Differential privacy (DP) is a formal notion that restricts the privacy leakage of an algorithm when running on sensitive data, in which privacy-utility trade-off is one of the central problems in private data analysis. In this work, we investigate the fundamental limits of differential privacy in online learning algorithms and present evidence that separates three types of constraints: no DP, pure DP, and approximate DP. We first describe a hypothesis class that is online learnable under approximate DP but not online learnable under pure DP under the adaptive adversarial setting. This indicates that approximate DP must be adopted when dealing with adaptive adversaries. We then prove that any private online learner must make an infinite number of mistakes for almost all hypothesis classes. This essentially generalizes previous results and shows a strong separation between private and non-private settings since a finite mistake bound is always attainable (as long as the class is online learnable) when there is no privacy requirement.

We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only O(log(1/ε)) versus Ω(poly(1/ε)) iterations to output a sample which is ε-close to the target in χ

In modern deep learning, algorithmic choices (such as width, depth, and learning rate) are known to modulate nuanced resource tradeoffs. This work investigates how these complexities necessarily arise for feature learning in the presence of computational-statistical gaps. We begin by considering offline sparse parity learning, a supervised classification problem which admits a statistical query lower bound for gradient-based training of a multilayer perceptron. This lower bound can be interpreted as a multi-resource tradeoff frontier: successful learning can only occur if one is sufficiently rich (large model), knowledgeable (large dataset), patient (many training iterations), or lucky (many random guesses). We show, theoretically and experimentally, that sparse initialization and increasing network width yield significant improvements in sample efficiency in this setting. Here, width plays the role of parallel search: it amplifies the probability of finding "lottery ticket" neurons, which learn sparse features more sample-efficiently. Finally, we show that the synthetic sparse parity task can be useful as a proxy for real problems requiring axis-aligned feature learning. We demonstrate improved sample efficiency on tabular classification benchmarks by using wide, sparsely-initialized MLP models; these networks sometimes outperform tuned random forests.

The high-dimensional single index model (SIM), which assumes that the response is independent of the predictors given a linear combination of predictors, has drawn attention due to its flexibility and interpretability, but its efficiency is adversely affected by outlying observations and heavy-tailed distributions. This paper introduces a robust procedure by recasting the SIM into a pseudo-linear model with transformed responses. It relaxes the distributional conditions on random errors from sub-Gaussian to more general distributions and thus it is robust with substantial efficiency gain for heavy-tailed random errors. Under this paradigm, we provide asymptotically honest group inference procedures based on the idea of orthogonalization, which enjoys the feature that it does not require the zero and nonzero coefficients to be well-separated. Asymptotic null distribution and bootstrap implementation are both established. Moreover, we develop a multiple testing procedure for determining if the individual coefficients are relevant simultaneously, and show that it is able to control the false discovery rate asymptotically. Numerical results indicate that the new procedures can be highly competitive among existing methods, especially for heavy-tailed errors.

In this case, the lower bound of Ω( κ ln (µ /ϵ)) is well-known in the literature, as shown in [45, 44].

Cultural bias is pervasive in many large language models (LLMs), largely due to the deficiency of data representative of different cultures. Typically, cultural datasets and benchmarks are constructed either by extracting subsets of existing datasets or by aggregating from platforms such as Wikipedia and social media. However, these approaches are highly dependent on real-world data and human annotations, making them costly and difficult to scale. Inspired by cognitive theories on social communication, this paper introduces CulturePark, an LLM-powered multi-agent communication framework for cultural data collection. CulturePark simulates cross-cultural human communication with LLM-based agents playing roles in different cultures. It generates high-quality cross-cultural dialogues encapsulating human beliefs, norms, and customs. Using CulturePark, we generated 41,000 cultural samples to fine-tune eight culture-specific LLMs. We evaluated these models across three downstream tasks: content moderation, cultural alignment, and cultural education. Results show that for content moderation, our GPT-3.5-based

Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data.

Graphs data is crucial for many applications, and much of it exists in the relations described in textual format. As a result, being able to accurately recall and encode a graph described in earlier text is a basic yet pivotal ability that large language models (LLMs) need to demonstrate if they are to perform reasoning tasks that involve graph-structured information. Human performance at graph recall by has been studied by cognitive scientists for decades, and has been found to often exhibit certain structural patterns of bias that align with human handling of social relationships. To date, however, we know little about how LLMs behave in analogous graph recall tasks: do their recalled graphs also exhibit certain biased patterns, and if so, how do they compare with humans and affect other graph reasoning tasks? In this work, we perform the first systematical study of graph recall by LLMs, investigating the accuracy and biased microstructures (local subgraph patterns) in their recall. We find that LLMs not only underperform often in graph recall, but also tend to favor more triangles and alternating 2-paths. Moreover, we find that more advanced LLMs have a striking dependence on the domain that a real-world graph comes from -- by yielding the best recall accuracy when the graph is narrated in a language style consistent with its original domain.

Deployed language models decay over time due to shifting inputs, changing user needs, or emergent world-knowledge gaps. When such problems are identified, we want to make targeted edits while avoiding expensive retraining. However, current model editors, which modify such behaviors of pre-trained models, degrade model performance quickly across multiple, sequential edits. We propose GRACE, a lifelong model editing method, which implements spot-fixes on streaming errors of a deployed model, ensuring minimal impact on unrelated inputs. GRACE writes new mappings into a pre-trained model's latent space, creating a discrete, local codebook of edits without altering model weights. This is the first method enabling thousands of sequential edits using only streaming errors. Our experiments on T5, BERT, and GPT models show GRACE's state-of-the-art performance in making and retaining edits, while generalizing to unseen inputs. Our code is available at github.com/thartvigsen/grace.

Neural network architecture design requires making many crucial decisions. The common desiderata is that similar decisions, with little modifications, can be reused in a variety of tasks and applications. To satisfy that, architectures must provide promising latency and performance trade-offs, support a variety of tasks, scale efficiently with respect to the amounts of data and compute, leverage available data from other tasks, and efficiently support various hardware. To this end, we introduce AsCAN--a hybrid architecture, combining both convolutional and transformer blocks. We revisit the key design principles of hybrid architectures and propose a simple and effective asymmetric architecture, where the distribution of convolutional and transformer blocks is asymmetric, containing more convolutional blocks in the earlier stages, followed by more transformer blocks in later stages. AsCAN supports a variety of tasks: recognition, segmentation, class-conditional image generation, and features a superior trade-off between performance and latency.