Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of future events as a means to improve decision making quality, and enhance social welfare. However, if maximizing welfare is the ultimate goal, prediction is only a small piece of the puzzle. There are various other policy levers a social planner might pursue in order to improve bottom-line outcomes, such as expanding access to available goods, or increasing the effect sizes of interventions. Given this broad range of design decisions, a basic question to ask is: What is the relative value of prediction in algorithmic decision making? How do the improvements in welfare arising from better predictions compare to those of other policy levers? The goal of our work is to initiate the formal study of these questions. Our main results are theoretical in nature. We identify simple, sharp conditions determining the relative value of prediction vis-\`a-vis expanding access, within several statistical models that are popular amongst quantitative social scientists. Furthermore, we illustrate how these theoretical insights may be used to guide the design of algorithmic decision making systems in practice.
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An important aspect in developing language models that interact with humans is aligning their behavior to be useful and unharmful for their human users. This is usually achieved by tuning the model in a way that enhances desired behaviors and inhibits undesired ones, a process referred to as alignment. In this paper, we propose a theoretical approach called Behavior Expectation Bounds (BEB) which allows us to formally investigate several inherent characteristics and limitations of alignment in large language models. Importantly, we prove that within the limits of this framework, for any behavior that has a finite probability of being exhibited by the model, there exist prompts that can trigger the model into outputting this behavior, with probability that increases with the length of the prompt. This implies that any alignment process that attenuates an undesired behavior but does not remove it altogether, is not safe against adversarial prompting attacks. Furthermore, our framework hints at the mechanism by which leading alignment approaches such as reinforcement learning from human feedback make the LLM prone to being prompted into the undesired behaviors. This theoretical result is being experimentally demonstrated in large scale by the so called contemporary "chatGPT jailbreaks", where adversarial users trick the LLM into breaking its alignment guardrails by triggering it into acting as a malicious persona. Our results expose fundamental limitations in alignment of LLMs and bring to the forefront the need to devise reliable mechanisms for ensuring AI safety.
The free distance of a convolutional code is a reliable indicator of its performance. However its computation is not an easy task. In this paper, we present some algorithms to compute the free distance with good efficiency that work for convolutional codes of all rates and over any field. Furthermore we discuss why an algorithm which is claimed to be very efficient is incorrect.
We develop the formal theory of monads, as established by Street, in univalent foundations. This allows us to formally reason about various kinds of monads on the right level of abstraction. In particular, we define the bicategory of monads internal to a bicategory, and prove that it is univalent. We also define Eilenberg-Moore objects, and we show that both Eilenberg-Moore categories and Kleisli categories give rise to Eilenberg-Moore objects. Finally, we relate monads and adjunctions in arbitrary bicategories. Our work is formalized in Coq using the UniMath library.
Side Channel Analysis (SCA) presents a clear threat to privacy and security in modern computing systems. The vast majority of communications are secured through cryptographic algorithms. These algorithms are often provably-secure from a cryptographical perspective, but their implementation on real hardware introduces vulnerabilities. Adversaries can exploit these vulnerabilities to conduct SCA and recover confidential information, such as secret keys or internal states. The threat of SCA has greatly increased as machine learning, and in particular deep learning, enhanced attacks become more common. In this work, we will examine the latest state-of-the-art deep learning techniques for side channel analysis, the theory behind them, and how they are conducted. Our focus will be on profiling attacks using deep learning techniques, but we will also examine some new and emerging methodologies enhanced by deep learning techniques, such as non-profiled attacks, artificial trace generation, and others. Finally, different deep learning enhanced SCA schemes attempted against the ANSSI SCA Database (ASCAD) and their relative performance will be evaluated and compared. This will lead to new research directions to secure cryptographic implementations against the latest SCA attacks.
Image captioning models are typically trained by treating all samples equally, neglecting to account for mismatched or otherwise difficult data points. In contrast, recent work has shown the effectiveness of training models by scheduling the data using curriculum learning strategies. This paper contributes to this direction by actively curating difficult samples in datasets without increasing the total number of samples. We explore the effect of using three data curation methods within the training process: complete removal of an sample, caption replacement, or image replacement via a text-to-image generation model. Experiments on the Flickr30K and COCO datasets with the BLIP and BEiT-3 models demonstrate that these curation methods do indeed yield improved image captioning models, underscoring their efficacy.
In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory of statistical learning does not apply directly and guarantees of the generalization capacity of predictive rules learned from such data are left to establish. We analyze here the simple Kriging task from a statistical learning perspective, i.e. by carrying out a nonparametric finite-sample predictive analysis. Given $d\geq 1$ values taken by a realization of a square integrable random field $X=\{X_s\}_{s\in S}$, $S\subset \mathbb{R}^2$, with unknown covariance structure, at sites $s_1,\; \ldots,\; s_d$ in $S$, the goal is to predict the unknown values it takes at any other location $s\in S$ with minimum quadratic risk. The prediction rule being derived from a training spatial dataset: a single realization $X'$ of $X$, independent from those to be predicted, observed at $n\geq 1$ locations $\sigma_1,\; \ldots,\; \sigma_n$ in $S$. Despite the connection of this minimization problem with kernel ridge regression, establishing the generalization capacity of empirical risk minimizers is far from straightforward, due to the non independent and identically distributed nature of the training data $X'_{\sigma_1},\; \ldots,\; X'_{\sigma_n}$ involved in the learning procedure. In this article, non-asymptotic bounds of order $O_{\mathbb{P}}(1/\sqrt{n})$ are proved for the excess risk of a plug-in predictive rule mimicking the true minimizer in the case of isotropic stationary Gaussian processes, observed at locations forming a regular grid in the learning stage. These theoretical results are illustrated by various numerical experiments, on simulated data and on real-world datasets.
Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability $\eta(x)=\mathbb{P}(Y=1\mid X=x)$, we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of $2\eta(x)-1$ and apply the method to real datasets.
In the last decade, social planners have used crowdfunding to raise funds for public projects. As these public projects are non-excludable, the beneficiaries may free-ride. Thus, there is a need to design incentive mechanisms for such strategic agents to contribute to the project. The existing mechanisms, like PPR or PPRx, assume that the agent's beliefs about the project getting funded do not change over time, i.e., their beliefs are static. Researchers highlight that unless appropriately incentivized, the agents defer their contributions in static settings, leading to a ``race'' to contribute at the deadline. In this work, we model the evolution of agents' beliefs as a random walk. We study PPRx -- an existing mechanism for the static belief setting -- in this dynamic belief setting and refer to it as PPRx-DB for readability. We prove that in PPRx-DB, the project is funded at equilibrium. More significantly, we prove that under certain conditions on agent's belief evolution, agents will contribute as soon as they arrive at the mechanism. Thus, we believe that by incorporating dynamic belief evolution in analysis, the social planner can mitigate the concern of race conditions in many mechanisms.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
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