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The growing popularity of Deep Neural Networks, which often require computationally expensive training and access to a vast amount of data, calls for accurate authorship verification methods to deter unlawful dissemination of the models and identify the source of the leak. In DNN watermarking the owner may have access to the full network (white-box) or only be able to extract information from its output to queries (black-box), but a watermarked model may include both approaches in order to gather sufficient evidence to then gain access to the network. Although there has been limited research in white-box watermarking that considers traitor tracing, this problem is yet to be explored in the black-box scenario. In this paper, we propose a black-and-white-box watermarking method for DNN classifiers that opens the door to collusion-resistant traitor tracing in black-box, exploiting the properties of Tardos codes, and making it possible to identify the source of the leak before access to the model is granted. While experimental results show that the method can successfully identify traitors, even when further attacks have been performed, we also discuss its limitations and open problems for traitor tracing in black-box.

In this study, we explore the potential of Multimodal Large Language Models (MLLMs) in improving embodied decision-making processes for agents. While Large Language Models (LLMs) have been widely used due to their advanced reasoning skills and vast world knowledge, MLLMs like GPT4-Vision offer enhanced visual understanding and reasoning capabilities. We investigate whether state-of-the-art MLLMs can handle embodied decision-making in an end-to-end manner and whether collaborations between LLMs and MLLMs can enhance decision-making. To address these questions, we introduce a new benchmark called PCA-EVAL, which evaluates embodied decision-making from the perspectives of Perception, Cognition, and Action. Additionally, we propose HOLMES, a multi-agent cooperation framework that allows LLMs to leverage MLLMs and APIs to gather multimodal information for informed decision-making. We compare end-to-end embodied decision-making and HOLMES on our benchmark and find that the GPT4-Vision model demonstrates strong end-to-end embodied decision-making abilities, outperforming GPT4-HOLMES in terms of average decision accuracy (+3%). However, this performance is exclusive to the latest GPT4-Vision model, surpassing the open-source state-of-the-art MLLM by 26%. Our results indicate that powerful MLLMs like GPT4-Vision hold promise for decision-making in embodied agents, offering new avenues for MLLM research.

For the first time, the concept of CHTW-systems as a multidimensional representation of Petri nets, based on the assumption of the spatial distribution of tokens (resources) in positions (branes) and, accordingly, the spatial representation of transitions and arcs is proposed. The theoretical constructs are based on the concept of hybrid functional Petri nets [10]. The introduced concepts of branes and carriers are distant analogies of the corresponding concepts in superstring theory, but the theory of CHTW-systems is neither part of superstring theory nor its development. The description of CHTW-system as a dynamic system for stationary and non-stationary cases is considered. The initial classification of CHTW systems is provided enabling understanding of further research directions.

Given a graph $G$ that is modified by a sequence of edge insertions and deletions, we study the Maximum $k$-Edge Coloring problem Having access to $k$ colors, how can we color as many edges of $G$ as possible such that no two adjacent edges share the same color? While this problem is different from simply maintaining a $b$-matching with $b=k$, the two problems are closely related: a maximum $k$-matching always contains a $\frac{k+1}k$-approximate maximum $k$-edge coloring. However, maximum $b$-matching can be solved efficiently in the static setting, whereas the Maximum $k$-Edge Coloring problem is NP-hard and even APX-hard for $k \ge 2$. We present new results on both problems: For $b$-matching, we show a new integrality gap result and for the case where $b$ is a constant, we adapt Wajc's matching sparsification scheme~[STOC20]. Using these as basis, we give three new algorithms for the dynamic Maximum $k$-Edge Coloring problem: Our MatchO algorithm builds on the dynamic $(2+\epsilon)$-approximation algorithm of Bhattacharya, Gupta, and Mohan~[ESA17] for $b$-matching and achieves a $(2+\epsilon)\frac{k+1} k$-approximation in $O(poly(\log n, \epsilon^{-1}))$ update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic $8$-approximation algorithm by Bhattacharya, Henzinger, and Italiano~[SODA15] for fractional $b$-matching and achieves a $(8+\epsilon)\frac{3k+3}{3k-1}$-approximation in $O(poly(\log n, \epsilon^{-1}))$ update time against an adaptive adversary. Moreover, our reductions use the dynamic $b$-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic $b$-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm that runs in $O(\Delta+k)$ update time, while guaranteeing a $2.16$~approximation factor.

The learning with errors problem (LWE) is one of the most important building blocks for post-quantum cryptography. To better understand the quantum hardness of LWE, it is crucial to explore quantum variants of LWE, show quantum algorithms for those variants, or prove they are as hard as standard LWE. To this end, Chen, Liu, and Zhandry [Eurocrypt 2022] define the $\sf{S|LWE\rangle}$ problem, which encodes the error of LWE samples into quantum amplitudes. They then show efficient quantum algorithms for $\sf{S|LWE\rangle}$ with a few interesting amplitudes. However, the hardness of the most interesting amplitude, Gaussian, was not addressed by Chen et al., or only known for some restricted settings (for example, when the number of $\sf{S|LWE\rangle}$ samples is very small, it is well known that $\sf{S|LWE\rangle}$ is as hard as standard LWE). In this paper, we show new hardness and algorithms for $\sf{S|LWE\rangle}$ with Gaussian and other amplitudes. Our main results are 1. There exist quantum reductions from standard LWE or worst-case GapSVP to $\sf{S|LWE\rangle}$ with Gaussian amplitude with unknown phase, and arbitrarily many $\sf{S|LWE\rangle}$ samples. 2. There is a $2^{\widetilde{O}(\sqrt{n})}$-time algorithm for $\sf{S|LWE\rangle}$ with Gaussian amplitude with known phase, given $2^{\widetilde{O}(\sqrt{n})}$ many quantum samples. The algorithm is modified from Kuperberg's sieve, and in fact works for more general amplitudes as long as the amplitudes and phases are completely known. One way of interpreting our result is: to show a sub-exponential time quantum algorithm for standard LWE, all we need is to handle phases in $\sf{S|LWE\rangle}$ amplitudes better, either in the algorithm or the reduction.

This paper presents an approach to learning (deep) $n$D features equivariant under orthogonal transformations, utilizing hyperspheres and regular $n$-simplexes. Our main contributions are theoretical and tackle major challenges in geometric deep learning such as equivariance and invariance under geometric transformations. Namely, we enrich the recently developed theory of steerable 3D spherical neurons -- SO(3)-equivariant filter banks based on neurons with spherical decision surfaces -- by extending said neurons to $n$D, which we call deep equivariant hyperspheres, and enabling their multi-layer construction. Using synthetic and real-world data in $n$D, we experimentally verify our theoretical contributions and find that our approach is superior to the baselines for small training data sets in all but one case.

In this study, we aim to enhance the arithmetic reasoning ability of Large Language Models (LLMs) through zero-shot prompt optimization. We identify a previously overlooked objective of query dependency in such optimization and elucidate two ensuing challenges that impede the successful and economical design of prompt optimization techniques. One primary issue is the absence of an effective method to evaluate prompts during inference when the golden answer is unavailable. Concurrently, learning via interactions with the LLMs to navigate the expansive natural language prompting space proves to be resource-intensive. To address this, we introduce Prompt-OIRL, which harnesses offline inverse reinforcement learning to draw insights from offline prompting demonstration data. Such data exists as by-products when diverse prompts are benchmarked on open-accessible datasets. With Prompt-OIRL, the query-dependent prompt optimization objective is achieved by first learning an offline reward model. This model can evaluate any query-prompt pairs without accessing LLMs. Subsequently, a best-of-N strategy is deployed to recommend the optimal prompt. Our experimental evaluations across various LLM scales and arithmetic reasoning datasets underscore both the efficacy and economic viability of the proposed approach.

Uncertainties in the real world mean that is impossible for system designers to anticipate and explicitly design for all scenarios that a robot might encounter. Thus, robots designed like this are fragile and fail outside of highly-controlled environments. Causal models provide a principled framework to encode formal knowledge of the causal relationships that govern the robot's interaction with its environment, in addition to probabilistic representations of noise and uncertainty typically encountered by real-world robots. Combined with causal inference, these models permit an autonomous agent to understand, reason about, and explain its environment. In this work, we focus on the problem of a robot block-stacking task due to the fundamental perception and manipulation capabilities it demonstrates, required by many applications including warehouse logistics and domestic human support robotics. We propose a novel causal probabilistic framework to embed a physics simulation capability into a structural causal model to permit robots to perceive and assess the current state of a block-stacking task, reason about the next-best action from placement candidates, and generate post-hoc counterfactual explanations. We provide exemplar next-best action selection results and outline planned experimentation in simulated and real-world robot block-stacking tasks.

Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.

Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.