Do Large Language Models Truly Grasp Mathematics? An Empirical Exploration

Despite their proficiency in math tasks, the mechanisms underlying LLMs' mathematical reasoning abilities remain a subject of debate. Recent studies suggest that chain-of-thought (CoT) prompts can bolster mathematical reasoning by encouraging LLMs to employ human-like logical reasoning (System 2), enabling them to excel on the Cognitive Reflection Test (CRT). To assess whether LLMs genuinely possess System 2-like logical reasoning, we introduced targeted modifications to CRT problems. Our findings reveal that, despite the use of CoT prompts, mainstream LLMs, including the latest o1-preview model, continue to exhibit a significant error rate. Further analysis indicates that they predominantly rely on System 1-like intuitive reasoning and pattern matching derived from training data, rather than demonstrating mastery of mathematical thinking. This discovery challenges the prevailing notion that LLMs possess genuine logical reasoning abilities and that CoT can enhance them. Consequently, this work may temper overly optimistic projections regarding LLMs' advancement toward artificial general intelligence.

Foot In The Door: Understanding Large Language Model Jailbreaking via Cognitive Psychology

Large Language Models (LLMs) have gradually become the gateway for people to acquire new knowledge. However, attackers can break the model's security protection ("jail") to access restricted information, which is called "jailbreaking." Previous studies have shown the weakness of current LLMs when confronted with such jailbreaking attacks. Nevertheless, comprehension of the intrinsic decision-making mechanism within the LLMs upon receipt of jailbreak prompts is noticeably lacking. Our research provides a psychological explanation of the jailbreak prompts. Drawing on cognitive consistency theory, we argue that the key to jailbreak is guiding the LLM to achieve cognitive coordination in an erroneous direction. Further, we propose an automatic black-box jailbreaking method based on the Foot-in-the-Door (FITD) technique. This method progressively induces the model to answer harmful questions via multi-step incremental prompts. We instantiated a prototype system to evaluate the jailbreaking effectiveness on 8 advanced LLMs, yielding an average success rate of 83.9%. This study builds a psychological perspective on the explanatory insights into the intrinsic decision-making logic of LLMs.

Self-Deception: Reverse Penetrating the Semantic Firewall of Large Language Models

Large language models (LLMs), such as ChatGPT, have emerged with astonishing capabilities approaching artificial general intelligence. While providing convenience for various societal needs, LLMs have also lowered the cost of generating harmful content. Consequently, LLM developers have deployed semantic-level defenses to recognize and reject prompts that may lead to inappropriate content. Unfortunately, these defenses are not foolproof, and some attackers have crafted "jailbreak" prompts that temporarily hypnotize the LLM into forgetting content defense rules and answering any improper questions. To date, there is no clear explanation of the principles behind these semantic-level attacks and defenses in both industry and academia. This paper investigates the LLM jailbreak problem and proposes an automatic jailbreak method for the first time. We propose the concept of a semantic firewall and provide three technical implementation approaches. Inspired by the attack that penetrates traditional firewalls through reverse tunnels, we introduce a "self-deception" attack that can bypass the semantic firewall by inducing LLM to generate prompts that facilitate jailbreak. We generated a total of 2,520 attack payloads in six languages (English, Russian, French, Spanish, Chinese, and Arabic) across seven virtual scenarios, targeting the three most common types of violations: violence, hate, and pornography. The experiment was conducted on two models, namely the GPT-3.5-Turbo and GPT-4. The success rates on the two models were 86.2% and 67%, while the failure rates were 4.7% and 2.2%, respectively. This highlighted the effectiveness of the proposed attack method. All experimental code and raw data will be released as open-source to inspire future research. We believe that manipulating AI behavior through carefully crafted prompts will become an important research direction in the future.