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Large Language Models (LLMs) have shown excellent performance in language understanding, text generation, code synthesis, and many other tasks, while they still struggle in complex multi-step reasoning problems, such as mathematical reasoning. In this paper, through a newly proposed arithmetical puzzle problem, we show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that not only the model can reach a zero-shot pass@1 at 0.44 on the in-domain dataset, it also demonstrates certain generalization capabilities on the out-of-domain datasets. Specifically, this paper has designed two out-of-domain datasets in the form of extending the numerical range and the composing components of the arithmetical puzzle problem separately. The fine-tuned models have shown encouraging performance on these two far more difficult tasks with the zero-shot pass@1 at 0.33 and 0.35, respectively.

We give a new proof of the "transfer theorem" underlying adaptive data analysis: that any mechanism for answering adaptively chosen statistical queries that is differentially private and sample-accurate is also accurate out-of-sample. Our new proof is elementary and gives structural insights that we expect will be useful elsewhere. We show: 1) that differential privacy ensures that the expectation of any query on the posterior distribution on datasets induced by the transcript of the interaction is close to its true value on the data distribution, and 2) sample accuracy on its own ensures that any query answer produced by the mechanism is close to its posterior expectation with high probability. This second claim follows from a thought experiment in which we imagine that the dataset is resampled from the posterior distribution after the mechanism has committed to its answers. The transfer theorem then follows by summing these two bounds, and in particular, avoids the "monitor argument" used to derive high probability bounds in prior work. An upshot of our new proof technique is that the concrete bounds we obtain are substantially better than the best previously known bounds, even though the improvements are in the constants, rather than the asymptotics (which are known to be tight). As we show, our new bounds outperform the naive "sample-splitting" baseline at dramatically smaller dataset sizes compared to the previous state of the art, bringing techniques from this literature closer to practicality.

Given a hypergraph, influence maximization (IM) is to discover a seed set containing $k$ vertices that have the maximal influence. Although the existing vertex-based IM algorithms perform better than the hyperedge-based algorithms by generating random reverse researchable (RR) sets, they are inefficient because (i) they ignore important structural information associated with hyperedges and thus obtain inferior results, (ii) the frequently-used sampling methods for generating RR sets have low efficiency because of a large number of required samplings along with high sampling variances, and (iii) the vertex-based IM algorithms have large overheads in terms of running time and memory costs. To overcome these shortcomings, this paper proposes a novel approach, called \emph{HyperIM}. The key idea behind \emph{HyperIM} is to differentiate structural information of vertices for developing stratified sampling combined with highly-efficient strategies to generate the RR sets. With theoretical guarantees, \emph{HyperIM} is able to accelerate the influence spread, improve the sampling efficiency, and cut down the expected running time. To further reduce the running time and memory costs, we optimize \emph{HyperIM} by inferring the bound of the required number of RR sets in conjunction with stratified sampling. Experimental results on real-world hypergraphs show that \emph{HyperIM} is able to reduce the number of required RR sets and running time by orders of magnitude while increasing the influence spread by up to $2.73X$ on average, compared to the state-of-the-art IM algorithms.

Copyright infringement may occur when a generative model produces samples substantially similar to some copyrighted data that it had access to during the training phase. The notion of access usually refers to including copyrighted samples directly in the training dataset, which one may inspect to identify an infringement. We argue that such visual auditing largely overlooks a concealed copyright infringement, where one constructs a disguise that looks drastically different from the copyrighted sample yet still induces the effect of training Latent Diffusion Models on it. Such disguises only require indirect access to the copyrighted material and cannot be visually distinguished, thus easily circumventing the current auditing tools. In this paper, we provide a better understanding of such disguised copyright infringement by uncovering the disguises generation algorithm, the revelation of the disguises, and importantly, how to detect them to augment the existing toolbox. Additionally, we introduce a broader notion of acknowledgment for comprehending such indirect access. Our code is available at //github.com/watml/disguised_copyright_infringement.

In Terminal Monitoring Set (TMS), the input is an undirected graph $G=(V,E)$, together with a collection $T$ of terminal pairs and the goal is to find a subset $S$ of minimum size that hits a shortest path between every pair of terminals. We show that this problem is W[2]-hard with respect to solution size. On the positive side, we show that TMS is fixed parameter tractable with respect to solution size plus distance to cluster, solution size plus neighborhood diversity, and feedback edge number. For the weighted version of the problem, we obtain a FPT algorithm with respect to vertex cover number, and for a relaxed version of the problem, we show that it is W[1]-hard with respect to solution size plus feedback vertex number.

Due to common architecture designs, symmetries exist extensively in contemporary neural networks. In this work, we unveil the importance of the loss function symmetries in affecting, if not deciding, the learning behavior of machine learning models. We prove that every mirror-reflection symmetry, with reflection surface $O$, in the loss function leads to the emergence of a constraint on the model parameters $\theta$: $O^T\theta =0$. This constrained solution becomes satisfied when either the weight decay or gradient noise is large. Common instances of mirror symmetries in deep learning include rescaling, rotation, and permutation symmetry. As direct corollaries, we show that rescaling symmetry leads to sparsity, rotation symmetry leads to low rankness, and permutation symmetry leads to homogeneous ensembling. Then, we show that the theoretical framework can explain intriguing phenomena, such as the loss of plasticity and various collapse phenomena in neural networks, and suggest how symmetries can be used to design an elegant algorithm to enforce hard constraints in a differentiable way.

Safe deployment of AI models requires proactive detection of failures to prevent costly errors. To this end, we study the important problem of detecting failures in deep regression models. Existing approaches rely on epistemic uncertainty estimates or inconsistency w.r.t the training data to identify failure. Interestingly, we find that while uncertainties are necessary they are insufficient to accurately characterize failure in practice. Hence, we introduce PAGER (Principled Analysis of Generalization Errors in Regressors), a framework to systematically detect and characterize failures in deep regressors. Built upon the principle of anchored training in deep models, PAGER unifies both epistemic uncertainty and complementary manifold non-conformity scores to accurately organize samples into different risk regimes.

As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Neural machine translation (NMT) is a deep learning based approach for machine translation, which yields the state-of-the-art translation performance in scenarios where large-scale parallel corpora are available. Although the high-quality and domain-specific translation is crucial in the real world, domain-specific corpora are usually scarce or nonexistent, and thus vanilla NMT performs poorly in such scenarios. Domain adaptation that leverages both out-of-domain parallel corpora as well as monolingual corpora for in-domain translation, is very important for domain-specific translation. In this paper, we give a comprehensive survey of the state-of-the-art domain adaptation techniques for NMT.