Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases that are hard to quantify. The latter enjoy asymptotic consistency, but can suffer from high computational costs. In this paper we present a way of bridging the gap between deterministic and stochastic inference. Specifically, we suggest an efficient sequential Monte Carlo (SMC) algorithm for PGMs which can leverage the output from deterministic inference methods. While generally applicable, we show explicitly how this can be done with loopy belief propagation, expectation propagation, and Laplace approximations. The resulting algorithm can be viewed as a post-correction of the biases associated with these methods and, indeed, numerical results show clear improvements over the baseline deterministic methods as well as over plain SMC.

We study a safe reinforcement learning problem in which the constraints are defined as the expected cost over finite-length trajectories. We propose a constrained cross-entropy-based method to solve this problem. The method explicitly tracks its performance with respect to constraint satisfaction and thus is well-suited for safety-critical applications. We show that the asymptotic behavior of the proposed algorithm can be almost-surely described by that of an ordinary differential equation. Then we give sufficient conditions on the properties of this differential equation to guarantee the convergence of the proposed algorithm. At last, we show with simulation experiments that the proposed algorithm can effectively learn feasible policies without assumptions on the feasibility of initial policies, even with non-Markovian objective functions and constraint functions.

Training of deep learning models depends on gradient descent and end-to-end differentiation. Under the slogan of differentiable programming, there is an increasing demand for efficient automatic gradient computation for emerging network architectures that incorporate dynamic control flow, especially in NLP. In this paper we propose an implementation of backpropagation using functions with callbacks, where the forward pass is executed as a sequence of function calls, and the backward pass as a corresponding sequence of function returns. A key realization is that this technique of chaining callbacks is well known in the programming languages community as continuation-passing style (CPS). Any program can be converted to this form using standard techniques, and hence, any program can be mechanically converted to compute gradients. Our approach achieves the same flexibility as other reverse-mode automatic differentiation (AD) techniques, but it can be implemented without any auxiliary data structures besides the function call stack, and it can easily be combined with graph construction and native code generation techniques through forms of multi-stage programming, leading to a highly efficient implementation that combines the performance benefits of define-then-run software frameworks such as TensorFlow with the expressiveness of define-by-run frameworks such as PyTorch.

We study adversarial perturbations when the instances are uniformly distributed over {0,1}^n. We study both inherent bounds that apply to any problem and any classifier for such a problem as well as bounds that apply to specific problems and specific hypothesis classes. As the current literature contains multiple definitions of adversarial risk and robustness, we start by giving a taxonomy for these definitions based on their direct goals; we identify one of them as the one guaranteeing misclassification by pushing the instances to the error region. We then study some classic algorithms for learning monotone conjunctions and compare their adversarial risk and robustness under different definitions by attacking the hypotheses using instances drawn from the uniform distribution. We observe that sometimes these definitions lead to significantly different bounds. Thus, this study advocates for the use of the error-region definition, even though other definitions, in other contexts with context-dependent assumptions, may coincide with the error-region definition. Using the error-region definition of adversarial perturbations, we then study inherent bounds on risk and robustness of any classifier for any classification problem whose instances are uniformly distributed over {0,1}^n. Using the isoperimetric inequality for the Boolean hypercube, we show that for initial error 0.01, there always exists an adversarial perturbation that changes O( n) bits of the instances to increase the risk to 0.5, making classifier's decisions meaningless. Furthermore, by also using the central limit theorem we show that when n, at most c n bits of perturbations, for a universal constant c<1.17, suffice for increasing the risk to 0.5, and the same c n bits of perturbations on average suffice to increase the risk to 1, hence bounding the robustness by c n.

The inference of the causal relationship between a pair of observed variables is a fundamental problem in science, and most existing approaches are based on one single causal model. In practice, however, observations are often collected from multiple sources with heterogeneous causal models due to certain uncontrollable factors, which renders causal analysis results obtained by a single model skeptical. In this paper, we generalize the Additive Noise Model (ANM) to a mixture model, which consists of a finite number of ANMs, and provide the condition of its causal identifiability. To conduct model estimation, we propose Gaussian Process Partially Observable Model (GPPOM), and incorporate independence enforcement into it to learn latent parameter associated with each observation. Causal inference and clustering according to the underlying generating mechanisms of the mixture model are addressed in this work. Experiments on synthetic and real data demonstrate the effectiveness of our proposed approach.

NVIDIA claims DLSS 5 will deliver'photoreal' image quality with AI this fall The company plans to rely on AI for more than just additional frames. Just months after announcing DLSS 4.5 at CES, NVIDIA has unveiled its next major upscaling technology, DLSS 5. The company is doubling-down on AI for this next iteration, claiming DLSS 5 "infuses pixels with photoreal lighting and materials" using a real-time neural rendering model when it arrives this fall. So what does this mean in practice? In an on-stage demo at NVIDIA's GTC 2026 keynote, CEO Jensen Huang showed off the technology with and DLSS 5 adds a noticeable amount of detail to character's hair and skin tone, but it also appears it's being compared to those games without any DLSS features turned on.

The state-of-the-art hardware platforms for training deep neural networks are moving from traditional single precision (32-bit) computations towards 16 bits of precision - in large part due to the high energy efficiency and smaller bit storage associated with using reduced-precision representations. However, unlike inference, training with numbers represented with less than 16 bits has been challenging due to the need to maintain fidelity of the gradient computations during back-propagation. Here we demonstrate, for the first time, the successful training of deep neural networks using 8-bit floating point numbers while fully maintaining the accuracy on a spectrum of deep learning models and datasets. In addition to reducing the data and computation precision to 8 bits, we also successfully reduce the arithmetic precision for additions (used in partial product accumulation and weight updates) from 32 bits to 16 bits through the introduction of a number of key ideas including chunk-based accumulation and floating point stochastic rounding. The use of these novel techniques lays the foundation for a new generation of hardware training platforms with the potential for 2-4 times improved throughput over today's systems.

Stochastic Gradient Langevin Dynamics (SGLD) has emerged as a key MCMC algorithm for Bayesian learning from large scale datasets. While SGLD with decreasing step sizes converges weakly to the posterior distribution, the algorithm is often used with a constant step size in practice and has demonstrated spectacular successes in machine learning tasks. The current practice is to set the step size inversely proportional to N where N is the number of training samples. As N becomes large, we show that the SGLD algorithm has an invariant probability measure which significantly departs from the target posterior and behaves like as Stochastic Gradient Descent (SGD). This difference is inherently due to the high variance of the stochastic gradients. Several strategies have been suggested to reduce this effect; among them, SGLD Fixed Point (SGLDFP) uses carefully designed control variates to reduce the variance of the stochastic gradients. We show that SGLDFP gives approximate samples from the posterior distribution, with an accuracy comparable to the Langevin Monte Carlo (LMC) algorithm for a computational cost sublinear in the number of data points. We provide a detailed analysis of the Wasserstein distances between LMC, SGLD, SGLDFP and SGD and explicit expressions of the means and covariance matrices of their invariant distributions. Our findings are supported by limited numerical experiments.

Modern large-scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as stochastic gradients among different workers. In this paper, to reduce the communication cost, we propose a convex optimization formulation to minimize the coding length of stochastic gradients. The key idea is to randomly drop out coordinates of the stochastic gradient vectors and amplify the remaining coordinates appropriately to ensure the sparsified gradient to be unbiased. To solve the optimal sparsification efficiently, several simple and fast algorithms are proposed for an approximate solution, with a theoretical guarantee for sparseness.

Machine learning is data hungry; the more data a model has access to in training, the more likely it is to perform well at inference time. Distinct parties may want to combine their local data to gain the benefits of a model trained on a large corpus of data. We consider such a case: parties get access to the model trained on their joint data but do not see each others individual datasets. We show that one needs to be careful when using this multi-party model since a potentially malicious party can taint the model by providing contaminated data. We then show how adversarial training can defend against such attacks by preventing the model from learning trends specific to individual parties data, thereby also guaranteeing party-level membership privacy.