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Symmetry properties of the order parameter are among the most fundamental characteristics of a superconductor. UTe₂, which was found to feature an exceedingly large upper critical field and striking reentrant behavior at low temperatures, is widely believed to possess a spin-triplet pairing symmetry. However, unambiguous evidence for such a pairing symmetry is still lacking, especially at zero and low magnetic fields. The presence of an inversion crystalline symmetry in UTe₂requires that, if it is indeed a spin-triplet superconductor, the order parameter must be of odd parity. We report here phase-sensitive measurements of the symmetry of the orbital part of the order parameter using the Josephson effect. The selection rule in the orientation dependence of the Josephson coupling between In, ans-wave superconductor, and UTe₂suggests strongly that UTe₂possesses the odd-parity pairing state of B₁usymmetry near zero magnetic field, making it a spin-triplet superconductor. We also report the apparent formation of Andreev surface bound states on the (1−10) surface of UTe₂. 

Many computational tasks can be naturally expressed as a composition of a DNN followed by a program written in a traditional programming language or an API call to an LLM. We call such composites "neural programs" and focus on the problem of learning the DNN parameters when the training data consist of end-to-end input-output labels for the composite. When the program is written in a differentiable logic programming language, techniques from neurosymbolic learning are applicable, but in general, the learning for neural programs requires estimating the gradients of black-box components. We present an algorithm for learning neural programs, called ISED, that only relies on input-output samples of black-box components. For evaluation, we introduce new benchmarks that involve calls to modern LLMs such as GPT-4 and also consider benchmarks from the neurosymbolic learning literature. Our evaluation shows that for the latter benchmarks, ISED has comparable performance to state-of-the-art neurosymbolic frameworks. For the former, we use adaptations of prior work on gradient approximations of black-box components as a baseline, and show that ISED achieves comparable accuracy but in a more data- and sample-efficient manner. 

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to even formalize. We thereby seek to infer statistical rules from the data and quantify the extent to which a model has learned them. We propose a framework SQRL that integrates logic-based methods with statistical inference to derive these rules from a model’s training data without supervision. We further show how to adapt models at test time to reduce rule violations and produce more coherent predictions. SQRL generates up to 300K rules over datasets from vision, tabular, and language settings. We uncover up to 158K violations of those rules by state-of-the-art models for classification, object detection, and data imputation. Test-time adaptation reduces these violations by up to 68.7% with relative performance improvement up to 32%. SQRL is available at https://github.com/DebugML/sqrl. 

While Chain-of-Thought (CoT) prompting boosts Language Models’ (LM) performance on a gamut of complex reasoning tasks, the generated reasoning chain does not necessarily reflect how the model arrives at the answer (aka. faithfulness). We propose Faithful CoT, a reasoning framework involving two stages: Translation (Natural Language query → symbolic reasoning chain) and Problem Solving (reasoning chain → answer), using an LM and a deterministic solver respectively. This guarantees that the reasoning chain provides a faithful explanation of the final answer. Aside from interpretability, Faithful CoT also improves empirical performance: it outperforms standard CoT on 9 of 10 benchmarks from 4 diverse domains, with a relative accuracy gain of 6.3% on Math Word Problems (MWP), 3.4% on Planning, 5.5% on Multi-hop Question Answering (QA), and 21.4% on Relational Inference. Furthermore, with GPT-4 and Codex, it sets the new state-of-the-art few-shot performance on 7 datasets (with 95.0+ accuracy on 6 of them), showing a strong synergy between faithfulness and accuracy.