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This paper investigates the possibility of approximating multiple mathematical operations in latent space for expression derivation. To this end, we introduce different multi-operational representation paradigms, modelling mathematical operations as explicit geometric transformations. By leveraging a symbolic engine, we construct a large-scale dataset comprising 1.7M derivation steps stemming from 61K premises and 6 operators, analysing the properties of each paradigm when instantiated with state-of-the-art neural encoders. Specifically, we investigate how different encoding mechanisms can approximate equational reasoning in latent space, exploring the trade-off between learning different operators and specialising within single operations, as well as the ability to support multi-step derivations and out-of-distribution generalisation. Our empirical analysis reveals that the multi-operational paradigm is crucial for disentangling different operators, while discriminating the conclusions for a single operation is achievable in the original expression encoder. Moreover, we show that architectural choices can heavily affect the training dynamics, structural organisation, and generalisation of the latent space, resulting in significant variations across paradigms and classes of encoders.

We develop a general theory to optimize the frequentist regret for sequential learning problems, where efficient bandit and reinforcement learning algorithms can be derived from unified Bayesian principles. We propose a novel optimization approach to generate "algorithmic beliefs" at each round, and use Bayesian posteriors to make decisions. The optimization objective to create "algorithmic beliefs," which we term "Algorithmic Information Ratio," represents an intrinsic complexity measure that effectively characterizes the frequentist regret of any algorithm. To the best of our knowledge, this is the first systematical approach to make Bayesian-type algorithms prior-free and applicable to adversarial settings, in a generic and optimal manner. Moreover, the algorithms are simple and often efficient to implement. As a major application, we present a novel algorithm for multi-armed bandits that achieves the "best-of-all-worlds" empirical performance in the stochastic, adversarial, and non-stationary environments. And we illustrate how these principles can be used in linear bandits, bandit convex optimization, and reinforcement learning.

Distributional shift is a central challenge in the deployment of machine learning models as they can be ill-equipped for real-world data. This is particularly evident in text-to-audio generation where the encoded representations are easily undermined by unseen prompts, which leads to the degradation of generated audio -- the limited set of the text-audio pairs remains inadequate for conditional audio generation in the wild as user prompts are under-specified. In particular, we observe a consistent audio quality degradation in generated audio samples with user prompts, as opposed to training set prompts. To this end, we present a retrieval-based in-context prompt editing framework that leverages the training captions as demonstrative exemplars to revisit the user prompts. We show that the framework enhanced the audio quality across the set of collected user prompts, which were edited with reference to the training captions as exemplars.

Generative processes that involve solving differential equations, such as diffusion models, frequently necessitate balancing speed and quality. ODE-based samplers are fast but plateau in performance while SDE-based samplers deliver higher sample quality at the cost of increased sampling time. We attribute this difference to sampling errors: ODE-samplers involve smaller discretization errors while stochasticity in SDE contracts accumulated errors. Based on these findings, we propose a novel sampling algorithm called Restart in order to better balance discretization errors and contraction. The sampling method alternates between adding substantial noise in additional forward steps and strictly following a backward ODE. Empirically, Restart sampler surpasses previous SDE and ODE samplers in both speed and accuracy. Restart not only outperforms the previous best SDE results, but also accelerates the sampling speed by 10-fold / 2-fold on CIFAR-10 / ImageNet $64 \times 64$. In addition, it attains significantly better sample quality than ODE samplers within comparable sampling times. Moreover, Restart better balances text-image alignment/visual quality versus diversity than previous samplers in the large-scale text-to-image Stable Diffusion model pre-trained on LAION $512 \times 512$. Code is available at //github.com/Newbeeer/diffusion_restart_sampling

Feature bagging is a well-established ensembling method which aims to reduce prediction variance by combining predictions of many estimators trained on subsets or projections of features. Here, we develop a theory of feature-bagging in noisy least-squares ridge ensembles and simplify the resulting learning curves in the special case of equicorrelated data. Using analytical learning curves, we demonstrate that subsampling shifts the double-descent peak of a linear predictor. This leads us to introduce heterogeneous feature ensembling, with estimators built on varying numbers of feature dimensions, as a computationally efficient method to mitigate double-descent. Then, we compare the performance of a feature-subsampling ensemble to a single linear predictor, describing a trade-off between noise amplification due to subsampling and noise reduction due to ensembling. Our qualitative insights carry over to linear classifiers applied to image classification tasks with realistic datasets constructed using a state-of-the-art deep learning feature map.

We construct an algorithm for the accurate solution of mixed integer convex quadratic programming, which is the problem of minimizing a convex quadratic function over mixed integer points in a polyhedron. Our algorithm is fixed parameter tractable with parameter the number of integer variables. In particular, when the number of integer variables is fixed, the running time of our algorithm is bounded by a polynomial of the size of the problem. To design our algorithm, we prove a number of fundamental structural and algorithmic results for mixed integer linear and quadratic programming.

We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning flow-type data on networks where edge flows can be characterized by the discrete divergence and curl. Drawing upon the Hodge decomposition, we first develop classes of divergence-free and curl-free edge GPs, suitable for various applications. We then combine them to create \emph{Hodge-compositional edge GPs} that are expressive enough to represent any edge function. These GPs facilitate direct and independent learning for the different Hodge components of edge functions, enabling us to capture their relevance during hyperparameter optimization. To highlight their practical potential, we apply them for flow data inference in currency exchange, ocean flows and water supply networks, comparing them to alternative models.

Hypothesis testing is a central problem in statistical analysis, and there is currently a lack of differentially private tests which are both statistically valid and powerful. In this paper, we develop several new differentially private (DP) nonparametric hypothesis tests. Our tests are based on Kolmogorov-Smirnov, Kuiper, Cram\'er-von Mises, and Wasserstein test statistics, which can all be expressed as a pseudo-metric on empirical cumulative distribution functions (ecdfs), and can be used to test hypotheses on goodness-of-fit, two samples, and paired data. We show that these test statistics have low sensitivity, requiring minimal noise to satisfy DP. In particular, we show that the sensitivity of these test statistics can be expressed in terms of the base sensitivity, which is the pseudo-metric distance between the ecdfs of adjacent databases and is easily calculated. The sampling distribution of our test statistics are distribution-free under the null hypothesis, enabling easy computation of $p$-values by Monte Carlo methods. We show that in several settings, especially with small privacy budgets or heavy-tailed data, our new DP tests outperform alternative nonparametric DP tests.

Semantic communication has emerged as a new deep learning-based communication paradigm that drives the research of end-to-end data transmission in tasks like image classification, and image reconstruction. However, the security problem caused by semantic attacks has not been well explored, resulting in vulnerabilities within semantic communication systems exposed to potential semantic perturbations. In this paper, we propose a secure semantic communication system, DiffuSeC, which leverages the diffusion model and deep reinforcement learning (DRL) to address this issue. With the diffusing module in the sender end and the asymmetric denoising module in the receiver end, the DiffuSeC mitigates the perturbations added by semantic attacks, including data source attacks and channel attacks. To further improve the robustness under unstable channel conditions caused by semantic attacks, we developed a DRL-based channel-adaptive diffusion step selection scheme to achieve stable performance under fluctuating environments. A timestep synchronization scheme is designed for diffusion timestep coordination between the two ends. Simulation results demonstrate that the proposed DiffuSeC shows higher robust accuracy than previous works under a wide range of channel conditions, and can quickly adjust the model state according to signal-to-noise ratios (SNRs) in unstable environments.

In a model inversion (MI) attack, an adversary abuses access to a machine learning (ML) model to infer and reconstruct private training data. Remarkable progress has been made in the white-box and black-box setups, where the adversary has access to the complete model or the model's soft output respectively. However, there is very limited study in the most challenging but practically important setup: Label-only MI attacks, where the adversary only has access to the model's predicted label (hard label) without confidence scores nor any other model information. In this work, we propose LOKT, a novel approach for label-only MI attacks. Our idea is based on transfer of knowledge from the opaque target model to surrogate models. Subsequently, using these surrogate models, our approach can harness advanced white-box attacks. We propose knowledge transfer based on generative modelling, and introduce a new model, Target model-assisted ACGAN (T-ACGAN), for effective knowledge transfer. Our method casts the challenging label-only MI into the more tractable white-box setup. We provide analysis to support that surrogate models based on our approach serve as effective proxies for the target model for MI. Our experiments show that our method significantly outperforms existing SOTA Label-only MI attack by more than 15% across all MI benchmarks. Furthermore, our method compares favorably in terms of query budget. Our study highlights rising privacy threats for ML models even when minimal information (i.e., hard labels) is exposed. Our study highlights rising privacy threats for ML models even when minimal information (i.e., hard labels) is exposed. Our code, demo, models and reconstructed data are available at our project page: //ngoc-nguyen-0.github.io/lokt/