This paper introduces a novel method for inferring the "phylogenetic" relationships between large language models (LLMs), treating their development like the evolution of species. By analyzing the outputs of various LLMs on a standardized set of tasks, the researchers construct a distance matrix reflecting the similarity of their behaviors. This matrix then informs the creation of a phylogenetic tree, visually representing the inferred evolutionary relationships. The resulting tree reveals clusters of models based on their architectural similarities and training data, providing insights into the influence of these factors on LLM behavior. This approach offers a new perspective on understanding the development and diversification of LLMs, moving beyond simple performance comparisons to explore the deeper connections between them.
"Matrix Calculus (For Machine Learning and Beyond)" offers a comprehensive guide to matrix calculus, specifically tailored for its applications in machine learning. It covers foundational concepts like derivatives, gradients, Jacobians, Hessians, and their properties, emphasizing practical computation and usage over rigorous proofs. The resource presents various techniques for matrix differentiation, including the numerator-layout and denominator-layout conventions, and connects these theoretical underpinnings to real-world machine learning scenarios like backpropagation and optimization algorithms. It also delves into more advanced topics such as vectorization, chain rule applications, and handling higher-order derivatives, providing numerous examples and clear explanations throughout to facilitate understanding and application.
Hacker News users discussed the accessibility and practicality of the linked matrix calculus resource. Several commenters appreciated its clear explanations and examples, particularly for those without a strong math background. Some found the focus on differentials beneficial for understanding backpropagation and optimization algorithms. However, others argued that automatic differentiation makes manual matrix calculus less crucial in modern machine learning, questioning the resource's overall relevance. A few users also pointed out the existence of other similar resources, suggesting alternative learning paths. The overall sentiment leaned towards cautious praise, acknowledging the resource's quality while debating its necessity in the current machine learning landscape.
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.
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.
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 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.
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https://news.ycombinator.com/item?id=43736366
Several Hacker News commenters express skepticism about the paper's methodology and conclusions. Some doubt the reliability of using log-likelihoods on cherry-picked datasets to infer relationships, suggesting it's more a measure of dataset similarity than true model ancestry. Others question the assumption that LLMs even have a meaningful "phylogeny" like biological organisms, given their development process. The idea of "model paleontology" is met with both interest and doubt, with some arguing that internal model parameters would offer more robust insights than behavioral comparisons. There's also discussion on the limitations of relying solely on public data and the potential biases introduced by fine-tuning. A few commenters raise ethical concerns around potential misuse of such analysis for IP infringement claims, highlighting the difference between code lineage and learned knowledge.
The Hacker News post titled "Inferring the Phylogeny of Large Language Models" discussing the arXiv preprint at https://arxiv.org/abs/2404.04671 generated a moderate amount of discussion with several interesting points raised.
One commenter expressed skepticism regarding the core premise of the paper, questioning whether treating LLMs as evolving entities within a phylogenetic framework is appropriate. They argued that LLMs are artifacts designed and built by humans, not organisms subject to natural selection, and therefore the analogy doesn't hold. They also pointed out that the "mutations" introduced in LLMs are deliberate design choices or errors, not random variations, which further undermines the comparison to biological evolution.
Another commenter elaborated on this point by suggesting that the observed similarities between LLMs are more likely due to convergent engineering, where different teams arrive at similar solutions to common problems, rather than evolutionary descent. They proposed that the shared characteristics of LLMs are a reflection of the shared goals and constraints faced by their developers.
A different line of discussion focused on the practical implications of the research. One commenter questioned the usefulness of building a phylogeny of LLMs, arguing that the relevant information about their architecture and training data is already known and accessible. They suggested that focusing on these known factors would be more productive than constructing an evolutionary tree.
However, a counterpoint was raised that understanding the relationships between LLMs in a phylogenetic context could be valuable for tasks like identifying the origins of specific behaviors or biases. This commenter argued that tracing the lineage of an LLM could help pinpoint the source of undesirable characteristics, potentially aiding in their mitigation.
One commenter expressed interest in the potential for using phylogenetic methods to analyze the evolution of codebases in general, seeing this as a broader application of the principles explored in the paper.
Finally, some commenters discussed the technical details of the paper, such as the specific methods used for constructing the phylogenetic tree and the limitations of the approach. One pointed out the challenge of defining meaningful "traits" for LLMs, given their complexity.
In summary, the comments on the Hacker News post presented a range of perspectives on the paper, from skepticism about the underlying framework to enthusiasm for its potential applications. The discussion touched upon the appropriateness of the evolutionary analogy, the practical implications of the research, and the technical challenges involved in analyzing LLMs in a phylogenetic context.