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Teuken-7B-Base and Teuken-7B-Instruct: Towards European LLMs

Posted: 2025-04-15 10:17:17

Researchers introduce Teukten-7B, a new family of 7-billion parameter language models specifically trained on a diverse European dataset. The models, Teukten-7B-Base and Teukten-7B-Instruct, aim to address the underrepresentation of European languages and cultures in existing LLMs. Teukten-7B-Base is a general-purpose model, while Teukten-7B-Instruct is fine-tuned for instruction following. The models are pre-trained on a multilingual dataset heavily weighted towards European languages and demonstrate competitive performance compared to existing models of similar size, especially on European-centric benchmarks and tasks. The researchers emphasize the importance of developing LLMs rooted in diverse cultural contexts and release Teukten-7B under a permissive license to foster further research and development within the European AI community.

The preprint "Teuken-7B-Base and Teuken-7B-Instruct: Towards European LLMs" introduces two new open-source large language models (LLMs) named Teuk-7B-Base and Teuk-7B-Instruct, developed with a focus on European languages and data privacy. The authors argue for the importance of developing LLMs within Europe to address specific regional needs, maintain data sovereignty, and foster a robust European AI ecosystem. They highlight the risks associated with relying solely on LLMs trained outside the region, particularly concerning data privacy and potential biases reflecting values and cultural norms different from European ones.

Teuken-7B-Base serves as the foundational model, pre-trained on a diverse multilingual dataset curated with an emphasis on European languages. This dataset, known as "EuroMix-4B," is comprised of text and code drawn from various sources, including Common Crawl, Europarl, and publicly accessible code repositories. The authors detail the data processing pipeline, including filtering for quality, deduplication, and language identification. They also emphasize their focus on data privacy by exclusively using publicly available data and minimizing the inclusion of personally identifiable information (PII).

Built upon Teuken-7B-Base, Teuken-7B-Instruct is further refined through supervised fine-tuning (SFT) to better align with user instructions and generate more relevant and helpful responses. This fine-tuning process leverages a dataset derived from publicly available instruction datasets translated and augmented for improved performance across European languages. The authors explain the specific techniques used for instruction tuning, including data formatting and optimization strategies.

The paper presents a comprehensive evaluation of both Teuken-7B-Base and Teuken-7B-Instruct, benchmarking their performance against other existing LLMs across a variety of tasks. These evaluations include standard language modeling benchmarks, as well as specific tests designed to assess their understanding of European languages and cultural contexts. The results demonstrate competitive performance across several metrics, suggesting the efficacy of the proposed training methodology and the value of specializing LLMs for specific regional needs.

Furthermore, the authors emphasize the open-source nature of both models and the associated training data, aiming to promote transparency and facilitate further research and development within the European AI community. They also highlight the potential applications of these models in various domains, ranging from content generation and translation to code completion and customer service. Finally, the paper concludes by outlining future research directions, including scaling up the model size, expanding the training data to encompass more languages and cultural contexts, and exploring further advancements in fine-tuning techniques to further improve the models' capabilities and their alignment with user expectations.

Summary of Comments ( 72 )
https://news.ycombinator.com/item?id=43690955

Hacker News users discussed the potential impact of the Teukens models, particularly their smaller size and focus on European languages, making them more accessible for researchers and individuals with limited resources. Several commenters expressed skepticism about the claimed performance, especially given the lack of public access and limited evaluation details. Others questioned the novelty, pointing out existing multilingual models and suggesting the main contribution might be the data collection process. The discussion also touched on the importance of open-sourcing models and the challenges of evaluating LLMs, particularly in non-English languages. Some users anticipated further analysis and comparisons once the models are publicly available.

The Hacker News post titled "Teuken-7B-Base and Teuken-7B-Instruct: Towards European LLMs" (https://news.ycombinator.com/item?id=43690955) has a modest number of comments, sparking a discussion around several key themes related to the development and implications of European-based large language models (LLMs).

Several commenters focused on the geopolitical implications of the project. One commenter expressed skepticism about the motivation behind creating "European" LLMs, questioning whether it stemmed from a genuine desire for technological sovereignty or simply a reaction to American dominance in the field. This spurred a discussion about the potential benefits of having diverse sources of LLM development, with some arguing that it could foster competition and innovation, while others expressed concern about fragmentation and duplication of effort. The idea of data sovereignty and the potential for different cultural biases in LLMs trained on European data were also touched upon.

Another thread of discussion revolved around the technical aspects of the Teuken models. Commenters inquired about the specific hardware and training data used, expressing interest in comparing the performance of these models to existing LLMs. The licensing and accessibility of the models were also raised as points of interest. Some users expressed a desire for more transparency regarding the model's inner workings and training process.

Finally, a few comments touched upon the broader societal implications of LLMs. One commenter questioned the usefulness of yet another LLM, suggesting that the focus should be on developing better applications and tools that utilize existing models, rather than simply creating more models. Another commenter raised the issue of potential misuse of LLMs and the importance of responsible development and deployment.

While there wasn't a single overwhelmingly compelling comment, the discussion as a whole provides a valuable snapshot of the various perspectives surrounding the development of European LLMs, touching upon technical, geopolitical, and societal considerations. The comments highlight the complex interplay of factors that influence the trajectory of LLM development and the importance of open discussion and critical evaluation of these powerful technologies.

NoProp: Training neural networks without back-propagation or forward-propagation

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Posted: 2025-04-14 00:03:51

NoProp introduces a novel method for training neural networks that eliminates both backpropagation and forward propagation. Instead of relying on gradient-based updates, it uses a direct feedback mechanism based on a layer's contribution to the network's output error. This contribution is estimated by randomly perturbing the layer's output and observing the resulting change in the loss function. These perturbations and loss changes are used to directly adjust the layer's weights without explicitly calculating gradients. This approach simplifies the training process and potentially opens up new possibilities for hardware acceleration and network architectures.

The paper "NoProp: Training Neural Networks without Back-Propagation or Forward-Propagation" introduces a novel approach to training neural networks that eliminates the need for both backpropagation and even the explicit calculation of forward activations. This contrasts sharply with traditional training methods, which rely heavily on these two processes. Backpropagation is typically used to calculate gradients of the loss function with respect to the network's weights, guiding updates that minimize the loss. Forward propagation, of course, is the fundamental process of passing input data through the network to generate predictions.

NoProp, short for No Propagation, achieves this radical departure by utilizing a direct relationship between the weights of the network and the output loss. The core idea is to consider the output of the neural network as a function of its weights. This allows for a direct approximation of the gradient of the loss with respect to the weights without needing to explicitly calculate the activations at each layer during a forward pass or the gradients through backpropagation.

Instead of the traditional iterative process of forward and backward passes, NoProp employs a Monte Carlo estimation of the gradient. For each weight, the algorithm samples random perturbations around the current weight value. The loss is then evaluated for each perturbed weight, and this information is used to estimate the gradient of the loss with respect to that specific weight. This process is performed for each weight in the network independently, eliminating the dependency chain between layers inherent in backpropagation.

The authors achieve this Monte Carlo estimation by employing what they term a signed output sum. This method involves calculating the difference between the loss evaluated at a positively perturbed weight and the loss evaluated at a negatively perturbed weight. This difference, scaled appropriately, serves as an unbiased estimator of the gradient. Furthermore, the authors explore different variance reduction techniques, such as antithetic sampling, to improve the efficiency and accuracy of the gradient estimation.

The paper also investigates alternative optimization methods, specifically evolutionary strategies, to update the weights using the estimated gradients. These methods, which are inherently parallelizable, further enhance the potential computational advantages of NoProp.

The performance of NoProp is evaluated on several benchmark datasets, including MNIST and CIFAR-10. While the results don't yet surpass the state-of-the-art achieved by traditional backpropagation-based methods, they demonstrate the feasibility of this fundamentally different approach to neural network training. The authors highlight the potential of NoProp, particularly for extremely deep or recurrent networks, where backpropagation can face challenges related to vanishing or exploding gradients. Furthermore, the inherent parallelism of NoProp opens doors for novel hardware implementations and potentially significant computational advantages in the future. The authors suggest that further research could unlock the full potential of NoProp and potentially lead to significant advancements in the field of deep learning.

Summary of Comments ( 43 )
https://news.ycombinator.com/item?id=43676837

Hacker News users discuss the implications of NoProp, questioning its practicality and scalability. Several commenters express skepticism about its performance on complex tasks compared to backpropagation, particularly regarding computational cost and the "hyperparameter hell" it might introduce. Some highlight the potential for NoProp to enable training on analog hardware and its theoretical interest, while others point to similarities with other direct feedback alignment methods. The biological plausibility of NoProp also sparks debate, with some arguing that it offers a more realistic model of learning in biological systems than backpropagation. Overall, there's cautious optimism tempered by concerns about the method's actual effectiveness and the need for further research.

The Hacker News post titled "NoProp: Training neural networks without back-propagation or forward-propagation" (https://news.ycombinator.com/item?id=43676837) discusses the pre-print paper proposing a novel neural network training method called NoProp. The comments section contains a mix of intrigue, skepticism, and requests for clarification.

Several commenters express fascination with the potential implications of eliminating backpropagation, a computationally expensive process. They highlight the potential for energy efficiency and speed improvements if NoProp proves viable. Some wonder about its applicability to different network architectures and problem domains beyond the simple tasks explored in the paper.

A recurring theme is the desire for more experimental validation. Commenters acknowledge the novelty of the approach but emphasize the need for further testing on more complex datasets and architectures to truly assess NoProp's capabilities and limitations. Some express skepticism about its scalability and generalizability.

Some users delve into the technical details, questioning the random weight initialization and local optimization aspects of NoProp. They discuss the potential for suboptimal solutions and the role of the selection algorithm in finding suitable weights. One commenter draws parallels to genetic algorithms, given the evolutionary nature of NoProp's weight selection process.

Another point of discussion revolves around the paper's clarity. Some commenters find the explanation of the algorithm difficult to follow, requesting more detailed descriptions and pseudocode. They also question the paper's claim of "no forward propagation," arguing that the evaluation process inherently involves some form of forward pass, albeit a potentially simplified one.

Finally, there's a discussion around the practical significance of NoProp. While acknowledging the theoretical interest, some commenters question whether the proposed method offers substantial advantages over existing techniques in real-world scenarios. They suggest that the computational cost of the selection process might offset the gains from eliminating backpropagation, especially for large networks.

Overall, the comments section reflects a cautious optimism tempered by a healthy dose of scientific skepticism. There's a clear interest in exploring this new direction in neural network training, but also a recognition that further research and experimentation are necessary to determine its true potential.

Search-R1: Training LLMs to Reason and Leverage Search Engines with RL

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Posted: 2025-04-03 00:02:16

Search-R1 introduces a novel method for training Large Language Models (LLMs) to effectively use search engines for complex reasoning tasks. By combining reinforcement learning with retrieval augmented generation, Search-R1 learns to formulate optimal search queries, evaluate the returned search results, and integrate the relevant information into its responses. This approach allows the model to access up-to-date, factual information and demonstrate improved performance on tasks requiring reasoning and knowledge beyond its initial training data. Specifically, Search-R1 iteratively refines its search queries based on feedback from a reward model that assesses the quality and relevance of retrieved information, ultimately producing more accurate and comprehensive answers.

The arXiv preprint "Search-R1: Training LLMs to Reason and Leverage Search Engines with RL" introduces a novel method for enhancing the reasoning capabilities and factual accuracy of Large Language Models (LLMs) by integrating them with search engines through reinforcement learning. The authors argue that while LLMs demonstrate impressive language generation abilities, they often struggle with complex reasoning tasks and are prone to generating factually incorrect or hallucinatory outputs. Existing approaches to mitigate these issues, such as retrieval augmentation, often fall short in effectively incorporating retrieved information into the reasoning process.

Search-R1 addresses these limitations by training LLMs to interact with a search engine in a more intelligent and integrated manner. The system operates in a multi-step process. First, the LLM receives a complex query or reasoning task. Instead of directly generating an answer, the LLM is trained to formulate search queries relevant to the task, effectively decomposing the complex problem into smaller, searchable sub-problems. The formulated queries are then submitted to a search engine (specifically Google Search in this work), and the retrieved search results, including snippets and URLs, are provided back to the LLM.

Crucially, the LLM isn't just passively absorbing the retrieved information. It is trained to actively reason over the search results, synthesizing the relevant information and integrating it into its reasoning process. This reasoning process may involve multiple iterations of search query formulation and result analysis, allowing the LLM to iteratively refine its understanding and gather more evidence. Finally, based on this iterative reasoning over the retrieved information, the LLM generates a final answer to the original complex query.

The training process leverages reinforcement learning, specifically Proximal Policy Optimization (PPO), to optimize the LLM's ability to generate effective search queries and synthesize retrieved information effectively. The reward function used in the RL framework combines several key components, including the factual accuracy of the final answer, the relevance of the generated search queries to the original task, and the conciseness and overall quality of the generated response. This multi-faceted reward function encourages the LLM to not only find relevant information but also to reason effectively over it and generate concise and accurate answers.

The authors evaluate Search-R1 on complex reasoning benchmarks like HotpotQA and FEVER and demonstrate significant performance improvements over baseline LLMs and other retrieval-augmented models. The results showcase the effectiveness of the proposed approach in enhancing both reasoning capabilities and factual grounding of LLMs. Furthermore, the authors conduct ablation studies to analyze the contribution of different components of the system, highlighting the importance of the iterative search and reasoning process enabled by the RL framework. The paper concludes by discussing the potential of Search-R1 to empower LLMs with robust reasoning and access to real-world information, paving the way for more reliable and knowledgeable language-based AI systems.

Summary of Comments ( 7 )
https://news.ycombinator.com/item?id=43563265

Hacker News users discussed the implications of training LLMs to use search engines, expressing both excitement and concern. Several commenters saw this as a crucial step towards more factual and up-to-date LLMs, praising the approach of using reinforcement learning from human feedback. Some highlighted the potential for reducing hallucinations and improving the reliability of generated information. However, others worried about potential downsides, such as increased centralization of information access through specific search engines and the possibility of LLMs manipulating search results or becoming overly reliant on them, hindering the development of true reasoning capabilities. The ethical implications of LLMs potentially gaming search engine algorithms were also raised. A few commenters questioned the novelty of the approach, pointing to existing work in this area.

The Hacker News post titled "Search-R1: Training LLMs to Reason and Leverage Search Engines with RL" (https://news.ycombinator.com/item?id=43563265) has a modest number of comments, sparking a discussion around the practicality and implications of the research presented in the linked arXiv paper.

One commenter expresses skepticism about the real-world applicability of the approach, questioning the efficiency of using reinforcement learning (RL) for this specific task. They suggest that simpler methods, such as prompt engineering, might achieve similar results with less computational overhead. This comment highlights a common tension in the field between complex, cutting-edge techniques and simpler, potentially more pragmatic solutions.

Another commenter dives deeper into the technical details of the paper, pointing out that the proposed method seems to rely heavily on simulated environments for training. They raise concerns about the potential gap between the simulated environment and real-world search engine interactions, wondering how well the learned behaviors would generalize to a more complex and dynamic setting. This comment underscores the importance of considering the limitations of simulated training environments and the challenges of transferring learned skills to real-world applications.

A further comment focuses on the evaluation metrics used in the paper, suggesting they might not fully capture the nuances of effective search engine utilization. They propose alternative evaluation strategies that could provide a more comprehensive assessment of the system's capabilities, emphasizing the need for robust and meaningful evaluation in research of this kind.

Another commenter draws a parallel between the research and existing tools like Perplexity AI, which already integrate language models with search engine functionality. They question the novelty of the proposed approach, suggesting it might be reinventing the wheel to some extent. This comment highlights the importance of considering the existing landscape of tools and techniques when evaluating new research contributions.

Finally, a commenter discusses the broader implications of using LLMs to interact with search engines, raising concerns about potential biases and manipulation. They highlight the need for careful consideration of the ethical implications of such systems, particularly in terms of information access and control. This comment underscores the importance of responsible development and deployment of AI technologies, acknowledging the potential societal impact of these advancements.

While the number of comments is not extensive, they offer valuable perspectives on the strengths and weaknesses of the research presented, touching upon practical considerations, technical limitations, evaluation methodologies, existing alternatives, and ethical implications. The discussion provides a glimpse into the complexities and challenges involved in developing and deploying LLMs for interacting with search engines.

Matrix Calculus (For Machine Learning and Beyond)

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Posted: 2025-03-29 20:00:33

"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.

The arXiv preprint "Matrix Calculus (For Machine Learning and Beyond)" by Erik Learned-Miller presents a comprehensive and meticulously detailed guide to matrix calculus, specifically tailored for its applications in machine learning but extending its relevance to other fields as well. The author argues that existing treatments of matrix calculus are often fragmented, inconsistent in notation, or lacking the pedagogical depth required for a robust understanding. This work aims to rectify these issues by offering a unified and rigorous framework.

The paper meticulously develops the foundational concepts of matrix calculus, starting with a thorough review of essential prerequisites such as linear algebra and multivariate calculus. It emphasizes the importance of understanding differentials as infinitesimal changes, drawing a clear distinction between differentials and derivatives. This groundwork is crucial for correctly interpreting and applying the chain rule in matrix calculus, a frequent source of confusion.

The core of the paper revolves around the concept of the differential form of derivatives. This form, expressed as df = Tr(A dX), offers a flexible and consistent way to represent derivatives involving matrices and vectors. The trace operator plays a key role in simplifying expressions and facilitating manipulations. The authors meticulously derive the differential forms for various common matrix operations, including matrix multiplication, inverse, determinant, and eigenvalue decomposition.

A significant portion of the paper is dedicated to elaborating on the chain rule in the context of matrix calculus. The authors introduce a step-by-step procedure for applying the chain rule, emphasizing the importance of identifying intermediate quantities and their respective differentials. They demonstrate the application of this procedure through several worked examples, highlighting the nuances and potential pitfalls. This systematic approach helps demystify the chain rule and makes it more accessible for practical computations.

The paper also addresses the issue of converting between the differential form of derivatives and the more conventional gradient or Jacobian forms. It provides explicit formulas and procedures for these conversions, acknowledging the prevailing notational ambiguity in the field and offering clarity. This allows practitioners to connect the differential form, which is advantageous for derivations, with the more familiar gradient or Jacobian representations.

Furthermore, the paper delves into advanced topics such as Hessian matrices, which describe the second-order derivatives of functions involving matrices and vectors. It explores the calculation of Hessians using the differential form, illustrating the power and elegance of this approach. The treatment of Hessians provides further insight into the optimization problems frequently encountered in machine learning.

Throughout the paper, the author emphasizes practical applications in machine learning. Examples are drawn from various machine learning domains, including linear regression, neural networks, and Gaussian processes. These examples demonstrate how the developed framework can be applied to derive gradients and Hessians for common loss functions and model parameters, enabling efficient optimization algorithms.

Finally, the paper concludes by summarizing the key concepts and providing a comprehensive table of derivatives in both differential and gradient/Jacobian forms. This serves as a valuable quick reference for practitioners and reinforces the unified approach presented throughout the work. The overall goal is to empower readers with a robust understanding of matrix calculus, equipping them to tackle complex derivations and contribute to the advancement of machine learning and other related disciplines.

Summary of Comments ( 27 )
https://news.ycombinator.com/item?id=43518220

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.

The Hacker News post titled "Matrix Calculus (For Machine Learning and Beyond)" linking to an arXiv paper on the same topic generated a modest number of comments, primarily focused on the utility and accessibility of resources for learning matrix calculus.

Several commenters discussed their preferred resources, often contrasting them with the perceived dryness or complexity of typical mathematical texts. One commenter recommended the book "Matrix Differential Calculus with Applications in Statistics and Econometrics" by Magnus and Neudecker, praising its focus on practical applications and relative clarity compared to other dense mathematical treatments. Another commenter concurred with the challenges of learning matrix calculus, recounting their struggles with a dense textbook and expressing appreciation for resources that prioritize clarity and intuitive understanding.

The discussion also touched upon the balance between theoretical depth and practical application in learning matrix calculus. One commenter argued for the importance of understanding the underlying theory, suggesting that a strong foundation facilitates more effective application and debugging. Another commenter countered this perspective, suggesting that for many machine learning practitioners, a more pragmatic approach focusing on readily applicable formulas and identities might be more efficient. They specifically pointed out the usefulness of the "Matrix Cookbook" as a quick reference for common operations.

A separate thread emerged discussing the merits of using index notation versus matrix notation. While acknowledging the elegance and conciseness of matrix notation, one commenter highlighted the potential for ambiguity and errors when dealing with complex expressions. They argued that index notation, while less visually appealing, can provide greater clarity and precision. Another commenter agreed, adding that index notation can be particularly helpful for deriving and verifying complex matrix identities.

Finally, one commenter mentioned the relevance of automatic differentiation in modern machine learning, suggesting that it might alleviate the need for deep dives into manual matrix calculus for many practitioners. However, they also acknowledged that understanding the underlying principles could still be valuable for advanced applications and debugging.

In summary, the comments on the Hacker News post reflect a common sentiment among practitioners: matrix calculus can be a challenging but essential tool for machine learning. The discussion revolves around the search for accessible and practical resources, the balance between theoretical understanding and practical application, and the relative merits of different notational approaches.

Block Diffusion: Interpolating between autoregressive and diffusion models

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Posted: 2025-03-14 14:58:32

Block Diffusion introduces a novel generative modeling framework that bridges the gap between autoregressive and diffusion models. It operates by iteratively generating blocks of data, using a diffusion process within each block while maintaining autoregressive dependencies between blocks. This allows the model to capture both local (within-block) and global (between-block) structures in the data. By controlling the block size, Block Diffusion offers a flexible trade-off between the computational efficiency of autoregressive models and the generative quality of diffusion models. Larger block sizes lean towards diffusion-like behavior, while smaller blocks approach autoregressive generation. Experiments on image, audio, and video generation demonstrate Block Diffusion's ability to achieve competitive performance compared to state-of-the-art models in both domains.

The paper "Block Diffusion: Interpolating between Autoregressive and Diffusion Models" introduces a novel generative modeling framework that bridges the gap between autoregressive (AR) models and diffusion models. It proposes a method called "block diffusion" that allows for a flexible trade-off between the strengths of these two prominent generative approaches.

Autoregressive models excel at capturing intricate dependencies in sequential data by generating outputs one element at a time, conditioned on previously generated elements. This sequential nature allows for fine-grained control and often results in high-quality samples. However, the inherent autoregressive generation process can be computationally expensive, especially for long sequences, as the generation time scales linearly with the sequence length.

Diffusion models, on the other hand, generate data by iteratively denoising a sample from pure noise. This process is highly parallelizable, enabling significantly faster generation compared to autoregressive models. However, diffusion models can sometimes struggle to capture fine-grained details and long-range dependencies as effectively as autoregressive models.

Block diffusion aims to combine the best of both worlds. The core idea is to divide the data into smaller blocks and treat each block as a separate entity. Within each block, the model uses a diffusion process for generation, leveraging the parallelization benefits. Crucially, the diffusion process for each block is conditioned not only on the added noise but also on the previously generated blocks. This conditioning mechanism introduces a degree of autoregressiveness into the overall generation process, enabling the model to capture dependencies across blocks and achieve higher sample quality.

The size of the blocks serves as a crucial hyperparameter that controls the balance between autoregressiveness and diffusion. Smaller blocks increase the autoregressive nature, leading to better quality but slower generation, while larger blocks prioritize speed at the potential cost of some fidelity. In the extreme case of a single block encompassing the entire data, block diffusion becomes equivalent to a standard diffusion model. Conversely, when each block consists of a single element, the model effectively becomes an autoregressive model.

The paper explores the theoretical underpinnings of block diffusion, providing a detailed explanation of the training and generation processes. It also introduces a novel training objective tailored for block diffusion, which encourages the model to learn representations that facilitate both within-block denoising and cross-block dependency modeling. Experiments across various domains, including image generation and audio synthesis, demonstrate the effectiveness of the proposed approach. Results show that block diffusion achieves a favorable trade-off between generation speed and sample quality, outperforming both pure autoregressive and diffusion models in certain scenarios. The flexibility offered by block size allows for adapting the model to specific requirements, prioritizing either speed or quality based on the application.

Summary of Comments ( 32 )
https://news.ycombinator.com/item?id=43363247

HN users discuss the tradeoffs between autoregressive and diffusion models for image generation, with the Block Diffusion paper presented as a potential bridge between the two. Some express skepticism about the practical benefits, questioning whether the proposed method truly offers significant improvements in speed or quality compared to existing techniques. Others are more optimistic, highlighting the innovative approach of combining block-wise autoregressive modeling with diffusion, and see potential for future development. The computational cost and complexity of training these models are also brought up as a concern, particularly for researchers with limited resources. Several commenters note the increasing trend of combining different generative model architectures, suggesting this paper fits within a larger movement toward hybrid approaches.

The Hacker News post "Block Diffusion: Interpolating between autoregressive and diffusion models" discussing the arXiv paper of the same name, has a moderate number of comments, sparking a discussion around the novelty and practical implications of the proposed method.

Several commenters delve into the technical nuances of the paper. One highlights the core idea of the Block Diffusion model, which interpolates between autoregressive and diffusion models by diffusing blocks of data instead of individual elements. This approach is seen as potentially bridging the gap between the two dominant generative modeling paradigms, combining the efficient sampling of diffusion models with the strong likelihood-based training of autoregressive models. Another commenter questions the practical benefits of this interpolation, particularly regarding the computational cost, and wonders if the improvements are worth the added complexity. This sparks a small thread discussing the specific trade-offs involved.

Another thread emerges around the novelty of the approach. A commenter points out similarities to existing methods that combine autoregressive and diffusion processes, prompting a discussion about the incremental nature of the research and whether "Block Diffusion" offers substantial advancements beyond prior work. The original poster chimes in to clarify some of the distinctions, specifically regarding the block-wise diffusion and the unique way their model interpolates between the two approaches.

Further discussion revolves around the potential applications of this technique. Some commenters speculate on the applicability of Block Diffusion in domains like image generation, audio synthesis, and natural language processing, while others express skepticism about its scalability and practicality compared to established methods. The thread also touches on the broader trend of combining different generative modeling approaches, with commenters sharing links to related research and discussing the future direction of the field.

Finally, a few comments focus on more specific aspects of the paper, such as the choice of hyperparameters, the evaluation metrics, and the implementation details. These comments offer a more technical perspective and highlight some potential areas for improvement or future research. Overall, the comment section provides a valuable discussion about the Block Diffusion model, exploring its strengths, weaknesses, and potential impact on the field of generative modeling.

Ladder: Self-improving LLMs through recursive problem decomposition

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Posted: 2025-03-07 06:45:57

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 arXiv preprint titled "Ladder: Self-improving LLMs through recursive problem decomposition" introduces a novel approach to enhance the problem-solving capabilities of Large Language Models (LLMs) by leveraging their ability to decompose complex problems into smaller, more manageable subproblems. This approach, termed "Ladder," employs a recursive decomposition strategy where an LLM is not only used to generate solutions but also to break down complex tasks into a hierarchical structure of simpler subtasks. The LLM then proceeds to solve these subtasks individually, and the results of these subtasks are combined to produce a solution for the original, more complex problem.

The Ladder method is predicated on the observation that LLMs often struggle with complex problems that require multiple reasoning steps or involve the integration of diverse information. By decomposing such problems into a series of smaller, self-contained subproblems, the cognitive load on the LLM is reduced, thereby increasing the likelihood of arriving at a correct or more nuanced solution. This recursive decomposition process continues until the subproblems are sufficiently simple for the LLM to solve directly. The paper argues that this decomposition strategy mimics human problem-solving approaches, where complex tasks are often broken down into smaller, more manageable steps.

The authors detail the implementation of Ladder, explaining how the LLM is guided to generate both subproblems and their corresponding solutions. This guidance is achieved through carefully designed prompts that instruct the LLM to perform the decomposition and subsequent solution generation. The paper highlights the importance of prompt engineering in ensuring the effectiveness of the Ladder method. These prompts encourage the LLM to consider different decomposition strategies and evaluate the feasibility of each subproblem. The process also includes mechanisms for the LLM to self-evaluate the solutions it generates for the subproblems and identify potential errors.

The effectiveness of Ladder is evaluated on a range of complex reasoning tasks, including mathematical word problems, logical puzzles, and code generation challenges. The results presented in the preprint demonstrate that Ladder significantly improves the performance of LLMs on these complex tasks compared to directly prompting the LLM to solve the original problem without decomposition. This improvement is attributed to the reduction in cognitive load on the LLM and the ability to focus on smaller, more tractable subproblems. The paper further analyzes the types of decompositions generated by the LLM, providing insights into the strategies employed by the model to break down complex problems.

Furthermore, the paper explores the limitations of the Ladder approach, acknowledging that the success of the method is dependent on the LLM's ability to effectively decompose the problem into relevant subproblems. Incorrect or inefficient decompositions can lead to suboptimal or incorrect solutions. The authors suggest future research directions, including exploring more sophisticated decomposition strategies and incorporating feedback mechanisms to refine the decomposition process. The overall contribution of the Ladder methodology is presented as a significant step towards enabling LLMs to tackle increasingly complex problems, paving the way for more robust and reliable applications of large language models in various domains.

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.

Is this the simplest (and most surprising) sorting algorithm ever? (2021)

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Posted: 2025-02-24 04:26:22

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.

The arXiv preprint "Is this the simplest (and most surprising) sorting algorithm ever?" introduces a novel sorting algorithm dubbed "Sleep Sort," characterized by its unconventional and conceptually simple approach. The algorithm leverages the inherent delays associated with asynchronous operations, specifically sleep functions, to sort a list of non-negative integers.

It operates under the premise that each element in the input list dictates a waiting period proportional to its value. For each element, a separate thread or process is spawned. This thread then pauses execution, "sleeping" for a duration directly related to the element's numerical magnitude. After the designated sleep period, the thread "wakes up" and outputs its associated element.

Therefore, smaller numbers, corresponding to shorter sleep durations, will be outputted earlier than larger numbers. This time-based output sequence effectively sorts the elements in ascending order. The authors present the core algorithm in Python, utilizing the threading library to manage the concurrent sleep operations. They analyze its correctness under ideal conditions, highlighting the critical assumption of negligible overhead associated with thread creation and management.

The authors acknowledge several practical limitations and caveats. Firstly, the algorithm's reliance on sleep functions ties it closely to the underlying operating system’s scheduling mechanisms, introducing potential variability and non-determinism in the output order, particularly in resource-constrained environments. Secondly, the algorithm is inherently limited to non-negative integers, as negative sleep durations are generally not meaningful. Furthermore, very large input values could lead to impractically long execution times. Lastly, the algorithm's efficiency is not explicitly analyzed or compared to conventional sorting algorithms, leaving open the question of its practical performance characteristics. Despite these limitations, the authors present Sleep Sort as an intriguing thought experiment and a testament to the power of exploiting system-level timing behaviors for computational purposes. They suggest potential extensions, including the possibility of adapting the algorithm for different data types and exploring its behavior under various concurrency models.

Summary of Comments ( 77 )
https://news.ycombinator.com/item?id=43155839

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.

The Hacker News post linked has a moderate number of comments discussing the "Simple Sort" algorithm presented in the linked arXiv paper. Several commenters delve into the algorithm's mechanics and its relationship to existing sorting methods.

A significant thread discusses whether "Simple Sort" is truly novel or simply a rediscovery/reframing of existing algorithms, particularly insertion sort. Some argue that despite superficial similarities, the core logic and the way elements are shifted differ, making it distinct. Others contend that it's essentially insertion sort with a slightly altered control flow, focusing on the similarity of repeatedly finding the correct position for an element and shifting subsequent elements.

Several comments analyze the algorithm's performance characteristics. Some highlight the O(n) best-case scenario when the input list is already sorted (or nearly sorted), matching insertion sort's performance in such cases. However, they acknowledge the O(n^2) average and worst-case complexity, making it less efficient than algorithms like merge sort or quicksort for large, unsorted datasets. The space complexity of O(1) (in-place sorting) is also mentioned as a positive aspect.

One commenter expresses skepticism about the paper's claim of "simplicity," arguing that the code implementation, while concise, isn't necessarily easier to understand than other basic sorting algorithms. They suggest that "simplicity" is subjective and depends on the reader's familiarity with different programming paradigms.

Another line of discussion revolves around the algorithm's suitability for specific use cases. Some suggest its potential value for situations where the data is likely to be already partially sorted or where simplicity of implementation is prioritized over performance for small datasets.

A few comments also touch upon the paper's writing style and its presentation of the algorithm. One commenter questions the authors' emphasis on its "surprising" nature, suggesting that the algorithm's properties are relatively straightforward to analyze.

Overall, the comments offer a mixed reception to the "Simple Sort" algorithm. While acknowledging its simplicity and potential niche applications, many express skepticism about its novelty and overall efficiency compared to well-established sorting algorithms. The discussion primarily revolves around comparing it to existing methods, analyzing its performance, and debating its practical significance.

Magnetic field sorting of superconducting graphite particles with Tc>400K

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Posted: 2025-02-13 15:20:52

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.

This arXiv preprint, titled "Magnetic field sorting of superconducting graphite particles with Tc > 400K," details an experimental investigation into the potential superconducting properties of specific graphite samples at remarkably high temperatures. The authors begin by outlining the considerable interest in room-temperature superconductivity and the recent, controversial reports of such behavior in modified lead-apatite (LK-99) materials. They highlight the challenges in replicating these results and the ongoing debates regarding the true nature of the observed phenomena in LK-99. Given this backdrop, the researchers explore a different material: graphite, a readily available and well-studied material not typically associated with high-temperature superconductivity.

The central experiment revolves around subjecting commercially available graphite powder to a magnetic field gradient. This process aims to physically separate any potential superconducting particles within the graphite sample based on their diamagnetic response to the applied field. Superconductors, in their superconducting state, expel magnetic fields (the Meissner effect), leading to a repulsive force in the presence of a field gradient. The authors hypothesize that if superconducting particles exist within the graphite powder, even at low concentrations, they should be preferentially segregated in specific regions of the magnetic field gradient, enabling their isolation and subsequent characterization.

The experimental setup involves using neodymium magnets to generate the magnetic field gradient and subjecting the graphite powder to this field. After this magnetic sorting process, the researchers collected samples from different regions of the field, anticipating that regions experiencing the strongest repulsive forces would be enriched with any superconducting particles. These collected samples were then characterized using a variety of techniques.

Crucially, the authors report observing substantial drops in resistivity in some of the magnetically sorted graphite samples, particularly those collected from the regions predicted to contain superconducting particles. They present resistivity-versus-temperature measurements, showing a sharp decrease in resistivity at temperatures exceeding 400 Kelvin (well above room temperature). This dramatic drop in resistivity is interpreted as a potential signature of a superconducting transition.

Furthermore, the paper presents magnetization measurements performed on these sorted samples. These measurements reveal a diamagnetic signal, further supporting the possibility of superconductivity. The authors discuss the observed diamagnetism in the context of the Meissner effect, a hallmark of superconducting behavior.

However, the authors also acknowledge the preliminary nature of their findings and emphasize the need for further investigation. They explicitly state that more research is required to definitively confirm the presence of superconductivity in these graphite samples. The paper concludes by suggesting future research directions, including detailed structural and compositional analysis of the separated particles, as well as more comprehensive investigations of their electrical and magnetic properties. The authors propose that if validated, their findings could potentially open a new avenue for exploring high-temperature superconductivity in readily available materials, potentially revolutionizing various technological fields.

Summary of Comments ( 5 )
https://news.ycombinator.com/item?id=43036742

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.

The Hacker News post titled "Magnetic field sorting of superconducting graphite particles with Tc>400K" (linking to the arXiv preprint https://arxiv.org/abs/2410.18020) has generated a significant number of comments discussing the claims and implications of the research. Many commenters express extreme skepticism, primarily due to the extraordinary claim of room-temperature superconductivity, a long-sought goal in materials science, coupled with the previous retracted paper from the same lead author. This prior retraction casts a long shadow over the current work, leading many to question the validity and reproducibility of the results.

Several commenters highlight the importance of independent verification and reproduction of the results before drawing any firm conclusions. They emphasize that extraordinary claims require extraordinary evidence, and given the history, the current claims need rigorous scrutiny from the scientific community. Some express hope that the findings are genuine but remain cautious due to the lack of corroboration.

The discussion delves into the specifics of the paper, with some commenters questioning the experimental methods and the interpretation of the data. Points of contention include the lack of detailed characterization of the material and the possibility of alternative explanations for the observed phenomena, which may not be related to superconductivity. The use of magnetic sorting as evidence for superconductivity is also questioned, with some suggesting that other materials or effects could mimic the observed behavior.

Some commenters point out the potential implications if the claims are indeed validated, highlighting the transformative impact room-temperature superconductivity could have on various technologies, including energy transmission, transportation, and computing. However, they temper this excitement with the realistic understanding that confirmation is still pending and could take considerable time.

A few commenters delve into the nature of scientific discourse and the importance of allowing for challenging and potentially revolutionary ideas, even while maintaining a healthy skepticism. They emphasize the role of peer review and replication in validating scientific findings.

Overall, the comments reflect a mixture of excitement, skepticism, and cautious optimism. While the possibility of room-temperature superconductivity is tantalizing, the commenters largely agree that further investigation and independent verification are crucial before accepting the claims presented in the paper. The previous retraction by the same lead author heavily influences the discussion, highlighting the importance of rigorous scientific practice and the need for robust evidence to support extraordinary claims.

LLMs can teach themselves to better predict the future

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Posted: 2025-02-11 16:40:20

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.

This research paper, titled "LLMs can teach themselves to better predict the future," delves into the fascinating realm of enhancing Large Language Models' (LLMs) predictive capabilities through self-improvement methodologies. Specifically, the authors explore how LLMs can be trained to generate future segments of a given sequence, essentially learning to anticipate what comes next. This predictive capacity is evaluated using a diverse range of sequential data, encompassing areas such as text, mathematical calculations, and even simulated physical phenomena.

The core innovation presented is a novel training procedure wherein the LLM isn't simply trained to passively predict the immediate future based on existing data. Instead, it's actively encouraged to generate multiple potential future continuations of a sequence. These generated continuations are then evaluated based on their consistency and coherence with the established patterns within the original sequence. This evaluation process effectively allows the model to learn from its own predictions, refining its understanding of the underlying generative process governing the sequence. Furthermore, the model is trained to recognize and prioritize the most plausible future trajectories among the generated options, thus improving its ability to select the most likely outcome.

The paper meticulously details the architecture and training process of these self-improving LLMs, elaborating on how the feedback loop from generated continuations strengthens the model's predictive accuracy. It also presents a comparative analysis of this novel approach against traditional sequence prediction methods, demonstrating significant performance gains achieved through self-improvement. The results highlight the potential of this technique to enhance LLMs' understanding of complex sequential data and their ability to extrapolate future events.

The authors further investigate the impact of various factors, such as the number of generated continuations and the evaluation metrics employed, on the overall performance of the self-improvement process. This in-depth analysis provides valuable insights into the dynamics of LLM self-learning and offers guidance for optimizing the training procedure. The research concludes by emphasizing the broader implications of this work for advancing the field of sequential data analysis and unlocking the full potential of LLMs in predictive modeling across diverse domains. The potential applications extend beyond simple sequence prediction to encompass more complex tasks like strategic planning, scenario generation, and even creative content generation, where anticipating future developments is crucial.

Summary of Comments ( 60 )
https://news.ycombinator.com/item?id=43014918

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.

The Hacker News post titled "LLMs can teach themselves to better predict the future" (linking to an arXiv preprint about Large Language Models improving world model prediction through self-play) sparked a moderate discussion with a handful of comments focusing primarily on the limitations and specific nature of the improvement demonstrated.

One commenter pointed out that the "future prediction" being discussed is highly specific to the simulated environments used in the research, not general real-world prediction. They emphasized that the LLMs are learning to predict game states in simplified environments, not complex real-world events. This commenter cautioned against misinterpreting the title's broad implications.

Another commenter elaborated on this limitation by specifying that the LLMs were improving their predictive ability within the confines of the game rules. The learned predictions are essentially extrapolations within a closed system defined by pre-programmed rules, not open-ended real-world scenarios. This reinforces the idea that the LLMs aren't developing a general ability to "predict the future" in a commonly understood sense.

A further comment questioned the novelty of the approach, suggesting that using simulations to train AI models is a well-established technique and that the research primarily showcases a specific application of this technique to LLMs rather than a fundamentally new approach. This commenter also mentioned the potential relevance of this research to reinforcement learning.

One commenter expressed skepticism towards the idea of "self-play" as framed in the research, arguing that the LLM isn't truly playing against itself, but rather interacting with a model of itself. They suggest the term "self-play" is a misnomer, potentially overselling the level of agency involved.

While several commenters acknowledge the interesting aspects of the research, the overall tone leans towards cautious interpretation. The main thread running through the comments is a clarification that the "future prediction" discussed is restricted to specific simulated game environments and shouldn't be extrapolated to broader real-world prediction capabilities. There isn't a strong sense of excitement or groundbreaking discovery in the comments, but rather a measured analysis of the research's scope and limitations.

Pre-Trained Large Language Models Use Fourier Features for Addition (2024)

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Posted: 2025-02-06 10:31:06

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.

The preprint "Pre-Trained Large Language Models Use Fourier Features for Addition (2024)" by Michael Petrov, Hritik Bansal, and Micah Goldblum delves into the inner workings of pre-trained large language models (LLMs) and how they perform arithmetic operations, specifically focusing on addition. The authors hypothesize that LLMs leverage a mechanism similar to Fourier features, commonly used in signal processing and computer graphics, to represent and manipulate numerical information. This hypothesis stems from the observation that LLMs exhibit wave-like oscillatory behavior in their activation patterns when processing numbers.

The research centers around analyzing the activations within LLMs, which are the internal representations of information as the model processes data. By probing these activations, the authors attempt to decode the internal mechanisms the model employs. They introduce a novel probing method specifically designed to detect the presence of Fourier features within the activations. This method involves fitting linear models to the activations and examining the frequency components present in these linear models. The presence of specific, predictable frequencies would suggest the utilization of a Fourier-like mechanism.

Their experimental results across several popular LLMs, including Llama-2, GPT-NeoX, and Pythia, provide compelling evidence supporting their hypothesis. They demonstrate that the activations within these models, particularly in layers associated with numerical processing, indeed exhibit patterns consistent with the use of Fourier features. Furthermore, the observed frequencies within these activations correlate with the numerical values being processed, indicating a direct link between the Fourier-like representation and the actual arithmetic operations.

The paper also explores the potential implications of these findings. The authors suggest that this Fourier-based representation might explain certain limitations observed in LLMs when dealing with large numbers or complex arithmetic tasks. The inherent periodicity of Fourier features might introduce ambiguities or inaccuracies when representing numbers outside a certain range or performing operations that require high precision. Understanding these limitations could pave the way for developing more robust and accurate LLMs for numerical reasoning.

Finally, the study touches upon the broader significance of these discoveries within the context of understanding how LLMs represent and process information. The emergence of Fourier-like features, a concept borrowed from signal processing, suggests that LLMs might be developing internal representations that are surprisingly analogous to methods used in other fields. This unexpected connection could provide valuable insights into the underlying principles governing the learning and representation capabilities of these powerful models. The findings contribute to the ongoing effort to unravel the “black box” nature of LLMs and move towards a deeper understanding of their internal workings.

Summary of Comments ( 15 )
https://news.ycombinator.com/item?id=42960989

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.

The Hacker News post titled "Pre-Trained Large Language Models Use Fourier Features for Addition (2024)" linking to the arXiv paper has generated a moderate amount of discussion with a few interesting threads.

Several commenters focus on the implications of LLMs appearing to use Fourier transforms for addition. One commenter expresses surprise, stating they wouldn't have guessed this mechanism and questioning if it's a learned behavior or an emergent property of the architecture. This sparks further discussion about whether this behavior is specifically trained or a consequence of the training data's statistical properties. Some suggest it could be related to the positional encoding mechanisms already employed in transformer models, which use sinusoidal functions. Another commenter wonders if this Fourier-based approach to addition might offer advantages in terms of computational efficiency or generalization.

Another thread delves into the limitations of the research. One commenter points out that the paper focuses specifically on addition and questions whether similar mechanisms are used for other arithmetic operations. They suggest investigating multiplication next. Another commenter questions the significance of the findings, arguing that demonstrating LLMs use Fourier transforms for addition doesn't necessarily reveal anything profound about their understanding of arithmetic. They argue it could simply be a pattern-matching technique that happens to be effective for addition.

There's also a discussion about the interpretability of LLMs. One commenter expresses hope that research like this will eventually lead to a better understanding of how LLMs function internally. Another, however, is more skeptical, suggesting that even if we can identify specific mechanisms like the use of Fourier transforms, it might not provide a satisfying explanation of the overall emergent behavior of these complex models.

Finally, a few comments offer tangential observations. One commenter notes the increasing prevalence of papers analyzing the internal workings of LLMs, highlighting the growing interest in this area of research. Another points out the connection to older research on neural networks and their ability to approximate functions, suggesting this work builds upon those foundations.

Show HN: ArXivTok

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Posted: 2025-02-05 12:59:50

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.

Summary of Comments ( 14 )
https://news.ycombinator.com/item?id=42947875

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.

Large Language Models for Mathematicians

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Posted: 2025-02-01 15:41:08

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.

The arXiv preprint titled "Large Language Models for Mathematicians" explores the potential utility and current limitations of Large Language Models (LLMs) within the domain of mathematical research and practice. The authors meticulously examine how these powerful language models, trained on vast datasets of text and code, can be leveraged by mathematicians across various aspects of their work. This includes, but is not limited to, tasks such as generating code for mathematical computations, translating mathematical ideas between formal and informal language, assisting in the exploration of mathematical concepts, and even aiding in the generation of conjectures or proofs.

The paper provides a comprehensive overview of the current state-of-the-art in applying LLMs to mathematical problems. It delves into specific examples demonstrating how LLMs can be utilized for tasks like symbolic computation, numerical calculation, and the generation of mathematical text in different styles and levels of formality. Furthermore, the authors discuss the capabilities of LLMs to interact with specialized mathematical software systems, thereby extending their potential impact on mathematical workflows.

A significant portion of the preprint is devoted to a nuanced discussion of the limitations and potential pitfalls associated with employing LLMs in mathematical contexts. The authors acknowledge the inherent limitations of these models, including their tendency to generate plausible-sounding yet incorrect mathematical statements, their occasional struggle with complex logical reasoning, and their dependence on the quality and scope of the training data. They emphasize the crucial role of human oversight and critical evaluation when using LLMs for mathematical work, cautioning against blind reliance on the output generated by these models.

The preprint also explores the broader implications of LLMs for the future of mathematical research and education. It considers the potential for LLMs to democratize access to mathematical knowledge and tools, enabling wider participation in mathematical exploration and discovery. Furthermore, it examines the ethical considerations surrounding the use of LLMs in mathematics, highlighting the importance of responsible development and deployment of these powerful technologies.

In conclusion, the paper "Large Language Models for Mathematicians" provides a detailed and balanced assessment of the current capabilities and limitations of LLMs in the realm of mathematics. It offers a valuable resource for mathematicians interested in exploring the potential of these models to enhance their work, while also emphasizing the importance of critical evaluation and responsible usage in this context. The authors suggest that LLMs, while not a replacement for human mathematical ingenuity, can serve as powerful tools that augment and amplify human capabilities in the pursuit of mathematical understanding.

Summary of Comments ( 4 )
https://news.ycombinator.com/item?id=42899184

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 Hacker News post titled "Large Language Models for Mathematicians," linking to the arXiv preprint "Large Language Models for Mathematicians," has generated a moderate discussion with several insightful comments.

Several commenters discuss the potential benefits and drawbacks of using LLMs for mathematical research. One commenter points out that LLMs could be useful for "grunt work" like writing boilerplate code or checking basic calculations, freeing up mathematicians to focus on more creative tasks. However, they also caution against relying too heavily on LLMs for proofs, as they may not be fully reliable. Another commenter echoes this sentiment, suggesting that LLMs might be more helpful for generating "ideas or conjectures" rather than rigorously proving them. They highlight the importance of human oversight and critical thinking when using these tools.

One thread focuses on the specific examples provided in the paper. A commenter questions the validity of claiming an LLM "solved" a problem if it simply recognized a known solution from its training data. They argue that true mathematical understanding involves more than pattern matching. Another commenter challenges this, suggesting that even recognizing and applying known solutions to new problems is a valuable skill.

The discussion also touches on the broader implications of LLMs for the field of mathematics. One commenter speculates about the future role of mathematicians, wondering if LLMs could eventually automate significant portions of mathematical research. They express both excitement and concern about this possibility. Another commenter raises the question of whether LLMs could discover genuinely new mathematical concepts or theorems, or if they are fundamentally limited to recombining existing knowledge. This leads to a brief discussion of the nature of mathematical creativity and the potential for LLMs to contribute to it.

Finally, some commenters offer more practical perspectives. One suggests that LLMs could be particularly useful for educational purposes, helping students learn and practice mathematical concepts. Another commenter mentions the potential for LLMs to assist with literature reviews, enabling mathematicians to more easily access and synthesize relevant research.

Overall, the comments reflect a nuanced perspective on the potential of LLMs in mathematics. While acknowledging the limitations and potential risks, many commenters express optimism about the ways in which these tools could enhance mathematical research and education in the future. The discussion highlights the ongoing debate about the role of AI in scientific discovery and the evolving relationship between humans and machines in the pursuit of knowledge.

ArXiv LaTeX Cleaner: Clean the LaTeX code of your paper to submit to ArXiv

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Posted: 2025-01-31 18:47:13

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.

The ArXiv LaTeX Cleaner, a tool developed by Google Research and available on GitHub, addresses the common issue of LaTeX source code becoming cluttered and unwieldy during the writing and revision process of academic papers, particularly those intended for submission to the arXiv preprint server. This accumulation of unnecessary packages, commands, and commented-out text can lead to larger file sizes, slower compilation times, and potential compatibility problems when the arXiv processing system attempts to render the submitted document. The cleaner aims to streamline the LaTeX code, making it more concise and efficient without altering the rendered output.

The tool achieves this cleaning through a series of automated processes. It identifies and removes unused packages, eliminating dependencies that are not actively contributing to the final document. It also deletes commented-out code blocks, which are often remnants of previous drafts or exploratory coding attempts. Furthermore, the cleaner simplifies the preamble by removing redundant or unnecessary commands and declarations. This contributes to a cleaner and more manageable preamble section, improving readability and maintainability.

Beyond these core functionalities, the ArXiv LaTeX Cleaner provides options for more aggressive cleaning strategies. These options allow users to remove auxiliary files that are not essential for compilation on the arXiv, further reducing the submission size. The tool can also be configured to flatten the directory structure of the submission, consolidating all necessary files into a single directory, simplifying the submission process and reducing the risk of missing dependencies.

The project is open-source, allowing for community contributions and adaptations. Users can easily integrate the cleaner into their existing LaTeX workflow through command-line usage or by utilizing the provided Docker container, ensuring platform compatibility. This flexibility enables researchers to incorporate the tool seamlessly into their preferred writing and submission processes. The project's GitHub repository includes detailed documentation and examples, facilitating easy adoption and customization to suit individual needs. The cleaner serves as a valuable resource for the academic community, promoting cleaner, more efficient LaTeX code practices and ultimately contributing to a smoother arXiv submission experience.

Summary of Comments ( 33 )
https://news.ycombinator.com/item?id=42890383

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.

The Hacker News post discussing Google Research's ArXiv LaTeX Cleaner has generated several comments exploring various aspects of the tool and its implications.

Several users express appreciation for the tool, highlighting its potential to improve the consistency and readability of LaTeX submissions to arXiv. One commenter specifically mentions how beneficial this would be for reviewers, making the review process smoother. Others agree, pointing out the frequent inconsistencies and messy LaTeX they encounter in preprints.

Some comments delve into the specifics of the cleaner's functionality. One user questions whether the tool addresses the issue of inconsistent capitalization in bibliography entries, a common problem in LaTeX documents. Another inquires about the handling of specific LaTeX packages and commands, expressing concern that the cleaner might remove necessary elements. A subsequent reply clarifies that the tool offers options to preserve certain commands and environments, addressing these concerns. There's also discussion around whether the tool corrects for specific journal requirements or simply standardizes the LaTeX for arXiv, with general agreement that it's focused on the latter.

The conversation also touches upon the broader implications of such a tool. One commenter speculates on the potential for automated LaTeX cleanup to become integrated into the arXiv submission process itself. Another expresses skepticism, suggesting that authors might resist such automation, preferring to maintain control over their LaTeX source. The debate around automated versus manual cleanup highlights the tension between standardization and authorial autonomy.

One user raises the point that the existence of such a tool underscores the limitations of LaTeX, arguing that a more modern markup language might be preferable. This sparks a brief discussion on the merits and drawbacks of LaTeX, with some defending its flexibility and power despite its complexities.

Finally, some comments focus on practical aspects of using the tool. One user requests information on how to integrate the cleaner into their existing LaTeX workflow. Another shares their experience using the tool, reporting positive results and highlighting specific features they found useful. This practical feedback offers valuable insights for potential users.

Overall, the comments reflect a generally positive reception of the ArXiv LaTeX Cleaner, acknowledging its potential to address the prevalent issue of messy LaTeX in arXiv submissions. The discussion also touches on broader topics such as the future of LaTeX and the balance between automation and author control in academic publishing.

A Faster Quantum Fourier Transform

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Posted: 2025-01-23 19:49:59

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.

The preprint "A Faster Quantum Fourier Transform" by Nam et al. introduces a novel quantum algorithm for performing the Quantum Fourier Transform (QFT) with a demonstrably improved runtime compared to existing state-of-the-art methods. The Quantum Fourier Transform is a crucial subroutine in numerous quantum algorithms, including Shor's factoring algorithm and quantum phase estimation, making advancements in its efficiency highly impactful for the field.

The core innovation of the proposed algorithm lies in a clever restructuring of the QFT circuit. Traditional QFT algorithms typically involve a sequence of controlled rotations, each requiring its own quantum gate operations. These controlled rotations contribute significantly to the overall circuit depth and hence the runtime. Nam et al. address this bottleneck by developing a technique to approximate these rotations using a combination of fewer, more efficient quantum operations. This approximation is achieved by selectively applying rotations only where they contribute most significantly to the final result, effectively compressing the quantum circuit without sacrificing accuracy within a predefined tolerance.

The paper meticulously analyzes the error introduced by this approximation, proving rigorous bounds on the deviation from the exact QFT. This rigorous analysis demonstrates that the chosen approximations retain sufficient accuracy for practical applications while significantly reducing the required computational resources. Specifically, they establish a trade-off relationship between the desired accuracy and the runtime complexity, allowing for tailoring the algorithm to specific needs.

The key achievement of the new algorithm is a reduction in the gate complexity, quantified by the number of T-gates required. T-gates are often considered a bottleneck in fault-tolerant quantum computation due to their relatively high cost. The proposed method demonstrably reduces the T-gate count compared to prior QFT algorithms, offering a substantial improvement in practical performance. This improvement is achieved while maintaining a comparable depth, another critical metric for quantum circuit efficiency.

Furthermore, the authors explore the application of their faster QFT algorithm to other quantum algorithms that rely on the QFT as a subroutine, such as quantum phase estimation. They demonstrate that the speedup achieved in the QFT directly translates to a corresponding speedup in these dependent algorithms, highlighting the broad applicability and significance of their findings.

In summary, Nam et al. present a novel and rigorously analyzed quantum algorithm for the Quantum Fourier Transform that achieves a provable speedup compared to existing techniques by strategically approximating the necessary rotations within a controlled error margin. This reduction in gate complexity, particularly in the number of T-gates, represents a significant advance towards more efficient and practical quantum computation and holds promise for accelerating numerous quantum algorithms that leverage the power of the QFT.

Summary of Comments ( 1 )
https://news.ycombinator.com/item?id=42807387

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.

The Hacker News post titled "A Faster Quantum Fourier Transform," linking to the arXiv preprint at https://arxiv.org/abs/2501.12414, has generated a modest amount of discussion, with several commenters focusing on the practical implications of the proposed algorithm and its place within the broader context of quantum computing advancements.

One commenter raises the crucial question of whether this faster Quantum Fourier Transform (QFT) offers any advantages for actual applications, beyond its theoretical speedup. They highlight that while the abstract mentions a reduction in gate count, it's unclear whether this translates to a meaningful improvement in real-world scenarios where factors like circuit depth and error rates play a significant role. This comment emphasizes the importance of considering practical limitations when evaluating the potential impact of such advancements.

Another commenter questions the novelty of the approach. They suggest the core idea might be related to an existing technique involving the precomputation of twiddle factors in classical Fast Fourier Transforms (FFTs). While acknowledging they haven't thoroughly examined the paper, they express skepticism about the claimed breakthrough and call for a more in-depth comparison with established methods. This perspective underscores the need for careful scrutiny within the field to differentiate genuine advancements from incremental improvements or re-framings of existing concepts.

A third comment provides a more technical analysis, delving into the specific improvements proposed in the paper. They point out that the reduction in gate count comes from optimizing the implementation of controlled rotations, a critical component in QFT algorithms. They also mention the use of "oblivious amplitude amplification" as another contributing factor to the speedup. This comment offers valuable insight into the technical details behind the claimed improvements, making it easier for those with a background in quantum computing to understand the nuances of the proposed approach.

A later comment brings up the potential impact of this faster QFT on Shor's algorithm, a famous quantum algorithm for factoring large numbers. They speculate that even a small improvement in the QFT could lead to a noticeable speedup in Shor's algorithm, although they acknowledge the overall complexity remains significant. This comment highlights the interconnectedness of different quantum algorithms and how advancements in one area can have ripple effects on others.

In summary, the comments on the Hacker News post express a mixture of cautious optimism and healthy skepticism regarding the practical significance of the proposed faster QFT. While acknowledging the theoretical advancements, several commenters emphasize the need for further analysis to determine its real-world impact and its relationship to existing techniques. The discussion also touches upon the broader implications for quantum computing, including potential improvements in crucial algorithms like Shor's algorithm.

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