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We present BadGD, a unified theoretical framework that exposes the vulnerabilities of gradient descent algorithms through strategic backdoor attacks. Backdoor attacks involve embedding malicious triggers into a training dataset to disrupt the model's learning process. Our framework introduces three novel constructs: Max RiskWarp Trigger, Max GradWarp Trigger, and Max GradDistWarp Trigger, each designed to exploit specific aspects of gradient descent by distorting empirical risk, deterministic gradients, and stochastic gradients respectively. We rigorously define clean and backdoored datasets and provide mathematical formulations for assessing the distortions caused by these malicious backdoor triggers. By measuring the impact of these triggers on the model training procedure, our framework bridges existing empirical findings with theoretical insights, demonstrating how a malicious party can exploit gradient descent hyperparameters to maximize attack effectiveness. In particular, we show that these exploitations can significantly alter the loss landscape and gradient calculations, leading to compromised model integrity and performance. This research underscores the severe threats posed by such data-centric attacks and highlights the urgent need for robust defenses in machine learning. BadGD sets a new standard for understanding and mitigating adversarial manipulations, ensuring the reliability and security of AI systems.

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over Wasserstein distance. In this paper we prove that the infinite dimensionality of the space of probabilities drastically deteriorates its sample complexity, which is slower than any polynomial rate in the sample size. We propose a new distance that preserves many desirable properties of the former while achieving a parametric rate of convergence. In particular, our distance 1) metrizes weak convergence; 2) can be estimated numerically through samples with low complexity; 3) can be bounded analytically from above and below. The main ingredient are integral probability metrics, which lead to the name hierarchical IPM.

It is well-known that decision-making problems from stochastic control can be formulated by means of a forward-backward stochastic differential equation (FBSDE). Recently, the authors of Ji et al. 2022 proposed an efficient deep learning algorithm based on the stochastic maximum principle (SMP). In this paper, we provide a convergence result for this deep SMP-BSDE algorithm and compare its performance with other existing methods. In particular, by adopting a strategy as in Han and Long 2020, we derive a-posteriori estimate, and show that the total approximation error can be bounded by the value of the loss functional and the discretization error. We present numerical examples for high-dimensional stochastic control problems, both in case of drift- and diffusion control, which showcase superior performance compared to existing algorithms.

Backpropagation (BP) has been pivotal in advancing machine learning and remains essential in computational applications and comparative studies of biological and artificial neural networks. Despite its widespread use, the implementation of BP in the brain remains elusive, and its biological plausibility is often questioned due to inherent issues such as the need for symmetry of weights between forward and backward connections, and the requirement of distinct forward and backward phases of computation. Here, we introduce a novel neuroplasticity rule that offers a potential mechanism for implementing BP in the brain. Similar in general form to the classical Hebbian rule, this rule is based on the core principles of maintaining the balance of excitatory and inhibitory inputs as well as on retrograde signaling, and operates over three progressively slower timescales: neural firing, retrograde signaling, and neural plasticity. We hypothesize that each neuron possesses an internal state, termed credit, in addition to its firing rate. After achieving equilibrium in firing rates, neurons receive credits based on their contribution to the E-I balance of postsynaptic neurons through retrograde signaling. As the network's credit distribution stabilizes, connections from those presynaptic neurons are strengthened that significantly contribute to the balance of postsynaptic neurons. We demonstrate mathematically that our learning rule precisely replicates BP in layered neural networks without any approximations. Simulations on artificial neural networks reveal that this rule induces varying community structures in networks, depending on the learning rate. This simple theoretical framework presents a biologically plausible implementation of BP, with testable assumptions and predictions that may be evaluated through biological experiments.

We investigate the geometry of a family of log-linear statistical models called quasi-independence models. The toric fiber product is useful for understanding the geometry of parameter inference in these models because the maximum likelihood degree is multiplicative under the TFP. We define the coordinate toric fiber product, or cTFP, and give necessary and sufficient conditions under which a quasi-independence model is a cTFP of lower-order models. We show that the vanishing ideal of every 2-way quasi-independence model with ML-degree 1 can be realized as an iterated toric fiber product of linear ideals. We also classify which Lawrence lifts of 2-way quasi-independence models are cTFPs and give a necessary condition under which a $k$-way model has ML-degree 1 using its facial submodels.

This paper presents GMASK, a general algorithm for distributed approximate similarity search that accepts any arbitrary distance function. GMASK requires a clustering algorithm that induces Voronoi regions in a dataset and returns a representative element for each region. Then, it creates a multilevel indexing structure suitable for large datasets with high dimensionality and sparsity, usually stored in distributed systems. Many similarity search algorithms rely on $k$-means, typically associated with the Euclidean distance, which is inappropriate for specific problems. Instead, in this work we implement GMASK using $k$-medoids to make it compatible with any distance and a wider range of problems. Experimental results verify the applicability of this method with real datasets, improving the performance of alternative algorithms for approximate similarity search. In addition, results confirm existing intuitions regarding the advantages of using certain instances of the Minkowski distance in high-dimensional datasets.

Characteristic formulae give a complete logical description of the behaviour of processes modulo some chosen notion of behavioural semantics. They allow one to reduce equivalence or preorder checking to model checking, and are exactly the formulae in the modal logics characterizing classic behavioural equivalences and preorders for which model checking can be reduced to equivalence or preorder checking. This paper studies the complexity of determining whether a formula is characteristic for some finite, loop-free process in each of the logics providing modal characterizations of the simulation-based semantics in van Glabbeek's branching-time spectrum. Since characteristic formulae in each of those logics are exactly the consistent and prime ones, it presents complexity results for the satisfiability and primality problems, and investigates the boundary between modal logics for which those problems can be solved in polynomial time and those for which they become computationally hard. Amongst other contributions, this article also studies the complexity of constructing characteristic formulae in the modal logics characterizing simulation-based semantics, both when such formulae are presented in explicit form and via systems of equations.

Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time window, a continuous-time discrete-valued Markov process provides a natural description of the dynamics of each model component, typically taken to be the number of susceptible, exposed, infected or removed individuals. Fitting the SEIR model to time-course data is a challenging problem due incomplete observations and, consequently, the intractability of the observed data likelihood. Whilst sampling based inference schemes such as Markov chain Monte Carlo are routinely applied, their computational cost typically restricts analysis to data sets of no more than a few thousand infective cases. Instead, we develop a sequential inference scheme that makes use of a computationally cheap approximation of the most natural Markov process model. Crucially, the resulting model allows a tractable conditional parameter posterior which can be summarised in terms of a set of low dimensional statistics. This is used to rejuvenate parameter samples in conjunction with a novel bridge construct for propagating state trajectories conditional on the next observation of cumulative incidence. The resulting inference framework also allows for stochastic infection and reporting rates. We illustrate our approach using synthetic and real data applications.

Diagnosing and managing a patient is a complex, sequential decision making process that requires physicians to obtain information -- such as which tests to perform -- and to act upon it. Recent advances in artificial intelligence (AI) and large language models (LLMs) promise to profoundly impact clinical care. However, current evaluation schemes overrely on static medical question-answering benchmarks, falling short on interactive decision-making that is required in real-life clinical work. Here, we present AgentClinic: a multimodal benchmark to evaluate LLMs in their ability to operate as agents in simulated clinical environments. In our benchmark, the doctor agent must uncover the patient's diagnosis through dialogue and active data collection. We present two open medical agent benchmarks: a multimodal image and dialogue environment, AgentClinic-NEJM, and a dialogue-only environment, AgentClinic-MedQA. We embed cognitive and implicit biases both in patient and doctor agents to emulate realistic interactions between biased agents. We find that introducing bias leads to large reductions in diagnostic accuracy of the doctor agents, as well as reduced compliance, confidence, and follow-up consultation willingness in patient agents. Evaluating a suite of state-of-the-art LLMs, we find that several models that excel in benchmarks like MedQA are performing poorly in AgentClinic-MedQA. We find that the LLM used in the patient agent is an important factor for performance in the AgentClinic benchmark. We show that both having limited interactions as well as too many interaction reduces diagnostic accuracy in doctor agents. The code and data for this work is publicly available at //AgentClinic.github.io.

Mobile devices and the Internet of Things (IoT) devices nowadays generate a large amount of heterogeneous spatial-temporal data. It remains a challenging problem to model the spatial-temporal dynamics under privacy concern. Federated learning (FL) has been proposed as a framework to enable model training across distributed devices without sharing original data which reduce privacy concern. Personalized federated learning (PFL) methods further address data heterogenous problem. However, these methods don't consider natural spatial relations among nodes. For the sake of modeling spatial relations, Graph Neural Netowork (GNN) based FL approach have been proposed. But dynamic spatial-temporal relations among edge nodes are not taken into account. Several approaches model spatial-temporal dynamics in a centralized environment, while less effort has been made under federated setting. To overcome these challeges, we propose a novel Federated Adaptive Spatial-Temporal Attention (FedASTA) framework to model the dynamic spatial-temporal relations. On the client node, FedASTA extracts temporal relations and trend patterns from the decomposed terms of original time series. Then, on the server node, FedASTA utilize trend patterns from clients to construct adaptive temporal-spatial aware graph which captures dynamic correlation between clients. Besides, we design a masked spatial attention module with both static graph and constructed adaptive graph to model spatial dependencies among clients. Extensive experiments on five real-world public traffic flow datasets demonstrate that our method achieves state-of-art performance in federated scenario. In addition, the experiments made in centralized setting show the effectiveness of our novel adaptive graph construction approach compared with other popular dynamic spatial-temporal aware methods.