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These notes combine results from two papers by the present authors viz., Part I (arXiv:2205.10299) and Part II (arXiv:2212.13028) into one streamlined version for better readability, along with a review on theory of complex multiplication for non-singular complex projective varieties and complex tori that is aimed at string theorists. We think that it is worth posting this edition as a separate entry in arXiv for those reasons, although this edition contains no essential progress beyond Part I and Part II. S. Gukov and C. Vafa proposed a characterization of rational N=(1,1) superconformal field theories (SCFTs) on 1+1 dimensions with Ricci-flat Kahler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore. We refined this idea and obtained a conjectural statement on necessary and sufficient conditions for such SCFTs to be rational, which we indeed prove to be true in the case the target space is T^4. In the refined statement, the algebraicity of the geometric data of the target space turns out to be essential, and the Strominger--Yau--Zaslow fibration in the mirror correspondence also plays a vital role., Comment: Materials in sections 2.1.2--5.3 are from Part I (arXiv:2205.10299) and those in sections 5.4--6 are from Part II (arXiv:2212.13028). The appendix A was drafted for this submission. 111 pages

Reward-based finetuning is crucial for aligning language policies with intended behaviors (e.g., creativity and safety). A key challenge is to develop steerable language models that trade-off multiple (conflicting) objectives in a flexible and efficient manner. This paper presents Conditional Language Policy (CLP), a general framework for finetuning language models on multiple objectives. Building on techniques from multi-task training and parameter-efficient finetuning, CLP learn steerable models that effectively trade-off conflicting objectives at inference time. Notably, this does not require training or maintaining multiple models to achieve different trade-offs between the objectives. Through extensive experiments and ablations on two summarization datasets, we show that CLP learns steerable language models that outperform and Pareto-dominate the existing approaches for multi-objective finetuning., Comment: 40 pages. Findings of EMNLP 2024

We study an auction setting in which bidders bid for placement of their content within a summary generated by a large language model (LLM), e.g., an ad auction in which the display is a summary paragraph of multiple ads. This generalizes the classic ad settings such as position auctions to an LLM generated setting, which allows us to handle general display formats. We propose a novel factorized framework in which an auction module and an LLM module work together via a prediction model to provide welfare maximizing summary outputs in an incentive compatible manner. We provide a theoretical analysis of this framework and synthetic experiments to demonstrate the feasibility and validity of the system together with welfare comparisons.

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a preference or teacher model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

We demonstrate that ambient pressure x-ray photoelectron spectroscopy (APXPS) can be used for in situ studies of dynamic changes in surface chemistry in a plasma environment. Hexagonal boron nitride (h-BN) was used in this study as a model system since it exhibits a wide array of unique chemical, optical, and electrical properties that make it a prospective material for advanced electronics. To better understand the stability and surface chemistry of h-BN during plasma-assisted processing, we used polycrystalline Cu foils with single-layer h-BN, grown via chemical vapor deposition (CVD), and tracked in real-time the plasma-induced reduction of the underlying Cu oxide using APXPS equipped with 22 kHz 75 W discharge plasma source operating at 13 Pa. Residual gas analysis (RGA) mass-spectra were concurrently collected during plasma-XPS to track reaction products formed during plasma exposure. A clear reduction of CuxO is seen, while an h-BN layer remains intact, suggesting H radical species can attack the exposed and h-BN-covered Cu oxide patches and partially reduce the underlying substrate. In addition to the demonstration and discussion of plasma-XPS capabilities, our results indicate the h-BN encapsulated metallic Cu interface might be repaired without significantly damaging the overlaying h-BN, which is of practical importance for the development of h-BN encapsulated devices and interfaces

We study a class of newly-introduced CFTs associated with even quadratic forms of general signature, which we call generalized Narain theories. We first summarize the properties of these theories. We then consider orbifolds of these theories, thereby obtaining a large class of non-supersymmetric CFTs with exactly marginal deformations. We then discuss ensemble averages of such theories over their moduli space, and obtain a modular form associated with the quadratic form and an element of the discriminant group. The modular form can be written as a Poincare series, which contains novel invariants of lens spaces and suggests the interpretation of the holographic bulk as a theory of anyons., Comment: 33 pages, 2 figures, 5 appendices

Fairness, especially group fairness, is an important consideration in the context of machine learning systems. The most commonly adopted group fairness-enhancing techniques are in-processing methods that rely on a mixture of a fairness objective (e.g., demographic parity) and a task-specific objective (e.g., cross-entropy) during the training process. However, when data arrives in an online fashion -- one instance at a time -- optimizing such fairness objectives poses several challenges. In particular, group fairness objectives are defined using expectations of predictions across different demographic groups. In the online setting, where the algorithm has access to a single instance at a time, estimating the group fairness objective requires additional storage and significantly more computation (e.g., forward/backward passes) than the task-specific objective at every time step. In this paper, we propose Aranyani, an ensemble of oblique decision trees, to make fair decisions in online settings. The hierarchical tree structure of Aranyani enables parameter isolation and allows us to efficiently compute the fairness gradients using aggregate statistics of previous decisions, eliminating the need for additional storage and forward/backward passes. We also present an efficient framework to train Aranyani and theoretically analyze several of its properties. We conduct empirical evaluations on 5 publicly available benchmarks (including vision and language datasets) to show that Aranyani achieves a better accuracy-fairness trade-off compared to baseline approaches., Comment: ICLR 2024 (Spotlight)

This paper presents an adaptive robust nonlinear control method, which achieves reliable trajectory tracking control for a quadrotor unmanned aerial vehicle in the presence of gyroscopic effects, rotor dynamics, and external disturbances. Through novel mathematical manipulation in the error system development, the quadrotor dynamics are expressed in a control-oriented form, which explicitly incorporates the uncertainty in the gyroscopic term and control actuation term. An adaptive robust nonlinear control law is then designed to stabilize both the position and attitude loops of the quadrotor system. A rigorous Lyapunov-based analysis is utilized to prove asymptotic trajectory tracking, where the region of convergence can be made arbitrarily large through judicious control gain selection. Moreover, the stability analysis formally addresses gyroscopic effects and actuator uncertainty. To illustrate the performance of the control law, comparative numerical simulation results are provided, which demonstrate the improved closed-loop performance achieved under varying levels of parametric uncertainty and disturbance magnitudes.

We use the exact degeneracy formula of single-centred $\frac14$ BPS dyonic black holes with unit torsion in 4D $N=4$ toroidally compactified heterotic string theory to improve on the existing formulation of the corresponding quantum entropy function obtained using supersymmetric localization. The result takes the form of a sum over Euclidean backgrounds including orbifolds of the Euclidean $AdS_2 \times S^2$ attractor geometry. Using an $N=2$ formalism, we determine the explicit form of the Abelian gauge potentials supporting these backgrounds. We further show how a rewriting of the degeneracy formula is amenable, at a semi-classical level, to a gravitational interpretation involving 2D Euclidean wormholes. This alternative picture is useful to elucidate different aspects of the gravitational path integral capturing the microstate degeneracies. We also comment on the relation between the associated 1D holographic models., Comment: 32 pages, 1 figure; v2: clarifications and references added, minor typos corrected

We study the quantum degeneracies of BPS black holes of octonionic magical supergravity in five dimensions that is defined by the exceptional Jordan algebra. We define the quantum degeneracy purely number theoretically as the number of distinct states in the charge space with a given set of invariant labels of the discrete U-duality group. We argue that the quantum degeneracies of spherically symmetric stationary BPS black holes of octonionic magical supergravity in five dimensions are given by the Fourier coefficients of the modular forms of the exceptional group $E_{7(-25)}$. The charges of the black holes take values in the lattice defined by the exceptional Jordan algebra $J_3^{\mathbb{O}}(\mathcal{R})$ over integral octonions $\mathcal{R}$. The quantum degeneracies of charge states of rank one and rank two BPS black holes (zero area) are given by the Fourier coefficients of singular modular forms $E_4(Z)$ and $E_8(Z)=(E_4(Z))^2$ of $E_{7(-25)}(Z)$. The rank 3 (large) BPS black holes will be studied elsewhere. Following the work of N. Elkies and B. Gross on the embeddings of cubic rings $A$ into the exceptional Jordan algebra and their actions on the 24 dimensional orthogonal quadratic subspace of $J_3^{\mathbb{O}}(\mathcal{R})$, we show that the quantum degeneracies of rank one black holes described by such embeddings are given by the Fourier coefficients of the Hilbert modular forms of $SL(2,A)$. If the discriminant of the cubic ring $A$ is $D=p^2$ with $p$ a prime number then the isotropic lines in the 24 dimensional quadratic space define a pair of Niemeier lattices which can be taken as charge lattices of some BPS black holes. For $p=7$ they are the Leech lattice with no roots and the lattice $A_6^4$ with 168 root vectors. We also review the current status of the searches for the M/superstring theoretic origins of the octonionic magical supergravity., Comment: Further improvements in presentation; stressed further that our definition of quantum degeneracy is purely number theoretic ; uniformized the notation of math symbols; corrected numerous typos; reference added; This replaces the last submission which used erroneously an earlier version of the file

The study of rational conformal field theories in the moduli space is of particular interest since these theories correspond to points in moduli space where the algebraic and arithmetic structure are usually richer, while also being points where non--trivial physics occurs (such as in the study of attractor black holes and BPS states at rational points). This has led to various attempts to characterize and classify such rational points. In this paper, a conjectured characterization by Gukov--Vafa of rational conformal field theories whose target space is a Ricci flat K\"ahler manifold is analyzed carefully for the case of toroidal compactifications. We refine the conjectured statement as well as making an effort to verify it, using $T^4$ compactification as a test case. Seven common properties in terms of Hodge theory (including complex multiplication) have been identified for $T^4$-target rational conformal field theories. By imposing three properties out of the seven, however, there remain $\mathcal N = (1,1)$ SCFTs that are not rational. Open questions, implications and future lines of work are discussed., Comment: In v.2, numerous small errors and typos are corrected, and a little more explanations, a few figures and references are added

Conventional methods for query autocompletion aim to predict which completed query a user will select from a list. A shortcoming of this approach is that users often do not know which query will provide the best retrieval performance on the current information retrieval system, meaning that any query autocompletion methods trained to mimic user behavior can lead to suboptimal query suggestions. To overcome this limitation, we propose a new approach that explicitly optimizes the query suggestions for downstream retrieval performance. We formulate this as a problem of ranking a set of rankings, where each query suggestion is represented by the downstream item ranking it produces. We then present a learning method that ranks query suggestions by the quality of their item rankings. The algorithm is based on a counterfactual learning approach that is able to leverage feedback on the items (e.g., clicks, purchases) to evaluate query suggestions through an unbiased estimator, thus avoiding the assumption that users write or select optimal queries. We establish theoretical support for the proposed approach and provide learning-theoretic guarantees. We also present empirical results on publicly available datasets, and demonstrate real-world applicability using data from an online shopping store.

This article uses Deep Learning technologies to safeguard DNA sequencing against Bio-Cyber attacks. We consider a hybrid attack scenario where the payload is encoded into a DNA sequence to activate a Trojan malware implanted in a software tool used in the sequencing pipeline in order to allow the perpetrators to gain control over the resources used in that pipeline during sequence analysis. The scenario considered in the paper is based on perpetrators submitting synthetically engineered DNA samples that contain digitally encoded IP address and port number of the perpetrators machine in the DNA. Genetic analysis of the samples DNA will decode the address that is used by the software trojan malware to activate and trigger a remote connection. This approach can open up to multiple perpetrators to create connections to hijack the DNA sequencing pipeline. As a way of hiding the data, the perpetrators can avoid detection by encoding the address to maximise similarity with genuine DNAs, which we showed previously. However, in this paper we show how Deep Learning can be used to successfully detect and identify the trigger encoded data, in order to protect a DNA sequencing pipeline from trojan attacks. The result shows nearly up to 100% accuracy in detection in such a novel Trojan attack scenario even after applying fragmentation encryption and steganography on the encoded trigger data. In addition, feasibility of designing and synthesizing encoded DNA for such Trojan payloads is validated by a wet lab experiment.