The text produced by language models (LMs) can exhibit specific `behaviors,' such as a failure to follow alignment training, that we hope to detect and react to during deployment. Identifying these behaviors can often only be done post facto, i.e., after the entire text of the output has been generated. We provide evidence that there are times when we can predict how an LM will behave early in computation, before even a single token is generated. We show that probes trained on the internal representation of input tokens alone can predict a wide range of eventual behaviors over the entire output sequence. Using methods from conformal prediction, we provide provable bounds on the estimation error of our probes, creating precise early warning systems for these behaviors. The conformal probes can identify instances that will trigger alignment failures (jailbreaking) and instruction-following failures, without requiring a single token to be generated. An early warning system built on the probes reduces jailbreaking by 91%. Our probes also show promise in pre-emptively estimating how confident the model will be in its response, a behavior that cannot be detected using the output text alone. Conformal probes can preemptively estimate the final prediction of an LM that uses Chain-of-Thought (CoT) prompting, hence accelerating inference. When applied to an LM that uses CoT to perform text classification, the probes drastically reduce inference costs (65% on average across 27 datasets), with negligible accuracy loss. Encouragingly, probes generalize to unseen datasets and perform better on larger models, suggesting applicability to the largest of models in real-world settings.

We present a novel hybrid algorithm for training Deep Neural Networks that combines the state-of-the-art Gradient Descent (GD) method with a Mixed Integer Linear Programming (MILP) solver, outperforming GD and variants in terms of accuracy, as well as resource and data efficiency for both regression and classification tasks. Our GD+Solver hybrid algorithm, called GDSolver, works as follows: given a DNN D as input, GDSolver invokes GD to partially train D until it gets stuck in a local minima, at which point GDSolver invokes an MILP solver to exhaustively search a region of the loss landscape around the weight assignments of D’s final layer parameters with the goal of tunnelling through and escaping the local minima. The process is repeated until desired accuracy is achieved. In our experiments, we find that GDSolver not only scales well to additional data and very large model sizes, but also outperforms all other competing methods in terms of rates of convergence and data efficiency. For regression tasks, GDSolver produced models that, on average, had 31.5% lower MSE in 48% less time, and for classification tasks on MNIST and CIFAR10, GDSolver was able to achieve the highest accuracy over all competing methods, using only 50% of the training data that GD baselines required.

We present a novel Auxiliary Truth enhanced Genetic Algorithm (GA) that uses logical or mathematical constraints as a means of data augmentation as well as to compute loss (in conjunction with the traditional MSE), with the aim of increasing both data efficiency and accuracy of symbolic regression (SR) algorithms. Our method, logic-guided genetic algorithm (LGGA), takes as input a set of labelled data points and auxiliary truths (AT) (mathematical facts known a priori about the unknown function the regressor aims to learn) and outputs a specially generated and curated dataset that can be used with any SR method. We evaluate LGGA against state-of-the-art SR tools, namely, Eureqa and TuringBot and find that using these SR tools in conjunction with LGGA results in them solving up to 30% more equations, needing only a fraction of the amount of data compared to the same tool without LGGA, i.e., resulting in up to a 61.9% improvement in data efficiency.