We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes.

Consider ascenario inwhich data items are being generated one by one, e.g., IP traffic monitoring or web searches.

Human physical reasoning relies on internal "body" representations -- coarse, volumetric approximations that capture an object's extent and support intuitive predictions about motion and physics. While psychophysical evidence suggests humans use such coarse representations, their internal structure remains largely unknown. Here we test whether vision models trained for segmentation develop comparable representations. We adapt a psychophysical experiment conducted with 50 human participants to a semantic segmentation task and test a family of seven segmentation networks, varying in size. We find that smaller models naturally form human-like coarse body representations, whereas larger models tend toward overly detailed, fine-grain encodings. Our results demonstrate that coarse representations can emerge under limited computational resources, and that machine representations can provide a scalable path toward understanding the structure of physical reasoning in the brain.

In recent years, evaluating the Theory of Mind (ToM) capabilities of large language models (LLMs) has received significant attention within the research community. As the field rapidly evolves, navigating the diverse approaches and methodologies has become increasingly complex. This systematic review synthesizes current efforts to assess LLMs' ability to perform ToM tasks, an essential aspect of human cognition involving the attribution of mental states to oneself and others. Despite notable advancements, the proficiency of LLMs in ToM remains a contentious issue. By categorizing benchmarks and tasks through a taxonomy rooted in cognitive science, this review critically examines evaluation techniques, prompting strategies, and the inherent limitations of LLMs in replicating human-like mental state reasoning. A recurring theme in the literature reveals that while LLMs demonstrate emerging competence in ToM tasks, significant gaps persist in their emulation of human cognitive abilities.

We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the Stein-Haff identity, an extension of the classical Stein's identity used in previous fingerprinting lemma arguments.

Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms. Still, there are many problems in differential privacy for which we don't know suitable lower bounds, and even for problems that we do, the lower bounds are not smooth, and usually become vacuous when the error is larger than some threshold. In this work, we present a new framework and tools to generate smooth lower bounds on the sample complexity of differentially private algorithms satisfying very weak accuracy. We illustrate the applicability of our method by providing new lower bounds in various settings: 1. A tight lower bound for DP averaging in the low-accuracy regime, which in particular implies a lower bound for the private 1-cluster problem introduced by Nissim, Stemmer, and Vadhan (PODS 2016). 2. A lower bound on the additive error of DP algorithms for approximate k-means clustering, as a function of the multiplicative error, which is tight for a constant multiplication error. 3. A lower bound for estimating the top singular vector of a matrix under DP in low-accuracy regimes, which is a special case of DP subspace estimation studied by Singhal and Steinke (NeurIPS 2021). Our main technique is to apply a padding-and-permuting transformation to a fingerprinting code. However, rather than proving our results using a black-box access to an existing fingerprinting code (e.g., Tardos' code), we develop a new fingerprinting lemma that is stronger than those of Dwork et al. (FOCS 2015) and Bun et al. (SODA 2017), and prove our lower bounds directly from the lemma. Our lemma, in particular, gives a simpler fingerprinting code construction with optimal rate (up to polylogarithmic factors) that is of independent interest.

We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the covariance of a Gaussian up to spectral error $\alpha$ requires $\tilde{\Omega}\left(\frac{d^{3/2}}{\alpha \varepsilon} + \frac{d}{\alpha^2}\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\alpha \le O\left(\frac{1}{\sqrt{d}}\right)$, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded $k$th moments requires $\tilde{\Omega}\left(\frac{d}{\alpha^{k/(k-1)} \varepsilon} + \frac{d}{\alpha^2}\right)$ samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of $k = 2$. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples.

Theory of Mind (ToM), the capacity to comprehend the mental states of distinct individuals, is essential for numerous practical applications. With the development of large language models (LLMs), there is a heated debate about whether they are able to perform ToM tasks. Previous studies have used different tasks and prompts to test the ToM on LLMs and the results are inconsistent: some studies asserted these models are capable of exhibiting ToM, while others suggest the opposite. In this study, We present ToMChallenges, a dataset for comprehensively evaluating the Theory of Mind based on the Sally-Anne and Smarties tests with a diverse set of tasks. In addition, we also propose an auto-grader to streamline the answer evaluation process. We tested three models: davinci, turbo, and gpt-4. Our evaluation results and error analyses show that LLMs have inconsistent behaviors across prompts and tasks. Performing the ToM tasks robustly remains a challenge for the LLMs. In addition, our paper wants to raise awareness in evaluating the ToM in LLMs and we want to invite more discussion on how to design the prompts and tasks for ToM tasks that can better assess the LLMs' ability.

The escalating debate on AI's capabilities warrants developing reliable metrics to assess machine "intelligence". Recently, many anecdotal examples were used to suggest that newer large language models (LLMs) like ChatGPT and GPT-4 exhibit Neural Theory-of-Mind (N-ToM); however, prior work reached conflicting conclusions regarding those abilities. We investigate the extent of LLMs' N-ToM through an extensive evaluation on 6 tasks and find that while LLMs exhibit certain N-ToM abilities, this behavior is far from being robust. We further examine the factors impacting performance on N-ToM tasks and discover that LLMs struggle with adversarial examples, indicating reliance on shallow heuristics rather than robust ToM abilities. We caution against drawing conclusions from anecdotal examples, limited benchmark testing, and using human-designed psychological tests to evaluate models.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)--Project-ID 262513311--SFB 1187 Media of Cooperation.