HIL). This approach offers verifiability and transparency, while avoiding circular reliance on the same LLM, and increasing scientific rigor and generalizability. Specifically, LLMAuditor includes two phases of verification using humans: standardized evaluation criteria to verify responses, and a structured prompt template to generate desired probes. A case study using questions from the TruthfulQA dataset demonstrates that we can generate a reliable set of probes from one LLM that can be used to audit inconsistencies in a different LLM. This process is enhanced by our structured prompt template with HIL, which not only boosts the reliability of our approach in auditing but also yields the delivery of less hallucinated results. The novelty of our research stems from the development of a comprehensive, general-purpose framework that includes a HIL verified prompt template for auditing responses generated by LLMs.

Most applications of machine learning to classification assume a closed set of balanced classes. This is at odds with the real world, where class occurrence statistics often follow a long-tailed power-law distribution and it is unlikely that all classes are seen in a single sample. Nonparametric Bayesian models naturally capture this phenomenon, but have significant practical barriers to widespread adoption, namely implementation complexity and computational inefficiency. To address this, we present a method for extracting the inductive bias from a nonparametric Bayesian model and transferring it to an artificial neural network. By simulating data with a nonparametric Bayesian prior, we can metalearn a sequence model that performs inference over an unlimited set of classes. After training, this "neural circuit" has distilled the corresponding inductive bias and can successfully perform sequential inference over an open set of classes. Our experimental results show that the metalearned neural circuit achieves comparable or better performance than particle filter-based methods for inference in these models while being faster and simpler to use than methods that explicitly incorporate Bayesian nonparametric inference., Comment: 13 pages, 3 figures. Code available at https://github.com/jakesnell/neural-circuits

The recent explosion in the capabilities of large language models has led to a wave of interest in how best to prompt a model to perform a given task. While it may be tempting to simply choose a prompt based on average performance on a validation set, this can lead to a deployment where unexpectedly poor responses are generated, especially for the worst-off users. To mitigate this prospect, we propose Prompt Risk Control, a lightweight framework for selecting a prompt based on rigorous upper bounds on families of informative risk measures. We offer methods for producing bounds on a diverse set of metrics, including quantities that measure worst-case responses and disparities in generation quality across the population of users. In addition, we extend the underlying statistical bounding techniques to accommodate the possibility of distribution shifts in deployment. Experiments on applications such as open-ended chat, medical question summarization, and code generation highlight how such a framework can foster responsible deployment by reducing the risk of the worst outcomes., Comment: 34 pages, 10 figures, published as conference paper at ICLR 2024, and accepted to the Socially Responsible Language Modelling Research (SoLaR) workshop at NeurIPS 2023

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems., Comment: Under review at ICLR 2024

Explicit finite-sample statistical guarantees on model performance are an important ingredient in responsible machine learning. Previous work has focused mainly on bounding either the expected loss of a predictor or the probability that an individual prediction will incur a loss value in a specified range. However, for many high-stakes applications, it is crucial to understand and control the dispersion of a loss distribution, or the extent to which different members of a population experience unequal effects of algorithmic decisions. We initiate the study of distribution-free control of statistical dispersion measures with societal implications and propose a simple yet flexible framework that allows us to handle a much richer class of statistical functionals beyond previous work. Our methods are verified through experiments in toxic comment detection, medical imaging, and film recommendation., Comment: Accepted by NeurIPS as spotlight (top 3% among submissions)

For conformal geometries of Riemannian signature, we provide a comprehensive and explicit treatment of the core local theory for embedded submanifolds of arbitrary dimension. This is based in the conformal tractor calculus and includes a conformally invariant Gauss formula leading to conformal versions of the Gauss, Codazzi, and Ricci equations. It provides the tools for proliferating submanifold conformal invariants, as well for extending to conformally singular Riemannian manifolds the notions of mean curvature and of minimal and CMC submanifolds. A notion of distinguished submanifold is defined by asking the tractor second fundamental form to vanish. We show that for the case of curves this exactly characterises conformal geodesics (a.k.a. conformal circles) while for hypersurfaces it is the totally umbilic condition. So, for other codimensions, this unifying notion interpolates between these extremes, and we prove that in all dimensions this coincides with the submanifold being weakly conformally circular, meaning that ambient conformal circles remain in the submanifold. Stronger notions of conformal circularity are then characterised similarly. Next we provide a very general theory and construction of quantities that are necessarily conserved along distinguished submanifolds. This first integral theory thus vastly generalises the results available for conformal circles in [56]. We prove that any normal solution to an equation from the class of first BGG equations can yield such a conserved quantity, and show that it is easy to provide explicit formulae for these. Finally we prove that the property of being distinguished is also captured by a type of moving incidence relation. This second characterisation is used to show that, for suitable solutions of conformal Killing-Yano equations, a certain zero locus of the solution is necessarily a distinguished submanifold., Comment: 87 pages

Large language models are few-shot learners that can solve diverse tasks from a handful of demonstrations. This implicit understanding of tasks suggests that the attention mechanisms over word tokens may play a role in analogical reasoning. In this work, we investigate whether analogical reasoning can enable in-context composition over composable elements of visual stimuli. First, we introduce a suite of three benchmarks to test the generalization properties of a visual in-context learner. We formalize the notion of an analogy-based in-context learner and use it to design a meta-learning framework called Im-Promptu. Whereas the requisite token granularity for language is well established, the appropriate compositional granularity for enabling in-context generalization in visual stimuli is usually unspecified. To this end, we use Im-Promptu to train multiple agents with different levels of compositionality, including vector representations, patch representations, and object slots. Our experiments reveal tradeoffs between extrapolation abilities and the degree of compositionality, with non-compositional representations extending learned composition rules to unseen domains but performing poorly on combinatorial tasks. Patch-based representations require patches to contain entire objects for robust extrapolation. At the same time, object-centric tokenizers coupled with a cross-attention module generate consistent and high-fidelity solutions, with these inductive biases being particularly crucial for compositional generalization. Lastly, we demonstrate a use case of Im-Promptu as an intuitive programming interface for image generation.

An emerging method to cheaply improve a weaker language model is to finetune it on outputs from a stronger model, such as a proprietary system like ChatGPT (e.g., Alpaca, Self-Instruct, and others). This approach looks to cheaply imitate the proprietary model's capabilities using a weaker open-source model. In this work, we critically analyze this approach. We first finetune a series of LMs that imitate ChatGPT using varying base model sizes (1.5B--13B), data sources, and imitation data amounts (0.3M--150M tokens). We then evaluate the models using crowd raters and canonical NLP benchmarks. Initially, we were surprised by the output quality of our imitation models -- they appear far better at following instructions, and crowd workers rate their outputs as competitive with ChatGPT. However, when conducting more targeted automatic evaluations, we find that imitation models close little to none of the gap from the base LM to ChatGPT on tasks that are not heavily supported in the imitation data. We show that these performance discrepancies may slip past human raters because imitation models are adept at mimicking ChatGPT's style but not its factuality. Overall, we conclude that model imitation is a false promise: there exists a substantial capabilities gap between open and closed LMs that, with current methods, can only be bridged using an unwieldy amount of imitation data or by using more capable base LMs. In turn, we argue that the highest leverage action for improving open-source models is to tackle the difficult challenge of developing better base LMs, rather than taking the shortcut of imitating proprietary systems.