Such output distributions are typically assumed to be fully-factorized.

This often requires maximizing the likelihood of a symbolic constraint w.r.t the neural network's output distribution. Such output distributions are typically assumed to be fully-factorized. This limits the applicability of neuro-symbolic learning to the more expressive auto-regressive distributions, e.g., transformers. Under such distributions, computing the likelihood of even simple constraints is #P-hard. Instead of attempting to enforce the constraint on the entire likelihood distribution, we propose to do so on a random, local approximation thereof.

Training a diffusion model approximates a map from a data distribution $ρ$ to the optimal score function $s_t$ for that distribution. Can we differentiate this map? If we could, then we could predict how the score, and ultimately the model's samples, would change under small perturbations to the training set before committing to costly retraining. We give a closed-form procedure for computing this map's directional derivatives, relying only on black-box access to a pre-trained score model and its derivatives with respect to its inputs. We extend this result to estimate the sensitivity of a diffusion model's samples to additive perturbations of its target measure, with runtime comparable to sampling from a diffusion model and computing log-likelihoods along the sample path. Our method is robust to numerical and approximation error, and the resulting sensitivities correlate with changes in an image diffusion model's samples after retraining and fine-tuning.

Understanding the world through models is a fundamental goal of scientific research. While large language model (LLM) based approaches show promise in automating scientific discovery, they often overlook the importance of criticizing scientific models. Criticizing models deepens scientific understanding and drives the development of more accurate models. Automating model criticism is difficult because it traditionally requires a human expert to define how to compare a model with data and evaluate if the discrepancies are significant--both rely heavily on understanding the modeling assumptions and domain. Although LLM-based critic approaches are appealing, they introduce new challenges: LLMs might hallucinate the critiques themselves. Motivated by this, we introduce CriticAL (Critic Automation with Language Models). CriticAL uses LLMs to generate summary statistics that capture discrepancies between model predictions and data, and applies hypothesis tests to evaluate their significance. We can view CriticAL as a verifier that validates models and their critiques by embedding them in a hypothesis testing framework. In experiments, we evaluate CriticAL across key quantitative and qualitative dimensions. In settings where we synthesize discrepancies between models and datasets, CriticAL reliably generates correct critiques without hallucinating incorrect ones. We show that both human and LLM judges consistently prefer CriticAL's critiques over alternative approaches in terms of transparency and actionability. Finally, we show that CriticAL's critiques enable an LLM scientist to improve upon human-designed models on real-world datasets.

This often requires maximizing the likelihood of a symbolic constraint w.r.t the neural network's output distribution. Such output distributions are typically assumed to be fully-factorized. This limits the applicability of neuro-symbolic learning to the more expressive auto-regressive distributions, e.g., transformers. Under such distributions, computing the likelihood of even simple constraints is #P-hard. Instead of attempting to enforce the constraint on the entire likelihood distribution, we propose to do so on a random, local approximation thereof.

Neuro-symbolic AI bridges the gap between purely symbolic and neural approaches to learning. This often requires maximizing the likelihood of a symbolic constraint w.r.t the neural network's output distribution. Such output distributions are typically assumed to be fully-factorized. This limits the applicability of neuro-symbolic learning to the more expressive autoregressive distributions, e.g., transformers. Under such distributions, computing the likelihood of even simple constraints is #P-hard. Instead of attempting to enforce the constraint on the entire output distribution, we propose to do so on a random, local approximation thereof. More precisely, we optimize the likelihood of the constraint under a pseudolikelihood-based approximation centered around a model sample. Our approximation is factorized, allowing the reuse of solutions to sub-problems, a main tenet for efficiently computing neuro-symbolic losses. Moreover, it is a local, high-fidelity approximation of the likelihood, exhibiting low entropy and KL-divergence around the model sample. We evaluate our approach on Sudoku and shortest-path prediction cast as autoregressive generation, and observe that we greatly improve upon the base model's ability to predict logically-consistent outputs. We also evaluate on the task of detoxifying large language models. Using a simple constraint disallowing a list of toxic words, we are able to steer the model's outputs away from toxic generations, achieving SoTA detoxification compared to previous approaches.

Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves sampling times competitive with neural SGMs while running on consumer-grade CPUs.

The increasing fluency and widespread usage of large language models (LLMs) highlight the desirability of corresponding tools aiding detection of LLM-generated text. In this paper, we identify a property of the structure of an LLM's probability function that is useful for such detection. Specifically, we demonstrate that text sampled from an LLM tends to occupy negative curvature regions of the model's log probability function. Leveraging this observation, we then define a new curvature-based criterion for judging if a passage is generated from a given LLM. This approach, which we call DetectGPT, does not require training a separate classifier, collecting a dataset of real or generated passages, or explicitly watermarking generated text. It uses only log probabilities computed by the model of interest and random perturbations of the passage from another generic pre-trained language model (e.g., T5). We find DetectGPT is more discriminative than existing zero-shot methods for model sample detection, notably improving detection of fake news articles generated by 20B parameter GPT-NeoX from 0.81 AUROC for the strongest zero-shot baseline to 0.95 AUROC for DetectGPT. See https://ericmitchell.ai/detectgpt for code, data, and other project information.

We present a machine-learning approach, based on normalizing flows, for modelling atomic solids. Our model transforms an analytically tractable base distribution into the target solid without requiring ground-truth samples for training. We report Helmholtz free energy estimates for cubic and hexagonal ice modelled as monatomic water as well as for a truncated and shifted Lennard-Jones system, and find them to be in excellent agreement with literature values and with estimates from established baseline methods. We further investigate structural properties and show that the model samples are nearly indistinguishable from the ones obtained with molecular dynamics. Our results thus demonstrate that normalizing flows can provide high-quality samples and free energy estimates of solids, without the need for multi-staging or for imposing restrictions on the crystal geometry.