arXiv subjects

Peter S. Park

Publications and source records attributed to Peter S. Park.

16 recordsLinked to original sources

arXiv2026

When Large Language Models are More PersuasiveThan Incentivized Humans, and Why

Large Language Models (LLMs) have been shown to be highly persuasive, but when and why they outperform humans is still an open question. We compare the persuasiveness of two LLMs (Claude 3.5 Sonnet and DeepSeek v3) against humans who had incentives to persuade, using an interactive, real-time conversational setting. We demonstrate that LLMs persuasive superiority is context-dependent: it depends on whether the persuasion attempt is truthful (towards the right answer) or deceptive (towards the wrong answer) and on the LLM model, and wanes over repeated interactions (unlike human persuasiveness). In our first large-scale experiment, humans vs LLMs (Claude 3.5 Sonnet) interacted with other humans who were completing an online quiz for a reward, attempting to persuade them toward a given (either correct or incorrect) answer. Claude was more persuasive than incentivized human persuaders both in truthful and deceptive contexts and it significantly increased accuracy if persuasion was truthful, but decreased it if persuasion was deceptive. In a follow-up experiment with Deepseek v3, we replicated the findings about accuracy but found greater LLM persuasiveness only if the persuasion was deceptive. Linguistic analyses of the persuaders texts suggest that these effects may be due to LLMs expressing higher conviction than humans.

cs.CL↗

arXiv2024

AI-Augmented Predictions: LLM Assistants Improve Human Forecasting Accuracy

Large language models (LLMs) match and sometimes exceeding human performance in many domains. This study explores the potential of LLMs to augment human judgement in a forecasting task. We evaluate the effect on human forecasters of two LLM assistants: one designed to provide high-quality ("superforecasting") advice, and the other designed to be overconfident and base-rate neglecting, thus providing noisy forecasting advice. We compare participants using these assistants to a control group that received a less advanced model that did not provide numerical predictions or engaged in explicit discussion of predictions. Participants (N = 991) answered a set of six forecasting questions and had the option to consult their assigned LLM assistant throughout. Our preregistered analyses show that interacting with each of our frontier LLM assistants significantly enhances prediction accuracy by between 24 percent and 28 percent compared to the control group. Exploratory analyses showed a pronounced outlier effect in one forecasting item, without which we find that the superforecasting assistant increased accuracy by 41 percent, compared with 29 percent for the noisy assistant. We further examine whether LLM forecasting augmentation disproportionately benefits less skilled forecasters, degrades the wisdom-of-the-crowd by reducing prediction diversity, or varies in effectiveness with question difficulty. Our data do not consistently support these hypotheses. Our results suggest that access to a frontier LLM assistant, even a noisy one, can be a helpful decision aid in cognitively demanding tasks compared to a less powerful model that does not provide specific forecasting advice. However, the effects of outliers suggest that further research into the robustness of this pattern is needed.

cs.CY↗

arXiv2024

Wisdom of the Silicon Crowd: LLM Ensemble Prediction Capabilities Rival Human Crowd Accuracy

Human forecasting accuracy in practice relies on the 'wisdom of the crowd' effect, in which predictions about future events are significantly improved by aggregating across a crowd of individual forecasters. Past work on the forecasting ability of large language models (LLMs) suggests that frontier LLMs, as individual forecasters, underperform compared to the gold standard of a human crowd forecasting tournament aggregate. In Study 1, we expand this research by using an LLM ensemble approach consisting of a crowd of twelve LLMs. We compare the aggregated LLM predictions on 31 binary questions to that of a crowd of 925 human forecasters from a three-month forecasting tournament. Our preregistered main analysis shows that the LLM crowd outperforms a simple no-information benchmark and is not statistically different from the human crowd. In exploratory analyses, we find that these two approaches are equivalent with respect to medium-effect-size equivalence bounds. We also observe an acquiescence effect, with mean model predictions being significantly above 50%, despite an almost even split of positive and negative resolutions. Moreover, in Study 2, we test whether LLM predictions (of GPT-4 and Claude 2) can be improved by drawing on human cognitive output. We find that both models' forecasting accuracy benefits from exposure to the median human prediction as information, improving accuracy by between 17% and 28%: though this leads to less accurate predictions than simply averaging human and machine forecasts. Our results suggest that LLMs can achieve forecasting accuracy rivaling that of human crowd forecasting tournaments: via the simple, practically applicable method of forecast aggregation. This replicates the 'wisdom of the crowd' effect for LLMs, and opens up their use for a variety of applications throughout society.

cs.CY↗

arXiv2023

Divide-and-Conquer Dynamics in AI-Driven Disempowerment

AI companies are attempting to create AI systems that outperform humans at most economically valuable work. Current AI models are already automating away the livelihoods of some artists, actors, and writers. But there is infighting between those who prioritize current harms and future harms. We construct a game-theoretic model of conflict to study the causes and consequences of this disunity. Our model also helps explain why throughout history, stakeholders sharing a common threat have found it advantageous to unite against it, and why the common threat has in turn found it advantageous to divide and conquer. Under realistic parameter assumptions, our model makes several predictions that find preliminary corroboration in the historical-empirical record. First, current victims of AI-driven disempowerment need the future victims to realize that their interests are also under serious and imminent threat, so that future victims are incentivized to support current victims in solidarity. Second, the movement against AI-driven disempowerment can become more united, and thereby more likely to prevail, if members believe that their efforts will be successful as opposed to futile. Finally, the movement can better unite and prevail if its members are less myopic. Myopic members prioritize their future well-being less than their present well-being, and are thus disinclined to solidarily support current victims today at personal cost, even if this is necessary to counter the shared threat of AI-driven disempowerment.

cs.CY↗

arXiv2023

Devising and Detecting Phishing: Large Language Models vs. Smaller Human Models

AI programs, built using large language models, make it possible to automatically create phishing emails based on a few data points about a user. They stand in contrast to traditional phishing emails that hackers manually design using general rules gleaned from experience. The V-Triad is an advanced set of rules for manually designing phishing emails to exploit our cognitive heuristics and biases. In this study, we compare the performance of phishing emails created automatically by GPT-4 and manually using the V-Triad. We also combine GPT-4 with the V-Triad to assess their combined potential. A fourth group, exposed to generic phishing emails, was our control group. We utilized a factorial approach, sending emails to 112 randomly selected participants recruited for the study. The control group emails received a click-through rate between 19-28%, the GPT-generated emails 30-44%, emails generated by the V-Triad 69-79%, and emails generated by GPT and the V-Triad 43-81%. Each participant was asked to explain why they pressed or did not press a link in the email. These answers often contradict each other, highlighting the need for personalized content. The cues that make one person avoid phishing emails make another person fall for them. Next, we used four popular large language models (GPT, Claude, PaLM, and LLaMA) to detect the intention of phishing emails and compare the results to human detection. The language models demonstrated a strong ability to detect malicious intent, even in non-obvious phishing emails. They sometimes surpassed human detection, although often being slightly less accurate than humans. Finally, we make an analysis of the economic aspects of AI-enabled phishing attacks, showing how large language models can increase the incentives of phishing and spear phishing by reducing their costs.

cs.CR↗

arXiv2023

Large Language Model Prediction Capabilities: Evidence from a Real-World Forecasting Tournament

Accurately predicting the future would be an important milestone in the capabilities of artificial intelligence. However, research on the ability of large language models to provide probabilistic predictions about future events remains nascent. To empirically test this ability, we enrolled OpenAI's state-of-the-art large language model, GPT-4, in a three-month forecasting tournament hosted on the Metaculus platform. The tournament, running from July to October 2023, attracted 843 participants and covered diverse topics including Big Tech, U.S. politics, viral outbreaks, and the Ukraine conflict. Focusing on binary forecasts, we show that GPT-4's probabilistic forecasts are significantly less accurate than the median human-crowd forecasts. We find that GPT-4's forecasts did not significantly differ from the no-information forecasting strategy of assigning a 50% probability to every question. We explore a potential explanation, that GPT-4 might be predisposed to predict probabilities close to the midpoint of the scale, but our data do not support this hypothesis. Overall, we find that GPT-4 significantly underperforms in real-world predictive tasks compared to median human-crowd forecasts. A potential explanation for this underperformance is that in real-world forecasting tournaments, the true answers are genuinely unknown at the time of prediction; unlike in other benchmark tasks like professional exams or time series forecasting, where strong performance may at least partly be due to the answers being memorized from the training data. This makes real-world forecasting tournaments an ideal environment for testing the generalized reasoning and prediction capabilities of artificial intelligence going forward.

cs.CY↗

arXiv2023

Diminished Diversity-of-Thought in a Standard Large Language Model

We test whether Large Language Models (LLMs) can be used to simulate human participants in social-science studies. To do this, we run replications of 14 studies from the Many Labs 2 replication project with OpenAI's text-davinci-003 model, colloquially known as GPT3.5. Based on our pre-registered analyses, we find that among the eight studies we could analyse, our GPT sample replicated 37.5% of the original results and 37.5% of the Many Labs 2 results. However, we were unable to analyse the remaining six studies due to an unexpected phenomenon we call the "correct answer" effect. Different runs of GPT3.5 answered nuanced questions probing political orientation, economic preference, judgement, and moral philosophy with zero or near-zero variation in responses: with the supposedly "correct answer." In one exploratory follow-up study, we found that a "correct answer" was robust to changing the demographic details that precede the prompt. In another, we found that most but not all "correct answers" were robust to changing the order of answer choices. One of our most striking findings occurred in our replication of the Moral Foundations Theory survey results, where we found GPT3.5 identifying as a political conservative in 99.6% of the cases, and as a liberal in 99.3% of the cases in the reverse-order condition. However, both self-reported 'GPT conservatives' and 'GPT liberals' showed right-leaning moral foundations. Our results cast doubts on the validity of using LLMs as a general replacement for human participants in the social sciences. Our results also raise concerns that a hypothetical AI-led future may be subject to a diminished diversity-of-thought.

cs.HC↗

arXiv2023

AI Deception: A Survey of Examples, Risks, and Potential Solutions

This paper argues that a range of current AI systems have learned how to deceive humans. We define deception as the systematic inducement of false beliefs in the pursuit of some outcome other than the truth. We first survey empirical examples of AI deception, discussing both special-use AI systems (including Meta's CICERO) built for specific competitive situations, and general-purpose AI systems (such as large language models). Next, we detail several risks from AI deception, such as fraud, election tampering, and losing control of AI systems. Finally, we outline several potential solutions to the problems posed by AI deception: first, regulatory frameworks should subject AI systems that are capable of deception to robust risk-assessment requirements; second, policymakers should implement bot-or-not laws; and finally, policymakers should prioritize the funding of relevant research, including tools to detect AI deception and to make AI systems less deceptive. Policymakers, researchers, and the broader public should work proactively to prevent AI deception from destabilizing the shared foundations of our society.

cs.CY↗

arXiv2019

Conjugacy growth of commutators

For the free group $F_r$ on $r>1$ generators (respectively, the free product $G_1 * G_2$ of two nontrivial finite groups $G_1$ and $G_2$), we obtain the asymptotic for the number of conjugacy classes of commutators in $F_r$ (respectively, $G_1 * G_2$) with a given word length in a fixed set of free generators (respectively, the set of generators given by the nontrivial elements of $G_1$ and $G_2$). Our result is proven by using the classification of commutators in free groups and in free products by Wicks, and builds on the works of Rivin and Sharp, who asymptotically counted the conjugacy classes of commutator-subgroup elements in $F_r$ with a given word length.

math.GR↗

arXiv2019

Probability laws for the distribution of geometric lengths when sampling by a random walk in a Fuchsian fundamental group

Let $S=Γ\backslash \mathbb{H}$ be a hyperbolic surface of finite topological type, such that the Fuchsian group $Γ\le \operatorname{PSL}_2(\mathbb{R})$ is non-elementary, and consider any generating set $\mathfrak S$ of $Γ$. When sampling by an $n$-step random walk in $π_1(S) \cong Γ$ with each step given by an element in $\mathfrak S$, the subset of this sampled set comprised of hyperbolic elements approaches full measure as $n\to \infty$, and for this subset, the distribution of geometric lengths obeys a Law of Large Numbers, Central Limit Theorem, Large Deviations Principle, and Local Limit Theorem. We give a proof of this known theorem using Gromov's theorem on translation lengths of Gromov-hyperbolic groups.

math.GT↗

arXiv2017

Bounded Gaps Between Products of Distinct Primes

Let $r \ge 2$ be an integer. We adapt the Maynard-Tao sieve to produce the asymptotically best-known bounded gaps between products of $r$ distinct primes. Our result applies to positive-density subsets of the primes that satisfy certain equidistribution conditions. This improves on the work of Thorne and Sono.

math.NT↗

arXiv2016

The van der Waerden complex

We introduce the van der Waerden complex ${\rm vdW}(n,k)$ defined as the simplicial complex whose facets correspond to arithmetic progressions of length $k$ in the vertex set $\{1, 2, \ldots, n\}$. We show the van der Waerden complex ${\rm vdW}(n,k)$ is homotopy equivalent to a $CW$-complex whose cells asymptotically have dimension at most $\log k / \log \log k$. Furthermore, we give bounds on $n$ and $k$ which imply that the van der Waerden complex is contractible.

math.CO↗

arXiv2016

The "Riemann Hypothesis" is True for Period Polynomials of Almost All Newforms

The period polynomial $r_f(z)$ for a weight $k \geq 3$ newform $f \in S_k(Γ_0(N),χ)$ is the generating function for special values of $L(s,f)$. The functional equation for $L(s, f)$ induces a functional equation on $r_f(z)$. Jin, Ma, Ono, and Soundararajan proved that for all newforms $f$ of even weight $k \ge 4$ and trivial nebetypus, the "Riemann Hypothesis" holds for $r_f(z)$: that is, all roots of $r_f(z)$ lie on the circle of symmetry $|z| =1/\sqrt{N}$. We generalize their methods to prove that this phenomenon holds for all but possibly finitely many newforms $f$ of weight $k \ge 3$ with any nebentypus. We also show that the roots of $r_f(z)$ are equidistributed if $N$ or $k$ is sufficiently large.

math.NT↗

arXiv2016

Elliptic Curve Variants of the Least Quadratic Nonresidue Problem and Linnik's Theorem

Let $E_1$ and $E_2$ be $\overline{\mathbb{Q}}$-nonisogenous, semistable elliptic curves over $\mathbb{Q}$, having respective conductors $N_{E_1}$ and $N_{E_2}$ and both without complex multiplication. For each prime $p$, denote by $a_{E_i}(p) := p+1-\#E_i(\mathbb{F}_p)$ the trace of Frobenius. Under the assumption of the Generalized Riemann Hypothesis (GRH) for the convolved symmetric power $L$-functions $L(s, \mathrm{Sym}^i E_1\otimes\mathrm{Sym}^j E_2)$ where $i,j\in\{0,1,2\}$, we prove an explicit result that can be stated succinctly as follows: there exists a prime $p\nmid N_{E_1}N_{E_2}$ such that $a_{E_1}(p)a_{E_2}(p)<0$ and \[ p < \big( (32+o(1))\cdot \log N_{E_1} N_{E_2}\big)^2. \] This improves and makes explicit a result of Bucur and Kedlaya. Now, if $I\subset[-1,1]$ is a subinterval with Sato-Tate measure $μ$ and if the symmetric power $L$-functions $L(s, \mathrm{Sym}^k E_1)$ are functorial and satisfy GRH for all $k \le 8/μ$, we employ similar techniques to prove an explicit result that can be stated succinctly as follows: there exists a prime $p\nmid N_{E_1}$ such that $a_{E_1}(p)/(2\sqrt{p})\in I$ and \[ p < \left((21+o(1)) \cdot μ^{-2}\log (N_{E_1}/μ)\right)^2. \]

math.NT↗

arXiv2015

On Logarithmically Benford Sequences

Let $\mathcal{I} \subset \mathbb{N}$ be an infinite subset, and let $\{a_i\}_{i \in \mathcal{I}}$ be a sequence of nonzero real numbers indexed by $\mathcal{I}$ such that there exist positive constants $m, C_1$ for which $|a_i| \leq C_1 \cdot i^m$ for all $i \in \mathcal{I}$. Furthermore, let $c_i \in [-1,1]$ be defined by $c_i = \frac{a_i}{C_1 \cdot i^m}$ for each $i \in \mathcal{I}$, and suppose the $c_i$'s are equidistributed in $[-1,1]$ with respect to a continuous, symmetric probability measure $μ$. In this paper, we show that if $\mathcal{I} \subset \mathbb{N}$ is not too sparse, then the sequence $\{a_i\}_{i \in \mathcal{I}}$ fails to obey Benford's Law with respect to arithmetic density in any sufficiently large base, and in fact in any base when $μ([0,t])$ is a strictly convex function of $t \in (0,1)$. Nonetheless, we also provide conditions on the density of $\mathcal{I} \subset \mathbb{N}$ under which the sequence $\{a_i\}_{i \in \mathcal{I}}$ satisfies Benford's Law with respect to logarithmic density in every base. As an application, we apply our general result to study Benford's Law-type behavior in the leading digits of Frobenius traces of newforms of positive, even weight. Our methods of proof build on the work of Jameson, Thorner, and Ye, who studied the particular case of newforms without complex multiplication.

math.NT↗

arXiv2015

Linnik's Theorem for Sato-Tate Laws on Elliptic Curves with Complex Multiplication

Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication (CM), and for each prime $p$ of good reduction, let $a_E(p) = p + 1 - \#E(\mathbb{F}_p)$ denote the trace of Frobenius. By the Hasse bound, $a_E(p) = 2\sqrt{p} \cos θ_p$ for a unique $θ_p \in [0, π]$. In this paper, we prove that the least prime $p$ such that $θ_p \in [α, β] \subset [0, π]$ satisfies \[ p \ll \left(\frac{N_E}{β- α}\right)^A, \] where $N_E$ is the conductor of $E$ and the implied constant and exponent $A > 2$ are absolute and effectively computable. Our result is an analogue for CM elliptic curves of Linnik's Theorem for arithmetic progressions, which states that the least prime $p \equiv a \pmod q$ for $(a,q)=1$ satisfies $p \ll q^L$ for an absolute constant $L > 0$.

math.NT↗