A wide range of empirical and theoretical works have shown that overparameterisation can amplify the performance of neural networks. According to the lottery ticket hypothesis, overparameterised networks have an increased chance of containing a sub-network that is well-initialised to solve the task at hand. A more parsimonious approach, inspired by animal learning, consists in guiding the learner towards solving the task by curating the order of the examples, i.e. providing a curriculum. However, this learning strategy seems to be hardly beneficial in deep learning applications. In this work, we undertake an analytical study that connects curriculum learning and overparameterisation. In particular, we investigate their interplay in the online learning setting for a 2-layer network in the XOR-like Gaussian Mixture problem. Our results show that a high degree of overparameterisation -- while simplifying the problem -- can limit the benefit from curricula, providing a theoretical account of the ineffectiveness of curricula in deep learning.

Alignment is the most critical step in building large language models (LLMs) that meet human needs. With the rapid development of LLMs gradually surpassing human capabilities, traditional alignment methods based on human-annotation are increasingly unable to meet the scalability demands. Therefore, there is an urgent need to explore new sources of automated alignment signals and technical approaches. In this paper, we systematically review the recently emerging methods of automated alignment, attempting to explore how to achieve effective, scalable, automated alignment once the capabilities of LLMs exceed those of humans. Specifically, we categorize existing automated alignment methods into 4 major categories based on the sources of alignment signals and discuss the current status and potential development of each category. Additionally, we explore the underlying mechanisms that enable automated alignment and discuss the essential factors that make automated alignment technologies feasible and effective from the fundamental role of alignment.

The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability of neural networks is largely missing. Several recent results have established hardness results for learning feedforward and equivariant neural networks under i.i.d. Gaussian or uniform Boolean data distributions. In this paper, we investigate the hardness of learning under the manifold hypothesis. We ask which minimal assumptions on the curvature and regularity of the manifold, if any, render the learning problem efficiently learnable. We prove that learning is hard under input manifolds of bounded curvature by extending proofs of hardness in the SQ and cryptographic settings for Boolean data inputs to the geometric setting. On the other hand, we show that additional assumptions on the volume of the data manifold alleviate these fundamental limitations and guarantee learnability via a simple interpolation argument. Notable instances of this regime are manifolds which can be reliably reconstructed via manifold learning. Looking forward, we comment on and empirically explore intermediate regimes of manifolds, which have heterogeneous features commonly found in real world data.

The replicability crisis is a major issue across nearly all areas of empirical science, calling for the formal study of replicability in statistics. Motivated in this context, [Impagliazzo, Lei, Pitassi, and Sorrell STOC 2022] introduced the notion of replicable learning algorithms, and gave basic procedures for $1$-dimensional tasks including statistical queries. In this work, we study the computational and statistical cost of replicability for several fundamental high dimensional statistical tasks, including multi-hypothesis testing and mean estimation. Our main contribution establishes a computational and statistical equivalence between optimal replicable algorithms and high dimensional isoperimetric tilings. As a consequence, we obtain matching sample complexity upper and lower bounds for replicable mean estimation of distributions with bounded covariance, resolving an open problem of [Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sivakumar, and Sorrell, STOC2023] and for the $N$-Coin Problem, resolving a problem of [Karbasi, Velegkas, Yang, and Zhou, NeurIPS2023] up to log factors. While our equivalence is computational, allowing us to shave log factors in sample complexity from the best known efficient algorithms, efficient isoperimetric tilings are not known. To circumvent this, we introduce several relaxed paradigms that do allow for sample and computationally efficient algorithms, including allowing pre-processing, adaptivity, and approximate replicability. In these cases we give efficient algorithms matching or beating the best known sample complexity for mean estimation and the coin problem, including a generic procedure that reduces the standard quadratic overhead of replicability to linear in expectation.

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based approaches rely primarily on generative models that yield exact sample likelihoods. This work introduces a method that lifts this restriction and opens the possibility to employ highly expressive latent variable models like diffusion models. Our approach is conceptually based on a loss that upper bounds the reverse Kullback-Leibler divergence and evades the requirement of exact sample likelihoods. We experimentally validate our approach in data-free Combinatorial Optimization and demonstrate that our method achieves a new state-of-the-art on a wide range of benchmark problems.

We study the problem of gradient descent learning of a single-index target function $f_*(\boldsymbol{x}) = \textstyle\sigma_*\left(\langle\boldsymbol{x},\boldsymbol{\theta}\rangle\right)$ under isotropic Gaussian data in $\mathbb{R}^d$, where the link function $\sigma_*:\mathbb{R}\to\mathbb{R}$ is an unknown degree $q$ polynomial with information exponent $p$ (defined as the lowest degree in the Hermite expansion). Prior works showed that gradient-based training of neural networks can learn this target with $n\gtrsim d^{\Theta(p)}$ samples, and such statistical complexity is predicted to be necessary by the correlational statistical query lower bound. Surprisingly, we prove that a two-layer neural network optimized by an SGD-based algorithm learns $f_*$ of arbitrary polynomial link function with a sample and runtime complexity of $n \asymp T \asymp C(q) \cdot d\mathrm{polylog} d$, where constant $C(q)$ only depends on the degree of $\sigma_*$, regardless of information exponent; this dimension dependence matches the information theoretic limit up to polylogarithmic factors. Core to our analysis is the reuse of minibatch in the gradient computation, which gives rise to higher-order information beyond correlational queries.

We establish a new model-agnostic optimization framework for out-of-distribution generalization via multicalibration, a criterion that ensures a predictor is calibrated across a family of overlapping groups. Multicalibration is shown to be associated with robustness of statistical inference under covariate shift. We further establish a link between multicalibration and robustness for prediction tasks both under and beyond covariate shift. We accomplish this by extending multicalibration to incorporate grouping functions that consider covariates and labels jointly. This leads to an equivalence of the extended multicalibration and invariance, an objective for robust learning in existence of concept shift. We show a linear structure of the grouping function class spanned by density ratios, resulting in a unifying framework for robust learning by designing specific grouping functions. We propose MC-Pseudolabel, a post-processing algorithm to achieve both extended multicalibration and out-of-distribution generalization. The algorithm, with lightweight hyperparameters and optimization through a series of supervised regression steps, achieves superior performance on real-world datasets with distribution shift.

Current language models decode text token by token according to probabilistic distribution, and determining the appropriate candidates for the next token is crucial to ensure generation quality. This study introduces adaptive decoding, a mechanism that dynamically empowers language models to ascertain a sensible candidate set during generation. Specifically, we introduce an entropy-based metric called confidence and conceptualize determining the optimal candidate set as a confidence-increasing process. The rationality of including a token in the candidate set is assessed by leveraging the increment of confidence. Experimental results reveal that our method balances diversity and coherence well. The human evaluation shows that our method can generate human-preferred text. Additionally, our method can potentially improve the reasoning ability of language models.

SARS-CoV-2, the highly contagious pathogen responsible for the COVID-19 pandemic, has persistent effects that begin four weeks after initial infection and last for an undetermined duration. These chronic effects are more harmful than acute ones. This review explores the long-term impact of the virus on various human organs, including the pulmonary, cardiovascular, neurological, reproductive, gastrointestinal, musculoskeletal, endocrine, and lymphoid systems, particularly in older adults. Regarding diagnosis, RT-PCR is the gold standard for detecting COVID-19, though it requires specialized equipment, skilled personnel, and considerable time to produce results. To address these limitations, artificial intelligence in imaging and microfluidics technologies offers promising alternatives for diagnosing COVID-19 efficiently. Pharmacological and non-pharmacological strategies are effective in mitigating the persistent impacts of COVID-19. These strategies enhance immunity in post-COVID-19 patients by reducing cytokine release syndrome, improving T cell response, and increasing the circulation of activated natural killer and CD8 T cells in blood and tissues. This, in turn, alleviates symptoms such as fever, nausea, fatigue, muscle weakness, and pain. Vaccines, including inactivated viral, live attenuated viral, protein subunit, viral vectored, mRNA, DNA, and nanoparticle vaccines, significantly reduce the adverse long-term effects of the virus. However, no vaccine has been reported to provide lifetime protection against COVID-19. Consequently, protective measures such as physical distancing, mask usage, and hand hygiene remain essential strategies. This review offers a comprehensive understanding of the persistent effects of COVID-19 on individuals of varying ages, along with insights into diagnosis, treatment, vaccination, and future preventative measures against the spread of SARS-CoV-2.

While there are a plethora of methods for link prediction in knowledge graphs, state-of-the-art approaches are often black box, obfuscating model reasoning and thereby limiting the ability of users to make informed decisions about model predictions. Recently, methods have emerged to generate prediction explanations for Knowledge Graph Embedding models, a widely-used class of methods for link prediction. The question then becomes, how well do these explanation systems work? To date this has generally been addressed anecdotally, or through time-consuming user research. In this work, we present an in-depth exploration of a simple link prediction explanation method we call LinkLogic, that surfaces and ranks explanatory information used for the prediction. Importantly, we construct the first-ever link prediction explanation benchmark, based on family structures present in the FB13 dataset. We demonstrate the use of this benchmark as a rich evaluation sandbox, probing LinkLogic quantitatively and qualitatively to assess the fidelity, selectivity and relevance of the generated explanations. We hope our work paves the way for more holistic and empirical assessment of knowledge graph prediction explanation methods in the future.