Miracle-dz/UniFAR-FTUs huggingface dataset:
FGeo-HyperGNet: Geometry Problem Solving Integrating Formal Symbolic System and Hypergraph Neural Network

Geometry problem solving has always been a long-standing challenge in the fields of automated reasoning and artificial intelligence. This is the fifth article in a series of our works, we built a neural-symbolic system to automatically perform human-like geometric deductive reasoning. The symbolic part is a formal system built on FormalGeo, which can automatically perform geomertic relational reasoning and algebraic calculations and organize the solving process into a solution hypertree with conditions as hypernodes and theorems as hyperedges. The neural part, called HyperGNet, is a hypergraph neural network based on the attention mechanism, including a encoder to effectively encode the structural and semantic information of the hypertree, and a solver to provide problem-solving guidance. The neural part predicts theorems according to the hypertree, and the symbolic part applies theorems and updates the hypertree, thus forming a Predict-Apply Cycle to ultimately achieve readable and traceable automatic solving of geometric problems. Experiments demonstrate the correctness and effectiveness of this neural-symbolic architecture. We achieved a step-wised accuracy of 87.65% and an overall accuracy of 85.53% on the formalgeo7k datasets. The code and data is available at https://github.com/BitSecret/HyperGNet.
Measuring the magnetic dipole moment and magnetospheric fluctuations of SXP 18.3 with a Kalman filter

The magnetic dipole moment $\mu$ of an accretion-powered pulsar in magnetocentrifugal equilibrium cannot be inferred uniquely from time-averaged pulse period and aperiodic X-ray flux data, because the radiative efficiency $\eta_0$ of the accretion is unknown, as are the mass, radius, and distance of the star. The degeneracy associated with the radiative efficiency is circumvented, if fluctuations of the pulse period and aperiodic X-ray flux are tracked with a Kalman filter, whereupon $\mu$ can be measured uniquely up to the uncertainties in the mass, radius, and distance. Here the Kalman filter analysis is demonstrated successfully in practice for the first time on Rossi X-ray Timing Explorer observations of the X-ray transient SXP 18.3 in the Small Magellanic Cloud, which is monitored regularly. The analysis yields $\mu = 8.0^{+1.3}_{-1.2} \, \times \, 10^{30} \, {\rm G \, cm^3}$ and $\eta_0 = 0.04^{+0.02}_{-0.01}$, compared to $\mu = 5.0^{+1.0}_{-1.0} \times 10^{30} \, {\rm G \, cm^3}$ as inferred traditionally from time-averaged data assuming $\eta_0=1$. The analysis also yields time-resolved estimates of two hidden state variables, the mass accretion rate and the Maxwell stress at the disk-magnetosphere boundary. The success of the demonstration confirms that the Kalman filter analysis can be applied in the future to study the magnetic moments and disk-magnetosphere physics of accretion-powered pulsar populations in the Small Magellanic Cloud and elsewhere.
On solvable Lie superalgebras of maximal rank

In this paper we establish some basic properties of superderivations of Lie superalgebras. Under certain conditions, for solvable Lie superalgebras with given nilradicals, we give estimates for upper bounds to dimensions of complementary subspaces to the nilradicals. Moreover, under these conditions we describe the solvable Lie superalgebras of maximal rank. Namely, we prove that an arbitrary solvable Lie superalgebra of maximal rank is isomorphic to the maximal solvable extension of nilradical of maximal rank.
The multigraded BGG correspondence in Macaulay2

We give an overview of a Macaulay2 package for computing with the multigraded BGG correspondence. This software builds on the package BGG due to Abo-Decker-Eisenbud-Schreyer-Smith-Stillman, which concerns the standard graded BGG correspondence. In addition to implementing the multigraded BGG functors, this package includes an implementation of differential modules and their minimal free resolutions, and it contains a method for computing strongly linear strands of multigraded free resolutions.
Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates

We investigate a filtered Lie-Trotter splitting scheme for the ``good"Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use of discrete Bourgain spaces, our analysis extends to initial data in $H^{s}$ for $01/2$ imposed by the bilinear estimate in smooth Sobolev spaces. We establish convergence rates of order $\tau^{s/2}$ in $L^2$ for such levels of regularity. Our analytical findings are supported by numerical experiments.
Branched covers of twist-roll spun knots

We prove that the double branched cover of a twist-roll spun knot in $S^4$ is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun knot connected sum with a trivial projective plane is preserved after two twists are added. As a consequence, we conclude that a family of homotopy $\mathbb{CP}^2$s recently constructed by Miyazawa are each diffeomorphic to $\mathbb{CP}^2$.
Thermodynamically consistent Cahn-Hilliard-Navier-Stokes equations using the metriplectic dynamics formalism

Cahn-Hilliard-Navier-Stokes (CHNS) systems describes flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such a systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the thermodynamic conjugates of concentration and chemical potential are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. This general CHNS system reduces to cases in the literature, to which we can compare.
Optimizing Warfarin Dosing Using Contextual Bandit: An Offline Policy Learning and Evaluation Method

Warfarin, an anticoagulant medication, is formulated to prevent and address conditions associated with abnormal blood clotting, making it one of the most prescribed drugs globally. However, determining the suitable dosage remains challenging due to individual response variations, and prescribing an incorrect dosage may lead to severe consequences. Contextual bandit and reinforcement learning have shown promise in addressing this issue. Given the wide availability of observational data and safety concerns of decision-making in healthcare, we focused on using exclusively observational data from historical policies as demonstrations to derive new policies; we utilized offline policy learning and evaluation in a contextual bandit setting to establish the optimal personalized dosage strategy. Our learned policies surpassed these baseline approaches without genotype inputs, even when given a suboptimal demonstration, showcasing promising application potential.
Inexact and Implementable Accelerated Newton Proximal Extragradient Method for Convex Optimization

In this paper, we investigate the convergence behavior of the Accelerated Newton Proximal Extragradient (A-NPE) method when employing inexact Hessian information. The exact A-NPE method was the pioneer near-optimal second-order approach, exhibiting an oracle complexity of $\Tilde{O}(\epsilon^{-2/7})$ for convex optimization. Despite its theoretical optimality, there has been insufficient attention given to the study of its inexact version and efficient implementation. We introduce the inexact A-NPE method (IA-NPE), which is shown to maintain the near-optimal oracle complexity. In particular, we design a dynamic approach to balance the computational cost of constructing the Hessian matrix and the progress of the convergence. Moreover, we show the robustness of the line-search procedure, which is a subroutine in IA-NPE, in the face of the inexactness of the Hessian. These nice properties enable the implementation of highly effective machine learning techniques like sub-sampling and various heuristics in the method. Extensive numerical results illustrate that IA-NPE compares favorably with state-of-the-art second-order methods, including Newton's method with cubic regularization and Trust-Region methods.
From Prejudice to Parity: A New Approach to Debiasing Large Language Model Word Embeddings

Embeddings play a pivotal role in the efficacy of Large Language Models. They are the bedrock on which these models grasp contextual relationships and foster a more nuanced understanding of language and consequently perform remarkably on a plethora of complex tasks that require a fundamental understanding of human language. Given that these embeddings themselves often reflect or exhibit bias, it stands to reason that these models may also inadvertently learn this bias. In this work, we build on the seminal previous work and propose DeepSoftDebias, an algorithm that uses a neural network to perform 'soft debiasing'. We exhaustively evaluate this algorithm across a variety of SOTA datasets, accuracy metrics, and challenging NLP tasks. We find that DeepSoftDebias outperforms the current state-of-the-art methods at reducing bias across gender, race, and religion.
Molecule Generation and Optimization for Efficient Fragrance Creation

This research introduces a Machine Learning-centric approach to replicate olfactory experiences, validated through experimental quantification of perfume perception. Key contributions encompass a hybrid model connecting perfume molecular structure to human olfactory perception. This model includes an AI-driven molecule generator (utilizing Graph and Generative Neural Networks), quantification and prediction of odor intensity, and refinery of optimal solvent and molecule combinations for desired fragrances. Additionally, a thermodynamic-based model establishes a link between olfactory perception and liquid-phase concentrations. The methodology employs Transfer Learning and selects the most suitable molecules based on vapor pressure and fragrance notes. Ultimately, a mathematical optimization problem is formulated to minimize discrepancies between new and target olfactory experiences. The methodology is validated by reproducing two distinct olfactory experiences using available experimental data.
On the Cross-Dataset Generalization of Machine Learning for Network Intrusion Detection

Network Intrusion Detection Systems (NIDS) are a fundamental tool in cybersecurity. Their ability to generalize across diverse networks is a critical factor in their effectiveness and a prerequisite for real-world applications. In this study, we conduct a comprehensive analysis on the generalization of machine-learning-based NIDS through an extensive experimentation in a cross-dataset framework. We employ four machine learning classifiers and utilize four datasets acquired from different networks: CIC-IDS-2017, CSE-CIC-IDS2018, LycoS-IDS2017, and LycoS-Unicas-IDS2018. Notably, the last dataset is a novel contribution, where we apply corrections based on LycoS-IDS2017 to the well-known CSE-CIC-IDS2018 dataset. The results show nearly perfect classification performance when the models are trained and tested on the same dataset. However, when training and testing the models in a cross-dataset fashion, the classification accuracy is largely commensurate with random chance except for a few combinations of attacks and datasets. We employ data visualization techniques in order to provide valuable insights on the patterns in the data. Our analysis unveils the presence of anomalies in the data that directly hinder the classifiers capability to generalize the learned knowledge to new scenarios. This study enhances our comprehension of the generalization capabilities of machine-learning-based NIDS, highlighting the significance of acknowledging data heterogeneity.
OptEx: Expediting First-Order Optimization with Approximately Parallelized Iterations

First-order optimization (FOO) algorithms are pivotal in numerous computational domains such as machine learning and signal denoising. However, their application to complex tasks like neural network training often entails significant inefficiencies due to the need for many sequential iterations for convergence. In response, we introduce first-order optimization expedited with approximately parallelized iterations (OptEx), the first framework that enhances the efficiency of FOO by leveraging parallel computing to mitigate its iterative bottleneck. OptEx employs kernelized gradient estimation to make use of gradient history for future gradient prediction, enabling parallelization of iterations -- a strategy once considered impractical because of the inherent iterative dependency in FOO. We provide theoretical guarantees for the reliability of our kernelized gradient estimation and the iteration complexity of SGD-based OptEx, confirming that estimation errors diminish to zero as historical gradients accumulate and that SGD-based OptEx enjoys an effective acceleration rate of $\Omega(\sqrt{N})$ over standard SGD given parallelism of N. We also use extensive empirical studies, including synthetic functions, reinforcement learning tasks, and neural network training across various datasets, to underscore the substantial efficiency improvements achieved by OptEx.
A Question Answering Based Pipeline for Comprehensive Chinese EHR Information Extraction

Electronic health records (EHRs) hold significant value for research and applications. As a new way of information extraction, question answering (QA) can extract more flexible information than conventional methods and is more accessible to clinical researchers, but its progress is impeded by the scarcity of annotated data. In this paper, we propose a novel approach that automatically generates training data for transfer learning of QA models. Our pipeline incorporates a preprocessing module to handle challenges posed by extraction types that are not readily compatible with extractive QA frameworks, including cases with discontinuous answers and many-to-one relationships. The obtained QA model exhibits excellent performance on subtasks of information extraction in EHRs, and it can effectively handle few-shot or zero-shot settings involving yes-no questions. Case studies and ablation studies demonstrate the necessity of each component in our design, and the resulting model is deemed suitable for practical use.
Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview

This paper attempts to provide an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one-dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the subspace of data consistent solutions through explicit guidance to satisfy specific semantic or textural properties.
Learning Conditional Invariances through Non-Commutativity

Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder $\varphi^*$ that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder $\Phi^*_\tau$. We prove that non-commutativity steers the optimization towards $\Phi^*_\tau$ instead of $\varphi^*$, bringing the $\mathcal{H}$-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning $\Phi^*_\tau$, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over $2\%$, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.
TrialEmulation: An R Package to Emulate Target Trials for Causal Analysis of Observational Time-to-event Data

Randomised controlled trials (RCTs) are regarded as the gold standard for estimating causal treatment effects on health outcomes. However, RCTs are not always feasible, because of time, budget or ethical constraints. Observational data such as those from electronic health records (EHRs) offer an alternative way to estimate the causal effects of treatments. Recently, the `target trial emulation' framework was proposed by Hernan and Robins (2016) to provide a formal structure for estimating causal treatment effects from observational data. To promote more widespread implementation of target trial emulation in practice, we develop the R package TrialEmulation to emulate a sequence of target trials using observational time-to-event data, where individuals who start to receive treatment and those who have not been on the treatment at the baseline of the emulated trials are compared in terms of their risks of an outcome event. Specifically, TrialEmulation provides (1) data preparation for emulating a sequence of target trials, (2) calculation of the inverse probability of treatment and censoring weights to handle treatment switching and dependent censoring, (3) fitting of marginal structural models for the time-to-event outcome given baseline covariates, (4) estimation and inference of marginal intention to treat and per-protocol effects of the treatment in terms of marginal risk differences between treated and untreated for a user-specified target trial population. In particular, TrialEmulation can accommodate large data sets (e.g., from EHRs) within memory constraints of R by processing data in chunks and applying case-control sampling. We demonstrate the functionality of TrialEmulation using a simulated data set that mimics typical observational time-to-event data in practice.
Simplifying Hyperparameter Tuning in Online Machine Learning - The spotRiverGUI

Batch Machine Learning (BML) reaches its limits when dealing with very large amounts of streaming data. This is especially true for available memory, handling drift in data streams, and processing new, unknown data. Online Machine Learning (OML) is an alternative to BML that overcomes the limitations of BML. OML is able to process data in a sequential manner, which is especially useful for data streams. The `river` package is a Python OML-library, which provides a variety of online learning algorithms for classification, regression, clustering, anomaly detection, and more. The `spotRiver` package provides a framework for hyperparameter tuning of OML models. The `spotRiverGUI` is a graphical user interface for the `spotRiver` package. The `spotRiverGUI` releases the user from the burden of manually searching for the optimal hyperparameter setting. After the data is provided, users can compare different OML algorithms from the powerful `river` package in a convenient way and tune the selected algorithms very efficiently.
ArtPrompt: ASCII Art-based Jailbreak Attacks against Aligned LLMs

Safety is critical to the usage of large language models (LLMs). Multiple techniques such as data filtering and supervised fine-tuning have been developed to strengthen LLM safety. However, currently known techniques presume that corpora used for safety alignment of LLMs are solely interpreted by semantics. This assumption, however, does not hold in real-world applications, which leads to severe vulnerabilities in LLMs. For example, users of forums often use ASCII art, a form of text-based art, to convey image information. In this paper, we propose a novel ASCII art-based jailbreak attack and introduce a comprehensive benchmark Vision-in-Text Challenge (ViTC) to evaluate the capabilities of LLMs in recognizing prompts that cannot be solely interpreted by semantics. We show that five SOTA LLMs (GPT-3.5, GPT-4, Gemini, Claude, and Llama2) struggle to recognize prompts provided in the form of ASCII art. Based on this observation, we develop the jailbreak attack ArtPrompt, which leverages the poor performance of LLMs in recognizing ASCII art to bypass safety measures and elicit undesired behaviors from LLMs. ArtPrompt only requires black-box access to the victim LLMs, making it a practical attack. We evaluate ArtPrompt on five SOTA LLMs, and show that ArtPrompt can effectively and efficiently induce undesired behaviors from all five LLMs.
Adaptive Decision-Making for Autonomous Vehicles: A Learning-Enhanced Game-Theoretic Approach in Interactive Environments

This paper proposes an adaptive behavioral decision-making method for autonomous vehicles (AVs) focusing on complex merging scenarios. Leveraging principles from non-cooperative game theory, we develop a vehicle interaction behavior model that defines key traffic elements and integrates a multifactorial reward function. Maximum entropy inverse reinforcement learning (IRL) is employed for behavior model parameter optimization. Optimal matching parameters can be obtained using the interaction behavior feature vector and the behavior probabilities output by the vehicle interaction model. Further, a behavioral decision-making method adapted to dynamic environments is proposed. By establishing a mapping model between multiple environmental variables and model parameters, it enables parameters online learning and recognition, and achieves to output interactive behavior probabilities of AVs. Quantitative analysis employing naturalistic driving datasets (highD and exiD) and real-vehicle test data validates the model's high consistency with human decision-making. In 188 tested interaction scenarios, the average human-like similarity rate is 81.73%, with a notable 83.12% in the highD dataset. Furthermore, in 145 dynamic interactions, the method matches human decisions at 77.12%, with 6913 consistence instances. Moreover, in real-vehicle tests, a 72.73% similarity with 0% safety violations are obtained. Results demonstrate the effectiveness of our proposed method in enabling AVs to make informed adaptive behavior decisions in interactive environments.
Opening the black box of language acquisition

Recent advances in large language models using deep learning techniques have renewed interest on how languages can be learned from data. However, it is unclear whether or how these models represent grammatical information from the learned languages. In addition, the models must be pre-trained on large corpora before they can be used. In this work, we propose an alternative, more transparent and cognitively plausible architecture for learning language. Instead of using deep learning, our approach uses a minimal cognitive architecture based on sequence memory and chunking. The learning mechanism is based on the principles of reinforcement learning. We test our architecture on a number of natural-like toy languages. Results show that the model can learn these artificial languages from scratch and extract grammatical information that supports learning. Our study demonstrates the power of this simple architecture and stresses the importance of sequence memory as a key component of the language learning process. Since other animals do not seem to have a faithful sequence memory, this may explain why only humans have developed complex languages.