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We develop a new, unsupervised symmetry learning method that starts with raw data, and gives the minimal (discrete) generator of an underlying Lie group of symmetries, together with a symmetry equivariant representation of the data. The method is able to learn the pixel translation operator from a dataset with only an approximate translation symmetry, and can learn quite different types of symmetries which are not apparent to the naked eye, equally well. The method is based on the formulation of an information-theoretic loss function that measures both the degree to which the dataset is symmetric under a given candidate symmetry, and also, the degree of locality of the samples in the dataset with respect to this symmetry. We demonstrate that this coupling between symmetry and locality, together with a special optimization technique developed for entropy estimation, results in a highly stable system that gives reproducible results. The symmetry actions we consider are group representations, however, we believe the approach has the potential to be generalized to more general, nonlinear actions of non-commutative Lie groups.

LLM-based NLP systems typically work by embedding their input data into prompt templates which contain instructions and/or in-context examples, creating queries which are submitted to a LLM, and then parsing the LLM response in order to generate the system outputs. Prompt Injection Attacks (PIAs) are a type of subversion of these systems where a malicious user crafts special inputs which interfere with the prompt templates, causing the LLM to respond in ways unintended by the system designer. Recently, Sun and Miceli-Barone proposed a class of PIAs against LLM-based machine translation. Specifically, the task is to translate questions from the TruthfulQA test suite, where an adversarial prompt is prepended to the questions, instructing the system to ignore the translation instruction and answer the questions instead. In this test suite, we extend this approach to all the language pairs of the WMT 2024 General Machine Translation task. Moreover, we include additional attack formats in addition to the one originally studied.

Nonparametric procedures are more powerful for detecting interaction in two-way ANOVA when the data are non-normal. In this paper, we compute null critical values for the aligned rank-based tests (APCSSA/APCSSM) where the levels of the factors are between 2 and 6. We compare the performance of these new procedures with the ANOVA F-test for interaction, the adjusted rank transform test (ART), Conover's rank transform procedure (RT), and a rank-based ANOVA test (raov) using Monte Carlo simulations. The new procedures APCSSA/APCSSM are comparable with existing competitors in all settings. Even though there is no single dominant test in detecting interaction effects for non-normal data, nonparametric procedure APCSSM is the most highly recommended procedure for Cauchy errors settings.

A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation formats studied in this area range from ordered binary decision diagrams (OBDDs) to circuits in decomposable negation normal form (DNNFs). While it is known that there exist CNF formulas that require exponential size representations, the situation is less well studied for other types of constraints than Boolean disjunctive clauses. The constraint satisfaction problem (CSP) is a powerful framework that generalizes CNF-SAT by allowing arbitrary sets of constraints over any finite domain. The main goal of our work is to understand for which type of constraints (also called the constraint language) it is possible to efficiently compute representations of polynomial size. We answer this question completely and prove two tight characterizations of efficiently compilable constraint languages, depending on whether target format is structured. We first identify the combinatorial property of ``strong blockwise decomposability'' and show that if a constraint language has this property, we can compute DNNF representations of linear size. For all other constraint languages we construct families of CSP-instances that provably require DNNFs of exponential size. For a subclass of ``strong uniformly blockwise decomposable'' constraint languages we obtain a similar dichotomy for structured DNNFs. In fact, strong (uniform) blockwise decomposability even allows efficient compilation into multi-valued analogs of OBDDs and FBDDs, respectively. Thus, we get complete characterizations for all knowledge compilation classes between O(B)DDs and DNNFs.

We develop confidence sets which provide spatial uncertainty guarantees for the output of a black-box machine learning model designed for image segmentation. To do so we adapt conformal inference to the imaging setting, obtaining thresholds on a calibration dataset based on the distribution of the maximum of the transformed logit scores within and outside of the ground truth masks. We prove that these confidence sets, when applied to new predictions of the model, are guaranteed to contain the true unknown segmented mask with desired probability. We show that learning appropriate score transformations on a learning dataset before performing calibration is crucial for optimizing performance. We illustrate and validate our approach on a polpys tumor dataset. To do so we obtain the logit scores from a deep neural network trained for polpys segmentation and show that using distance transformed scores to obtain outer confidence sets and the original scores for inner confidence sets enables tight bounds on tumor location whilst controlling the false coverage rate.

Black-box runtime verification methods for cyber-physical systems can be used to discover errors in systems whose inputs and outputs are expressed as signals over time and their correctness requirements are specified in a temporal logic. Existing methods, such as requirement falsification, often focus on finding a single input that is a counterexample to system correctness. In this paper, we study how to create test generators that can produce multiple and diverse counterexamples for a single requirement. Several counterexamples expose system failures in varying input conditions and support the root cause analysis of the faults. We present the WOGAN algorithm to create such test generators automatically. The algorithm works by training iteratively a Wasserstein generative adversarial network that models the target distribution of the uniform distribution on the set of counterexamples. WOGAN is an algorithm that trains generative models that act as test generators for runtime verification. The training is performed online without the need for a previous model or dataset. We also propose criteria to evaluate such test generators. We evaluate the trained generators on several well-known problems including the ARCH-COMP falsification benchmarks. Our experimental results indicate that generators trained by the WOGAN algorithm are as effective as state-of-the-art requirement falsification algorithms while producing tests that are as diverse as a sample from uniform random sampling. We conclude that WOGAN is a viable method to produce test generators automatically and that these test generators can generate multiple and diverse counterexamples for the runtime verification of cyber-physical systems.

Quantum computing holds the unparalleled potentials to enhance, speed up or innovate machine learning. However, an unambiguous demonstration of quantum learning advantage has not been achieved so far. Here, we rigorously establish a noise-robust, unconditional quantum learning advantage in terms of expressivity, inference speed, and training efficiency, compared to commonly-used classical machine learning models. Our proof is information-theoretic and pinpoints the origin of this advantage: quantum entanglement can be used to reduce the communication required by non-local machine learning tasks. In particular, we design a fully classical task that can be solved with unit accuracy by a quantum model with a constant number of variational parameters using entanglement resources, whereas commonly-used classical models must scale at least linearly with the size of the task to achieve a larger-than-exponentially-small accuracy. We further show that the quantum model can be trained with constant time and a number of samples inversely proportional to the problem size. We prove that this advantage is robust against constant depolarization noise. We show through numerical simulations that even though the classical models can have improved performance as their sizes are increased, they would suffer from overfitting. The constant-versus-linear separation, bolstered by the overfitting problem, makes it possible to demonstrate the quantum advantage with relatively small system sizes. We demonstrate, through both numerical simulations and trapped-ion experiments on IonQ Aria, the desired quantum-classical learning separation. Our results provide a valuable guide for demonstrating quantum learning advantages in practical applications with current noisy intermediate-scale quantum devices.

Researchers have long run regressions of an outcome variable (Y) on a treatment (D) and covariates (X) to estimate treatment effects. Even absent unobserved confounding, the regression coefficient on D in this setup reports a conditional variance weighted average of strata-wise average effects, not generally equal to the average treatment effect (ATE). Numerous proposals have been offered to cope with this "weighting problem", including interpretational tools to help characterize the weights and diagnostic aids to help researchers assess the potential severity of this problem. We make two contributions that together suggest an alternative direction for researchers and this literature. Our first contribution is conceptual, demystifying these weights. Simply put, under heterogeneous treatment effects (and varying probability of treatment), the linear regression of Y on D and X will be misspecified. The "weights" of regression offer one characterization for the coefficient from regression that helps to clarify how it will depart from the ATE. We also derive a more general expression for the weights than what is usually referenced. Our second contribution is practical: as these weights simply characterize misspecification bias, we suggest simply avoiding them through an approach that tolerate heterogeneous effects. A wide range of longstanding alternatives (regression-imputation/g-computation, interacted regression, and balancing weights) relax specification assumptions to allow heterogeneous effects. We make explicit the assumption of "separate linearity", under which each potential outcome is separately linear in X. This relaxation of conventional linearity offers a common justification for all of these methods and avoids the weighting problem, at an efficiency cost that will be small when there are few covariates relative to sample size.

The effectiveness of automatic evaluation of generative models is typically measured by comparing it to human evaluation using correlation metrics. However, metrics like Krippendorff's $\alpha$ and Randolph's $\kappa$, originally designed to measure the reliability of human labeling, make assumptions about human behavior and the labeling process. In this paper, we show how *relying on a single aggregate correlation score* can obscure fundamental differences between human behavior and automatic evaluation methods, including LLM-as-a-Judge. Specifically, we demonstrate that when the proportion of samples with variation or uncertainty in human labels (gathered during human evaluation) is relatively high, machine labels (generated by automatic evaluation methods) may superficially appear to have similar or better correlation with the human majority label compared to human-to-human (HH) correlation. This can create the misleading impression that automatic evaluation is accurate enough to approximate the human majority label. However, as the proportion of samples with consistent human labels increases, the correlation between machine labels and human majority labels declines, falling below HH correlation. Based on these findings, we first propose stratifying results by human label uncertainty to provide a more robust analysis of automatic evaluation performance. Second, recognizing that uncertainty and variation are inherent in perception-based human evaluations, such as those involving attitudes or preferences, we introduce a new metric - *binned Jensen-Shannon Divergence for perception* for such scenarios to better measure the effectiveness of automatic evaluations. Third, we present visualization techniques -- *perception charts*, to compare the strengths and limitations of automatic evaluation and to contextualize correlation measures appropriately

This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the thesis, we will empirically study how training deep networks via stochastic gradient descent implicitly controls the networks' capacity. Subsequently, to show how this leads to better generalization, we will derive {\em data-dependent} {\em uniform-convergence-based} generalization bounds with improved dependencies on the parameter count. Uniform convergence has in fact been the most widely used tool in deep learning literature, thanks to its simplicity and generality. Given its popularity, in this thesis, we will also take a step back to identify the fundamental limits of uniform convergence as a tool to explain generalization. In particular, we will show that in some example overparameterized settings, {\em any} uniform convergence bound will provide only a vacuous generalization bound. With this realization in mind, in the last part of the thesis, we will change course and introduce an {\em empirical} technique to estimate generalization using unlabeled data. Our technique does not rely on any notion of uniform-convergece-based complexity and is remarkably precise. We will theoretically show why our technique enjoys such precision. We will conclude by discussing how future work could explore novel ways to incorporate distributional assumptions in generalization bounds (such as in the form of unlabeled data) and explore other tools to derive bounds, perhaps by modifying uniform convergence or by developing completely new tools altogether.