The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling is attractive and is well developed. But a fundamental requirement in almost all applications is stability of the fitted model. And this has not been addressed in the rank reduced case. Here, we develop, for the first time, a closed-form formula for an estimator of a rank reduced transition matrix which is guaranteed to be stable. We show that our estimator is consistent and asymptotically statistically efficient and illustrate it in comparative simulations.
Machine learning has revolutionized data analysis and pattern recognition, but its resource-intensive training has limited accessibility. Machine Learning as a Service (MLaaS) simplifies this by enabling users to delegate their data samples to an MLaaS provider and obtain the inference result using a pre-trained model. Despite its convenience, leveraging MLaaS poses significant privacy and reliability concerns to the client. Specifically, sensitive information from the client inquiry data can be leaked to an adversarial MLaaS provider. Meanwhile, the lack of a verifiability guarantee can potentially result in biased inference results or even unfair payment issues. While existing trustworthy machine learning techniques, such as those relying on verifiable computation or secure computation, offer solutions to privacy and reliability concerns, they fall short of simultaneously protecting the privacy of client data and providing provable inference verifiability. In this paper, we propose vPIN, a privacy-preserving and verifiable CNN inference scheme that preserves privacy for client data samples while ensuring verifiability for the inference. vPIN makes use of partial homomorphic encryption and commit-and-prove succinct non-interactive argument of knowledge techniques to achieve desirable security properties. In vPIN, we develop various optimization techniques to minimize the proving circuit for homomorphic inference evaluation thereby, improving the efficiency and performance of our technique. We fully implemented and evaluated our vPIN scheme on standard datasets (e.g., MNIST, CIFAR-10). Our experimental results show that vPIN achieves high efficiency in terms of proving time, verification time, and proof size, while providing client data privacy guarantees and provable verifiability.
Learning modular object-centric representations is crucial for systematic generalization. Existing methods show promising object-binding capabilities empirically, but theoretical identifiability guarantees remain relatively underdeveloped. Understanding when object-centric representations can theoretically be identified is crucial for scaling slot-based methods to high-dimensional images with correctness guarantees. To that end, we propose a probabilistic slot-attention algorithm that imposes an aggregate mixture prior over object-centric slot representations, thereby providing slot identifiability guarantees without supervision, up to an equivalence relation. We provide empirical verification of our theoretical identifiability result using both simple 2-dimensional data and high-resolution imaging datasets.
Function-correcting codes were introduced in the work "Function-Correcting Codes" (FCC) by Lenz et al. 2023, which provides a graphical representation for the problem of constructing function-correcting codes. We use this function dependent graph to get a lower bound on the redundancy required for function correction. By considering the function to be a bijection, such an approach leads to a lower bound on the redundancy required for classical systematic error correcting codes (ECCs) of small distances. We propose a range of parameters for which the bound is tight. For single error correcting codes, we show that this bound is at least as good as a bound proposed by Zinoviev, Litsyn, and Laihonen in 1998. Thus, this framework helps to study systematic classical error correcting codes. Further, we study the structure of this function dependent graph for linear functions, which leads to bounds on the redundancy of linear-function correcting codes. We show that the Plotkin-like bound for Function-Correcting Codes that was proposed by Lenz et.al 2023 is simplified for linear functions. Also, we propose a version of the sphere packing bound for linear-function correcting codes. We identify a class of linear functions for which an upper bound proposed by Lenz et al., is tight and also identify a class of functions for which coset-wise coding is equivalent to a lower dimensional classical error correction problem.
The recent introduction of large language models (LLMs) has revolutionized the field of robotics by enabling contextual reasoning and intuitive human-robot interaction in domains as varied as manipulation, locomotion, and self-driving vehicles. When viewed as a stand-alone technology, LLMs are known to be vulnerable to jailbreaking attacks, wherein malicious prompters elicit harmful text by bypassing LLM safety guardrails. To assess the risks of deploying LLMs in robotics, in this paper, we introduce RoboPAIR, the first algorithm designed to jailbreak LLM-controlled robots. Unlike existing, textual attacks on LLM chatbots, RoboPAIR elicits harmful physical actions from LLM-controlled robots, a phenomenon we experimentally demonstrate in three scenarios: (i) a white-box setting, wherein the attacker has full access to the NVIDIA Dolphins self-driving LLM, (ii) a gray-box setting, wherein the attacker has partial access to a Clearpath Robotics Jackal UGV robot equipped with a GPT-4o planner, and (iii) a black-box setting, wherein the attacker has only query access to the GPT-3.5-integrated Unitree Robotics Go2 robot dog. In each scenario and across three new datasets of harmful robotic actions, we demonstrate that RoboPAIR, as well as several static baselines, finds jailbreaks quickly and effectively, often achieving 100% attack success rates. Our results reveal, for the first time, that the risks of jailbroken LLMs extend far beyond text generation, given the distinct possibility that jailbroken robots could cause physical damage in the real world. Indeed, our results on the Unitree Go2 represent the first successful jailbreak of a deployed commercial robotic system. Addressing this emerging vulnerability is critical for ensuring the safe deployment of LLMs in robotics. Additional media is available at: //robopair.org
We show that variational learning can significantly improve the accuracy and calibration of Low-Rank Adaptation (LoRA) without a substantial increase in the cost. We replace AdamW by the Improved Variational Online Newton (IVON) algorithm to finetune large language models. For Llama-2 with 7 billion parameters, IVON improves the accuracy over AdamW by 2.8% and expected calibration error by 4.6%. The accuracy is also better than the other Bayesian alternatives, yet the cost is lower and the implementation is easier. Our work provides additional evidence for the effectiveness of IVON for large language models. The code is available at //github.com/team-approx-bayes/ivon-lora.
While large language models (LLMs) have advanced the field of natural language processing (NLP), their "black box" nature obscures their decision-making processes. To address this, researchers developed structured approaches using higher order tensors. These are able to model linguistic relations, but stall when training on classical computers due to their excessive size. Tensors are natural inhabitants of quantum systems and training on quantum computers provides a solution by translating text to variational quantum circuits. In this paper, we develop MultiQ-NLP: a framework for structure-aware data processing with multimodal text+image data. Here, "structure" refers to syntactic and grammatical relationships in language, as well as the hierarchical organization of visual elements in images. We enrich the translation with new types and type homomorphisms and develop novel architectures to represent structure. When tested on a main stream image classification task (SVO Probes), our best model showed a par performance with the state of the art classical models; moreover the best model was fully structured.
Assumption-based Argumentation (ABA) is advocated as a unifying formalism for various forms of non-monotonic reasoning, including logic programming. It allows capturing defeasible knowledge, subject to argumentative debate. While, in much existing work, ABA frameworks are given up-front, in this paper we focus on the problem of automating their learning from background knowledge and positive/negative examples. Unlike prior work, we newly frame the problem in terms of brave reasoning under stable extensions for ABA. We present a novel algorithm based on transformation rules (such as Rote Learning, Folding, Assumption Introduction and Fact Subsumption) and an implementation thereof that makes use of Answer Set Programming. Finally, we compare our technique to state-of-the-art ILP systems that learn defeasible knowledge.
Despite the strong performance of large language models (LLMs) in tasks like mathematical reasoning, their practical use is limited by high computational demands and proprietary restrictions. Chain-of-thought (CoT) and program-of-thought (PoT) fine-tuning are common methods to transfer LLM knowledge to small language models (SLMs). However, CoT often leads to calculation errors in SLMs, while PoT has shown more promise. While most PoT-based approaches focus on direct problem-to-code conversion or extracting only the key information from questions and then providing code solution for it, this work emphasizes filling the gaps in the question to clearly illustrate the solution path, which can be challenging for an SLM to understand when such information is not explicitly provided. Therefore, this paper introduces Gap-Filling Prompting (GFP), a novel two-step prompting strategy designed to enhance the problem-solving process for SLMs. The first step identifies these gaps and provides hints for filling them, while the second step adds the hints to the question to generate a final code solution. Experimental results on two benchmark datasets demonstrate that GFP significantly improves the mathematical reasoning abilities of SLMs.
In semi-supervised semantic segmentation (SSS), weak-to-strong consistency regularization techniques are widely utilized in recent works, typically combined with input-level and feature-level perturbations. However, the integration between weak-to-strong consistency regularization and network perturbation has been relatively rare. We note several problems with existing network perturbations in SSS that may contribute to this phenomenon. By revisiting network perturbations, we introduce a new approach for network perturbation to expand the existing weak-to-strong consistency regularization for unlabeled data. Additionally, we present a volatile learning process for labeled data, which is uncommon in existing research. Building upon previous work that includes input-level and feature-level perturbations, we present MLPMatch (Multi-Level-Perturbation Match), an easy-to-implement and efficient framework for semi-supervised semantic segmentation. MLPMatch has been validated on the Pascal VOC and Cityscapes datasets, achieving state-of-the-art performance. Code is available from //github.com/LlistenL/MLPMatch.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.