Pre-trained language models derive substantial linguistic and factual knowledge from the massive corpora on which they are trained, and prompt engineering seeks to align these models to specific tasks. Unfortunately, existing prompt engineering methods require significant amounts of labeled data, access to model parameters, or both. We introduce a new method for selecting prompt templates without labeled examples and without direct access to the model. Specifically, over a set of candidate templates, we choose the template that maximizes the mutual information between the input and the corresponding model output. Across 8 datasets representing 7 distinct NLP tasks, we show that when a template has high mutual information, it also has high accuracy on the task. On the largest model, selecting prompts with our method gets 90% of the way from the average prompt accuracy to the best prompt accuracy and requires no ground truth labels.

pdf/an-information-theoretic-approach-to-prompt-engineering-2tjobcuv.pdf

An Information-theoretic Approach to Prompt Engineering Without Ground Truth Labels

We empirically show that the test error of deep networks can be estimated by simply training the same architecture on the same training set but with a different run of Stochastic Gradient Descent (SGD), and measuring the disagreement rate between the two networks on unlabeled test data. This builds on -- and is a stronger version of -- the observation in Nakkiran & Bansal '20, which requires the second run to be on an altogether fresh training set. We further theoretically show that this peculiar phenomenon arises from the \emph{well-calibrated} nature of \emph{ensembles} of SGD-trained models. This finding not only provides a simple empirical measure to directly predict the test error using unlabeled test data, but also establishes a new conceptual connection between generalization and calibration.

Assessing Generalization of SGD via Disagreement

The application of computational methods in enantioselective catalysis has evolved from the rationalization of the observed stereochemical outcome to their prediction and application to the design of chiral ligands. This Perspective provides an overview of the current methods used, ranging from atomistic modeling of the transition structures involved to correlation-based methods with particular emphasis placed on the Q2MM/CatVS method. Using three enantioselective palladium-catalyzed reactions, namely, the conjugate addition of arylboronic acids to enones, the enantioselective redox relay Heck reaction, and the Tsuji–Trost allylic amination as case studies, we argue that computational methods have become truly equal partners to experimental studies in that, in some cases, they are able to correct published stereochemical assignments. Finally, the consequences of this approach to data-driven methods are discussed. 

Interplay of Computation and Experiment in Enantioselective Catalysis: Rationalization, Prediction, and─Correction?

We revisit on-average algorithmic stability of Gradient Descent (GD) for training overparameterised shallow neural networks and prove new generalisation and excess risk bounds without the Neural Tangent Kernel (NTK) or Polyak-Łojasiewicz (PL) assumptions. In particular, we show oracle type bounds which reveal that the generalisation and excess risk of GD is controlled by an interpolating network with the shortest GD path from initialisation (in a sense, an interpolating network with the smallest relative norm). While this was known for kernelised interpolants, our proof applies directly to networks trained by GD without intermediate kernelisation. At the same time, by relaxing oracle inequalities developed here we recover existing NTK-based risk bounds in a straightforward way, which demonstrates that our analysis is tighter. Finally, unlike most of the NTK-based analyses we focus on regression with label noise and show that GD with early stopping is consistent.

Stability & Generalisation of Gradient Descent for Shallow Neural Networks without the Neural Tangent Kernel

Abstract Lung cancer is a leading cause of cancer mortality globally, highlighting the importance of understanding its mortality risks to design effective patient-centered therapies. The National Lung Screening Trial (NLST) employed computed tomography texture analysis, which provides objective measurements of texture patterns on CT scans, to quantify the mortality risks of lung cancer patients. Partially linear Cox models have gained popularity for survival analysis by dissecting the hazard function into parametric and nonparametric components, allowing for the effective incorporation of both well-established risk factors (such as age and clinical variables) and emerging risk factors (eg, image features) within a unified framework. However, when the dimension of parametric components exceeds the sample size, the task of model fitting becomes formidable, while nonparametric modeling grapples with the curse of dimensionality. We propose a novel Penalized Deep Partially Linear Cox Model (Penalized DPLC), which incorporates the smoothly clipped absolute deviation (SCAD) penalty to select important texture features and employs a deep neural network to estimate the nonparametric component of the model. We prove the convergence and asymptotic properties of the estimator and compare it to other methods through extensive simulation studies, evaluating its performance in risk prediction and feature selection. The proposed method is applied to the NLST study dataset to uncover the effects of key clinical and imaging risk factors on patients’ survival. Our findings provide valuable insights into the relationship between these factors and survival outcomes. 

Penalized deep partially linear cox models with application to CT scans of lung cancer patients

This work studies the behavior of neural networks trained with the logistic loss via gradient descent on binary classification data where the underlying data distribution is general, and the (optimal) Bayes risk is not necessarily zero. In this setting, it is shown that gradient descent with early stopping achieves population risk arbitrarily close to optimal in terms of not just logistic and misclassification losses, but also in terms of calibration, meaning the sigmoid mapping of its outputs approximates the true underlying conditional distribution arbitrarily finely. Moreover, the necessary iteration, sample, and architectural complexities of this analysis all scale naturally with a certain complexity measure of the true conditional model. Lastly, while it is not shown that early stopping is necessary, it is shown that any univariate classifier satisfying a local interpolation property is necessarily inconsistent.

Early-stopped neural networks are consistent

Stereoselective reactions (both chemical and enzymatic reactions) have been essential for origin of life, evolution, human biology and medicine. Since late 1960s, there have been numerous successes in the exciting new frontier of asymmetric catalysis. However, most industrial and academic asymmetric catalysis nowadays do follow the trial-and-error model, since the energetic difference for success or failure in asymmetric catalysis is incredibly small. Our current understanding about stereoselective reactions is mostly qualitative that stereoselectivity arises from differences in steric effects and electronic effects in multiple competing mechanistic pathways. Quantitatively understanding and modulating the stereoselectivity of for a given chemical reaction still remains extremely difficult. As a proof of principle, we herein present a novel machine learning technique, which combines a LASSO model and two Random Forest model via two Gaussian Mixture models, for quantitatively predicting stereoselectivity of chemical reactions. Compared to the recent ground-breaking approach [1], our approach is able to capture interactions between features and exploit complex data distributions, which are important for predicting stereoselectivity. Experimental results on a recently published dataset demonstrate that our approach significantly outperform [1]. The insight obtained from our results provide a solid foundation for further exploration of other synthetically valuable yet mechanistically intriguing stereoselective reactions.

Predicting the Stereoselectivity of Chemical Transformations by Machine Learning

This work studies the behavior of neural networks trained with the logistic
loss via gradient descent on binary classification data where the underlying
data distribution is general, and the (optimal) Bayes risk is not necessarily
zero. In this setting, it is shown that gradient descent with early stopping
achieves population risk arbitrarily close to optimal in terms of not just
logistic and misclassification losses, but also in terms of calibration,
meaning the sigmoid mapping of its outputs approximates the true underlying
conditional distribution arbitrarily finely. Moreover, the necessary iteration,
sample, and architectural complexities of this analysis all scale naturally
with a certain complexity measure of the true conditional model. Lastly, while
it is not shown that early stopping is necessary, it is shown that any
univariate classifier satisfying a local interpolation property is necessarily
inconsistent.

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Early-stopped neural networks are consistent

Predicting the Stereoselectivity of Chemical Transformations by Machine Learning

Early-stopped neural networks are consistent