Ladder is a novel approach for improving large language model (LLM) performance on complex tasks by recursively decomposing problems into smaller, more manageable subproblems. The model generates a plan to solve the main problem, breaking it down into subproblems which are then individually tackled. Solutions to subproblems are then combined, potentially through further decomposition and synthesis steps, until a final solution to the original problem is reached. This recursive decomposition process, which mimics human problem-solving strategies, enables LLMs to address tasks exceeding their direct capabilities. The approach is evaluated on various mathematical reasoning and programming tasks, demonstrating significant performance improvements compared to standard prompting methods.
The paper "Is this the simplest (and most surprising) sorting algorithm ever?" introduces the "Sleep Sort" algorithm, a conceptually simple, albeit impractical, sorting method. It relies on spawning a separate thread for each element to be sorted. Each thread sleeps for a duration proportional to the element's value and then outputs the element. Thus, smaller elements are outputted first, resulting in a sorted sequence. While intriguing in its simplicity, Sleep Sort's correctness depends on precise timing and suffers from significant limitations, including poor performance for large datasets, inability to handle negative or duplicate values directly, and reliance on system-specific thread scheduling. Its main contribution is as a thought-provoking curiosity rather than a practical sorting algorithm.
Hacker News users discuss the "Mirror Sort" algorithm, expressing skepticism about its novelty and practicality. Several commenters point out prior art, referencing similar algorithms like "Odd-Even Sort" and existing work on sorting networks. There's debate about the algorithm's true complexity, with some arguing the reliance on median-finding hides significant cost. Others question the value of minimizing comparisons when other operations, like swaps or data movement, dominate the performance in real-world scenarios. The overall sentiment leans towards viewing "Mirror Sort" as an interesting theoretical exercise rather than a practical breakthrough. A few users note its potential educational value for understanding sorting network concepts.
Researchers report observing room-temperature superconductivity (above 400K) in graphite powder samples. They claim to have isolated superconducting particles from non-superconducting graphite by applying a magnetic field gradient, which levitated a small fraction of the material. These levitated particles exhibited diamagnetic behavior consistent with the Meissner effect, a key characteristic of superconductors. While the observed effect is intriguing, the authors acknowledge the need for further investigation and independent verification to confirm these extraordinary claims.
Hacker News users discussed the extraordinary claims of room-temperature superconductivity in the linked arXiv preprint with heavy skepticism. Several commenters pointed to the lack of details about the experimental setup and methodology, making replication difficult. The unusual magnetic sorting technique employed raised questions, with some suggesting it might be separating impurities rather than different superconducting phases. Others highlighted the history of similar unsubstantiated claims of room-temperature superconductivity, leading to a general atmosphere of "wait and see." A few commenters offered alternative explanations for the observed phenomena, including ferromagnetism or diamagnetism in impurities. Overall, the prevailing sentiment was cautious disbelief pending further evidence and scrutiny from the scientific community.
Large language models (LLMs) can improve their future prediction abilities through self-improvement loops involving world modeling and action planning. Researchers demonstrated this by tasking LLMs with predicting future states in a simulated text-based environment. The LLMs initially used their internal knowledge, then refined their predictions by taking actions, observing the outcomes, and updating their world models based on these experiences. This iterative process allows the models to learn the dynamics of the environment and significantly improve the accuracy of their future predictions, exceeding the performance of supervised learning methods trained on environment logs. This research highlights the potential of LLMs to learn complex systems and make accurate predictions through active interaction and adaptation, even with limited initial knowledge of the environment.
Hacker News users discuss the implications of LLMs learning to predict the future by self-improving their world models. Some express skepticism, questioning whether "predicting the future" is an accurate framing, arguing it's more akin to sophisticated pattern matching within a limited context. Others find the research promising, highlighting the potential for LLMs to reason and plan more effectively. There's concern about the potential for these models to develop undesirable biases or become overly reliant on simulated data. The ethics of allowing LLMs to interact and potentially manipulate real-world systems are also raised. Several commenters debate the meaning of intelligence and consciousness in the context of these advancements, with some suggesting this work represents a significant step toward more general AI. A few users delve into technical details, discussing the specific methods used in the research and potential limitations.
This paper investigates how pre-trained large language models (LLMs) perform integer addition. It finds that LLMs, despite lacking explicit training on arithmetic, learn to leverage positional encoding based on Fourier features to represent numbers internally. This allows them to achieve surprisingly good accuracy on addition tasks, particularly within the range of numbers present in their training data. The authors demonstrate this by analyzing attention patterns and comparing LLM performance with models using alternative positional encodings. They also show how manipulating or ablating these Fourier features directly impacts the models' ability to add, strongly suggesting that LLMs have implicitly learned a form of Fourier-based arithmetic.
Hacker News users discussed the surprising finding that LLMs appear to use Fourier features internally to perform addition, as indicated by the linked paper. Several commenters expressed fascination with this emergent behavior, highlighting how LLMs discover and utilize mathematical concepts without explicit instruction. Some questioned the paper's methodology and the strength of its conclusions, suggesting alternative explanations or calling for further research to solidify the claims. A few users also discussed the broader implications of this discovery for understanding how LLMs function and how they might be improved. The potential link to the Fourier-based positional encoding used in Transformer models was also noted as a possible contributing factor.
ArXivTok presents arXiv research papers in a short-video format, aiming to make complex topics more accessible. The site leverages AI to summarize papers and generates engaging videos with visuals, voiceover narration, and background music. This allows users to quickly grasp the core ideas of a paper without needing to delve into the full text, offering a faster and potentially more engaging way to explore scientific research.
HN users generally praised ArXivTok for its accessibility, making dense academic papers more digestible. Several commenters appreciated the use of TikTok's format, highlighting its effectiveness in quickly conveying complex information. Some expressed concern over potential simplification or misrepresentation of research, but the prevailing sentiment was positive, viewing ArXivTok as a valuable tool for disseminating scientific knowledge to a wider audience and sparking curiosity. A few users suggested improvements like linking directly to the original papers and providing more context around the research being presented. There was also discussion about the broader implications of using social media platforms like TikTok for scientific communication.
This paper explores the potential of Large Language Models (LLMs) as tools for mathematicians. It examines how LLMs can assist with tasks like generating conjectures, finding proofs, simplifying expressions, and translating between mathematical formalisms. While acknowledging current limitations such as occasional inaccuracies and a lack of deep mathematical understanding, the authors demonstrate LLMs' usefulness in exploring mathematical ideas, automating tedious tasks, and providing educational support. They argue that future development focusing on formal reasoning and symbolic computation could significantly enhance LLMs' capabilities, ultimately leading to a more symbiotic relationship between mathematicians and AI. The paper also discusses the ethical implications of using LLMs in mathematics, including concerns about plagiarism and the potential displacement of human mathematicians.
Hacker News users discussed the potential for LLMs to assist mathematicians, but also expressed skepticism. Some commenters highlighted LLMs' current weaknesses in formal logic and rigorous proof construction, suggesting they're more useful for brainstorming or generating initial ideas than for producing finalized proofs. Others pointed out the importance of human intuition and creativity in mathematics, which LLMs currently lack. The discussion also touched upon the potential for LLMs to democratize access to mathematical knowledge and the possibility of future advancements enabling more sophisticated mathematical reasoning by AI. There was some debate about the specific examples provided in the paper, with some users questioning their significance. Overall, the sentiment was cautiously optimistic, acknowledging the potential but emphasizing the limitations of current LLMs in the field of mathematics.
The arXiv LaTeX Cleaner is a tool that automatically cleans up LaTeX source code for submission to arXiv, improving compliance and reducing potential processing errors. It addresses common issues like removing disallowed commands, fixing figure path problems, and converting EPS figures to PDF. The cleaner also standardizes fonts, removes unnecessary packages, and reduces file sizes, ultimately streamlining the arXiv submission process and promoting wider paper accessibility.
Hacker News users generally praised the arXiv LaTeX cleaner for its potential to improve the consistency and readability of submitted papers. Several commenters highlighted the tool's ability to strip unnecessary packages and commands, leading to smaller file sizes and faster processing. Some expressed hope that this would become a standard pre-submission step, while others were more cautious, pointing to the possibility of unintended consequences like breaking custom formatting or introducing subtle errors. The ability to remove comments was also a point of discussion, with some finding it useful for cleaning up draft versions before submission, while others worried about losing valuable context. A few commenters suggested additional features, like converting EPS figures to PDF and adding a DOI badge to the title page. Overall, the reception was positive, with many seeing the tool as a valuable contribution to the academic writing process.
This paper proposes a new quantum Fourier transform (QFT) algorithm that significantly reduces the circuit depth compared to the standard implementation. By leveraging a recursive structure and exploiting the symmetries inherent in the QFT matrix, the authors achieve a depth of O(log * n + log log n), where n is the number of qubits and log * denotes the iterated logarithm. This improvement represents an exponential speedup in depth compared to the O(log² n) depth of the standard QFT while maintaining the same asymptotic gate complexity. The proposed algorithm promises faster and more efficient quantum computations that rely on the QFT, particularly in near-term quantum computers where circuit depth is a crucial limiting factor.
Hacker News users discussed the potential impact of a faster Quantum Fourier Transform (QFT). Some expressed skepticism about the practicality due to the significant overhead of classical computation still required and questioned if this specific improvement truly addressed the bottleneck in quantum algorithms. Others were more optimistic, highlighting the mathematical elegance of the proposed approach and its potential to unlock new applications if the classical overhead can be mitigated in the future. Several commenters also debated the relevance of asymptotic complexity improvements given the current state of quantum hardware, with some arguing that more practical advancements are needed before these theoretical gains become significant. There was also a brief discussion regarding the paper's notation and clarity.
Summary of Comments ( 65 )
https://news.ycombinator.com/item?id=43287821
Several Hacker News commenters express skepticism about the Ladder paper's claims of self-improvement in LLMs. Some question the novelty of recursively decomposing problems, pointing out that it's a standard technique in computer science and that LLMs already implicitly use it. Others are concerned about the evaluation metrics, suggesting that measuring performance on decomposed subtasks doesn't necessarily translate to improved overall performance or generalization. A few commenters find the idea interesting but remain cautious, waiting for further research and independent verification of the results. The limited number of comments indicates a relatively low level of engagement with the post compared to other popular Hacker News threads.
The Hacker News post titled "Ladder: Self-improving LLMs through recursive problem decomposition" (https://news.ycombinator.com/item?id=43287821) discussing the arXiv paper (https://arxiv.org/abs/2503.00735) has a modest number of comments, generating a brief but interesting discussion.
Several commenters focus on the practicality and scalability of the proposed Ladder approach. One commenter questions the feasibility of recursively decomposing problems for real-world tasks, expressing skepticism about its effectiveness beyond toy examples. They argue that the overhead of managing the decomposition process might outweigh the benefits, particularly in complex scenarios. This concern about scaling to more intricate problems is echoed by another user who points out the potential for exponential growth in the number of sub-problems, making the approach computationally expensive.
Another line of discussion revolves around the novelty of the Ladder method. One commenter suggests that the core idea of recursively breaking down problems is not entirely new and has been explored in various forms, such as divide-and-conquer algorithms and hierarchical reinforcement learning. They question the extent of the contribution made by this specific paper. This prompts a response from another user who defends the paper, highlighting the integration of these concepts within the framework of large language models (LLMs) and the potential for leveraging their capabilities for more effective problem decomposition.
Furthermore, the evaluation methodology is brought into question. A commenter notes the reliance on synthetic benchmarks and expresses the need for evaluation on real-world datasets to demonstrate practical applicability. They emphasize the importance of assessing the robustness and generalization capabilities of the Ladder approach beyond controlled environments.
Finally, a few commenters discuss the broader implications of self-improving AI systems. While acknowledging the potential benefits of such approaches, they also express caution about the potential risks and the importance of careful design and control mechanisms to ensure safe and responsible development of such systems.
While the discussion is not extensive, it touches upon key issues related to the feasibility, novelty, and potential impact of the proposed Ladder method, reflecting a balanced perspective on its strengths and limitations.