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China AI Chip Leader Soars 20% Limit as Beijing Warns on Nvidia

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Authors:
(1) Albert Gu, Machine Learning Department, Carnegie Mellon University and with equal contribution;
(2) Tri Dao, Department of Computer Science, Princeton University and with equal contribution. Table of Links Abstract and 1 Introduction 2 State Space Models 3 Selective State Space Models and 3.1 Motivation: Selection as a Means of Compression 3.2 Improving SSMs with Selection 3.3 Efficient Implementation of Selective SSMs 3.4 A Simplified SSM Architecture 3.5 Properties of Selection Mechanisms 3.6 Additional Model Details 4 Empirical Evaluation and 4.1 Synthetic Tasks 4.2 Language Modeling 4.3 DNA Modeling 4.4 Audio Modeling and Generation 4.5 Speed and Memory Benchmarks 4.6 Model Ablations 5 Discussion 6 Conclusion and References A Discussion: Selection Mechanism B Related Work C Mechanics of Selective SSMs D Hardware-aware Algorithm For Selective SSMs E Experimental Details and Additional Results 3.5 Properties of Selection Mechanisms The selection mechanism is a broader concept that can be applied in different ways, such as to more traditional RNNs or CNNs, to different parameters (e.g. A in Algorithm 2), or using different transformations s(x). 3.5.1 Connection to Gating Mechanisms We highlight the most important connection: the classical gating mechanism of RNNs is an instance of our selection mechanism for SSMs. We note that the connection between RNN gating and the discretization of continuous-time systems is well established (Funahashi and Nakamura 1993; Tallec and Ollivier 2018). In fact, Theorem 1 is an improvement of Gu, Johnson, Goel, et al. (2021, Lemma 3.1) generalizing to the ZOH discretization and input-dependent gates (proof in Appendix C). More broadly, ∆ in SSMs can be seen to play a generalized role of the RNN gating mechanism. In line with prior work, we adopt the view that discretization of SSMs is the principled foundation of heuristic gating mechanisms. 3.5.2 Interpretation of Selection Mechanisms We elaborate on two particular mechanistic effects of selection. Filtering Context. It has been empirically observed that many sequence models do not improve with longer context (F. Shi et al. 2023), despite the principle that more context should lead to strictly better performance. An explanation is that many sequence models cannot effectively ignore irrelevant context when necessary; an intuitive example are global convolutions (and general LTI models). On the other hand, selective models can simply reset their state at any time to remove extraneous history, and thus their performance in principle improves monotonicly with context length (e.g. Section 4.3.2). Additionally, we elaborate on effects of each selective parameter. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Albert Gu, Machine Learning Department, Carnegie Mellon University and with equal contribution; (2) Tri Dao, Department of Computer Science, Princeton University and with equal contribution. Authors: Authors: (1) Albert Gu, Machine Learning Department, Carnegie Mellon University and with equal contribution; (2) Tri Dao, Department of Computer Science, Princeton University and with equal contribution. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 State Space Models 2 State Space Models 3 Selective State Space Models and 3.1 Motivation: Selection as a Means of Compression 3 Selective State Space Models and 3.1 Motivation: Selection as a Means of Compression 3.2 Improving SSMs with Selection 3.2 Improving SSMs with Selection 3.3 Efficient Implementation of Selective SSMs 3.3 Efficient Implementation of Selective SSMs 3.4 A Simplified SSM Architecture 3.4 A Simplified SSM Architecture 3.5 Properties of Selection Mechanisms 3.5 Properties of Selection Mechanisms 3.6 Additional Model Details 3.6 Additional Model Details 4 Empirical Evaluation and 4.1 Synthetic Tasks 4 Empirical Evaluation and 4.1 Synthetic Tasks 4.2 Language Modeling 4.2 Language Modeling 4.3 DNA Modeling 4.3 DNA Modeling 4.4 Audio Modeling and Generation 4.4 Audio Modeling and Generation 4.5 Speed and Memory Benchmarks 4.5 Speed and Memory Benchmarks 4.6 Model Ablations 4.6 Model Ablations 5 Discussion 5 Discussion 6 Conclusion and References 6 Conclusion and References A Discussion: Selection Mechanism A Discussion: Selection Mechanism B Related Work B Related Work C Mechanics of Selective SSMs C Mechanics of Selective SSMs D Hardware-aware Algorithm For Selective SSMs D Hardware-aware Algorithm For Selective SSMs E Experimental Details and Additional Results E Experimental Details and Additional Results 3.5 Properties of Selection Mechanisms The selection mechanism is a broader concept that can be applied in different ways, such as to more traditional RNNs or CNNs, to different parameters (e.g. A in Algorithm 2), or using different transformations s(x). 3.5.1 Connection to Gating Mechanisms 3.5.1 Connection to Gating Mechanisms We highlight the most important connection: the classical gating mechanism of RNNs is an instance of our selection mechanism for SSMs. We note that the connection between RNN gating and the discretization of continuous-time systems is well established (Funahashi and Nakamura 1993; Tallec and Ollivier 2018). In fact, Theorem 1 is an improvement of Gu, Johnson, Goel, et al. (2021, Lemma 3.1) generalizing to the ZOH discretization and input-dependent gates (proof in Appendix C). More broadly, ∆ in SSMs can be seen to play a generalized role of the RNN gating mechanism. In line with prior work, we adopt the view that discretization of SSMs is the principled foundation of heuristic gating mechanisms. 3.5.2 Interpretation of Selection Mechanisms 3.5.2 Interpretation of Selection Mechanisms We elaborate on two particular mechanistic effects of selection. Filtering Context. It has been empirically observed that many sequence models do not improve with longer context (F. Shi et al. 2023), despite the principle that more context should lead to strictly better performance. An explanation is that many sequence models cannot effectively ignore irrelevant context when necessary; an intuitive example are global convolutions (and general LTI models). On the other hand, selective models can simply reset their state at any time to remove extraneous history, and thus their performance in principle improves monotonicly with context length (e.g. Section 4.3.2). Filtering Context. Additionally, we elaborate on effects of each selective parameter. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

How Selection Mechanisms Address Long-Context Limitations in AI Sequence Models

Overcoming Limitations in Scaling Biomedical Syllogistic Reasoning

Ah, Transformers. These marvels of AI have taken the world by storm, haven’t they? From GPT models composing poetry to DALL·E generating stunning visuals, Transformers have become the bedrock of modern machine learning. But despite all their prowess, they have one Achilles’ heel that few outside research circles ever discuss—sequence length. Most people assume these models can take in and process as much data as we throw at them, but the truth is far from it. Transformers hit their computational ceiling far earlier than you'd think, and when we try to scale them up to handle long sequences, things start cracking under the strain. So, here’s the question: how do we smash through this barrier? And—let's be honest—isn't it time to rethink the way we approach this entirely? Before we unravel the latest innovations tackling this issue (some of which are downright brilliant), let’s take a moment to look at why this problem exists in the first place. Spoiler alert—it has everything to do with the self-attention mechanism, the very thing that makes Transformers so powerful in the first place. The Quadratic Conundrum: A Love-Hate Relationship With Self-Attention It’s hard to overstate just how game-changing the self-attention mechanism has been for AI. This mechanism allows Transformers to understand relationships between words, images, or even genes, no matter how far apart they are in the input sequence. That’s why when GPT-4 answers a question, it can pull context from an earlier sentence, no matter whether that sentence was 50 tokens ago or 2,000. But here’s the catch. Self-attention doesn’t scale gracefully. Its memory and compute costs grow quadratically as the sequence length increases. In simple terms, the longer your input sequence, the faster the complexity skyrockets. Here’s what’s actually happening under the hood: When you feed a sequence of length n into a Transformer model, it computes what’s called an attention matrix. This matrix tracks pairwise relationships between every single token in the sequence. So, if your sequence has 512 tokens, the attention matrix is 512 × 512. But double that sequence length to 1,024, and now, the matrix balloons to 1,024 × 1,024 —four times bigger. For sequences of 32,000 or 64,000 tokens (which some GPT models attempt to support), the computation required becomes mind-numbingly massive. Sure, our GPUs are powerful, but they’re not wizards. At some point, they just can’t keep up. That’s why long-sequence tasks—analyzing entire research papers, thousands of lines of code, or analyzing massive video datasets—become infeasible really fast. It’s like asking a master chef to whip up an exquisite 10-course meal with only a microwave and a plastic fork. No matter how skilled they are, the setup just isn’t adequate. Let’s bring this closer to home. Say you’re working on a legal AI tool, and you want your Transformer to analyze multi-hundred-page contracts. If the model can only handle 2,048 tokens (roughly five pages of text), you’re stuck splitting the contract into chunks and hoping the model doesn't lose critical context across chunks. Frustrating? Absolutely. But this isn’t just an academic problem—it’s hamstringing real-world applications left and right. So, What’s the Fix? And Why Are Researchers Getting So Creative About It? Here’s the great thing about limitations: they push us to innovate. AI researchers, armed with degrees in mathematics and a love for breaking things, aren’t taking this lying down. They’ve been coming up with all sorts of clever ways to make Transformers handle longer sequences without sending GPUs into spontaneous combustion. It’s not one-size-fits-all, though. Different tasks have different needs, and so the solutions range from tweaking the attention mechanism to completely rethinking how Transformers work. Let’s dive into some of the most exciting approaches. Sparse Attention: Because Not Every Token Deserves Attention Let’s start with the obvious. If computing attention for every pair of tokens is expensive, why not just…skip the unimportant ones? That’s exactly what sparse attention does: it reduces the computational load by selectively attending to subsets of tokens instead of all possible pairs. Take Longformer, for instance. Instead of building a full attention matrix, it focuses on local windows—that is, it only computes interactions between tokens within a sliding window (say, 512 tokens wide). For certain tasks, Longformer also includes a few “global attention” tokens that act as summary nodes and communicate with the entire sequence. Think of it like running a town council meeting: most of the chatter happens just within neighborhoods (local attention), but a few representatives interact with everyone (global attention). This approach works beautifully when your task doesn’t require every single token to talk to every other token—like summarizing documents or answering questions where most of the value comes from nearby words. That said, it's not flawless. Sparse attention can introduce blind spots. For example, if the answer to a question lies in one token at the start of a sequence and another token buried deep at the end, a sparsity-based model might fail to connect the dots. Low-Rank Approximations: Compressing the Chaos Now, let’s get a little more technical. What if you could approximate that monstrous  n × n  attention matrix with something smaller—say, a matrix that only captures the most important relationships? That’s the idea behind low-rank approximation techniques like Linformer. Linformer operates under the assumption that the attention matrix isn’t actually picking up on that much unique information. So, instead of storing its full size, it projects the sequence into a compressed k-dimensional space, where k << n. Suddenly, the quadratic problem becomes linear—or at least close to it—with computation dropping to O(n·k). The tradeoff, as you might guess, is precision. Compressing the attention matrix is a bit like summarizing an epic novel in two sentences: you capture the gist, but you might miss some subtle nuances. Hierarchical Transformers: Tackling the Problem Like Humans Do Here’s an idea inspired by how we humans process large amounts of information: why not break things down hierarchically? Think about how we read a book. We process it chapter by chapter, then try to boil each chapter down into key points before piecing them into a larger understanding of the story. Hierarchical Transformers, such as the Funnel Transformer, mimic this strategy. These models start by processing input sequences in smaller chunks. They then “pool” or down-sample these chunks into compressed summaries before passing them along to higher layers of the model. Later, when necessary, the model can restore full resolution for specific outputs. This hierarchical approach is clever because it allows Transformers to work efficiently while still capturing the broader story. But it’s not perfect—it might miss finer token-level details if your task demands high granularity. Fourier and Spectral Methods: Harnessing Math to Side-Step Attention Brace yourself for this one—it gets geeky. Transformers are all about capturing relationships between tokens, but instead of calculating those relationships in the time domain (as with regular attention), why not shift to the frequency domain? This is where Fourier-based methods like FNet come into the picture. FNet replaces the attention mechanism entirely with a Fast Fourier Transform (FFT). This mathematical operation captures long-range interactions by analyzing frequency patterns instead of token-to-token interactions. And because FFTs have O(nlogn) complexity, they’re mind-blowingly efficient compared to self-attention. Does this mean Fourier can replace attention altogether? Not quite. While it captures broad patterns, it doesn’t provide the fine-grained interpretability or token-specific precision of vanilla Transformers. In other words, it’s great for some tasks (e.g., capturing longer trends in data) but less suited for others. Where Do We Go From Here? So, that brings us to the million-dollar question: which path forward do we choose? Sparse attention? Low-rank approximations? Hierarchical methods? Or do we abandon self-attention altogether and venture into bold new architectures? Here’s my take: the future isn’t about choosing one solution—it’s about combining them. The next generation of long-context AI models will likely leverage a hybrid approach, combining sparse attention for local computation, memory-augmented methods for longer dependencies, and spectral methods for capturing global patterns efficiently. These models might even adapt dynamically based on the task at hand, deciding which mechanism to use on the fly. For now, though, tackling sequence-length limitations is still a work in progress. But one thing’s clear: when we finally break through these constraints, the possibilities will explode. Imagine analyzing entire libraries for insights, processing massive genomes in seconds, or creating AI that can think in contexts that span lifetimes. The ceiling may feel high now, but it’s not unbreakable. After all, limits are just opportunities waiting to be conquered. And Transformers? They’ve rewritten the rules of AI once before—they’ll do it again. Ah, Transformers. These marvels of AI have taken the world by storm, haven’t they? From GPT models composing poetry to DALL·E generating stunning visuals, Transformers have become the bedrock of modern machine learning. But despite all their prowess, they have one Achilles’ heel that few outside research circles ever discuss—sequence length. Most people assume these models can take in and process as much data as we throw at them, but the truth is far from it. Transformers hit their computational ceiling far earlier than you'd think, and when we try to scale them up to handle long sequences, things start cracking under the strain. So, here’s the question: how do we smash through this barrier? And—let's be honest—isn't it time to rethink the way we approach this entirely? Before we unravel the latest innovations tackling this issue (some of which are downright brilliant), let’s take a moment to look at why this problem exists in the first place. Spoiler alert—it has everything to do with the self-attention mechanism, the very thing that makes Transformers so powerful in the first place. The Quadratic Conundrum: A Love-Hate Relationship With Self-Attention It’s hard to overstate just how game-changing the self-attention mechanism has been for AI. This mechanism allows Transformers to understand relationships between words, images, or even genes, no matter how far apart they are in the input sequence. That’s why when GPT-4 answers a question, it can pull context from an earlier sentence, no matter whether that sentence was 50 tokens ago or 2,000. But here’s the catch. Self-attention doesn’t scale gracefully. Its memory and compute costs grow quadratically as the sequence length increases. In simple terms, the longer your input sequence, the faster the complexity skyrockets. Here’s what’s actually happening under the hood: quadratically When you feed a sequence of length n into a Transformer model, it computes what’s called an attention matrix . This matrix tracks pairwise relationships between every single token in the sequence. So, if your sequence has 512 tokens, the attention matrix is 512 × 512 . But double that sequence length to 1,024 , and now, the matrix balloons to 1,024 × 1,024 —four times bigger. n attention matrix 512 × 512 1,024 1,024 × 1,024 For sequences of 32,000 or 64,000 tokens (which some GPT models attempt to support), the computation required becomes mind-numbingly massive. Sure, our GPUs are powerful, but they’re not wizards. At some point, they just can’t keep up. That’s why long-sequence tasks—analyzing entire research papers, thousands of lines of code, or analyzing massive video datasets—become infeasible really fast. It’s like asking a master chef to whip up an exquisite 10-course meal with only a microwave and a plastic fork. No matter how skilled they are, the setup just isn’t adequate. Let’s bring this closer to home. Say you’re working on a legal AI tool, and you want your Transformer to analyze multi-hundred-page contracts. If the model can only handle 2,048 tokens (roughly five pages of text), you’re stuck splitting the contract into chunks and hoping the model doesn't lose critical context across chunks. Frustrating? Absolutely. But this isn’t just an academic problem—it’s hamstringing real-world applications left and right. So, What’s the Fix? And Why Are Researchers Getting So Creative About It? Here’s the great thing about limitations: they push us to innovate. AI researchers, armed with degrees in mathematics and a love for breaking things, aren’t taking this lying down. They’ve been coming up with all sorts of clever ways to make Transformers handle longer sequences without sending GPUs into spontaneous combustion. It’s not one-size-fits-all, though. Different tasks have different needs, and so the solutions range from tweaking the attention mechanism to completely rethinking how Transformers work. Let’s dive into some of the most exciting approaches. Sparse Attention: Because Not Every Token Deserves Attention Let’s start with the obvious. If computing attention for every pair of tokens is expensive, why not just…skip the unimportant ones? That’s exactly what sparse attention does: it reduces the computational load by selectively attending to subsets of tokens instead of all possible pairs. Take Longformer , for instance. Instead of building a full attention matrix, it focuses on local windows —that is, it only computes interactions between tokens within a sliding window (say, 512 tokens wide). For certain tasks, Longformer also includes a few “global attention” tokens that act as summary nodes and communicate with the entire sequence. Think of it like running a town council meeting: most of the chatter happens just within neighborhoods (local attention), but a few representatives interact with everyone (global attention). Longformer local windows This approach works beautifully when your task doesn’t require every single token to talk to every other token—like summarizing documents or answering questions where most of the value comes from nearby words. That said, it's not flawless. Sparse attention can introduce blind spots. For example, if the answer to a question lies in one token at the start of a sequence and another token buried deep at the end, a sparsity-based model might fail to connect the dots. Low-Rank Approximations: Compressing the Chaos Now, let’s get a little more technical. What if you could approximate that monstrous n × n attention matrix with something smaller—say, a matrix that only captures the most important relationships? That’s the idea behind low-rank approximation techniques like Linformer . n × n low-rank approximation Linformer Linformer operates under the assumption that the attention matrix isn’t actually picking up on that much unique information. So, instead of storing its full size, it projects the sequence into a compressed k -dimensional space, where k << n . Suddenly, the quadratic problem becomes linear—or at least close to it—with computation dropping to O(n·k) . k k << n O(n·k) The tradeoff, as you might guess, is precision. Compressing the attention matrix is a bit like summarizing an epic novel in two sentences: you capture the gist, but you might miss some subtle nuances. Hierarchical Transformers: Tackling the Problem Like Humans Do Here’s an idea inspired by how we humans process large amounts of information: why not break things down hierarchically? Think about how we read a book. We process it chapter by chapter, then try to boil each chapter down into key points before piecing them into a larger understanding of the story. Hierarchical Transformers, such as the Funnel Transformer , mimic this strategy. Funnel Transformer These models start by processing input sequences in smaller chunks. They then “pool” or down-sample these chunks into compressed summaries before passing them along to higher layers of the model. Later, when necessary, the model can restore full resolution for specific outputs. This hierarchical approach is clever because it allows Transformers to work efficiently while still capturing the broader story. But it’s not perfect—it might miss finer token-level details if your task demands high granularity. Fourier and Spectral Methods: Harnessing Math to Side-Step Attention Brace yourself for this one—it gets geeky. Transformers are all about capturing relationships between tokens, but instead of calculating those relationships in the time domain (as with regular attention), why not shift to the frequency domain ? This is where Fourier-based methods like FNet come into the picture. frequency domain Fourier-based methods FNet FNet replaces the attention mechanism entirely with a Fast Fourier Transform (FFT) . This mathematical operation captures long-range interactions by analyzing frequency patterns instead of token-to-token interactions. And because FFTs have O(nlogn) complexity, they’re mind-blowingly efficient compared to self-attention. Fast Fourier Transform (FFT) O(nlogn) Does this mean Fourier can replace attention altogether? Not quite. While it captures broad patterns, it doesn’t provide the fine-grained interpretability or token-specific precision of vanilla Transformers. In other words, it’s great for some tasks (e.g., capturing longer trends in data) but less suited for others. Where Do We Go From Here? So, that brings us to the million-dollar question: which path forward do we choose? Sparse attention? Low-rank approximations? Hierarchical methods? Or do we abandon self-attention altogether and venture into bold new architectures? Here’s my take: the future isn’t about choosing one solution—it’s about combining them . The next generation of long-context AI models will likely leverage a hybrid approach, combining sparse attention for local computation, memory-augmented methods for longer dependencies, and spectral methods for capturing global patterns efficiently. the future isn’t about choosing one solution—it’s about combining them These models might even adapt dynamically based on the task at hand, deciding which mechanism to use on the fly. For now, though, tackling sequence-length limitations is still a work in progress. But one thing’s clear: when we finally break through these constraints, the possibilities will explode. Imagine analyzing entire libraries for insights, processing massive genomes in seconds, or creating AI that can think in contexts that span lifetimes. The ceiling may feel high now, but it’s not unbreakable. After all, limits are just opportunities waiting to be conquered. And Transformers? They’ve rewritten the rules of AI once before—they’ll do it again.

Sequence Length Limitation in Transformer Models: How Do We Overcome Memory Constraints?

Google DeepMind researchers have unveiled a groundbreaking framework called Boundless Socratic Learning (BSL), a paradigm shift in artificial intelligence aimed at enabling systems to self-improve through structured language-based interactions. This approach could mark a pivotal step toward the elusive goal of artificial superintelligence (ASI), where AI systems drive their own development with minimal human input. The Concept: Language Games and Self-Sustaining Learning At its core, Boundless Socratic Learning relies on "language games," structured interactions where AI agents create, evaluate, and refine their learning environments. These games not only serve as a source of data but also provide embedded feedback mechanisms, ensuring continuous adaptation and optimization. The process unfolds in three primary dimensions: Input/Output Learning: Agents iteratively improve their responses using in-system feedback, without relying on external datasets.


Game Selection: The ability to choose or even design which "language games" to engage in further broadens the scope of learning.


Code Self-Modification: A theoretical but tantalizing possibility where agents might refine their own programming. The self-improvement potential here is limited primarily by compute resources and time, bypassing traditional constraints of data availability or human intervention. Why It Matters: A Blueprint for Autonomous AI Development The introduction of BSL addresses a long-standing challenge in AI development—how to extend learning and adaptability beyond the initial training phase. By enabling recursive learning processes within closed systems, DeepMind outlines a future where AI models can generate their own data, design their own tasks, and evaluate their performance without external input. This approach aligns with the broader ambition across AI labs to develop systems capable of autonomous self-training, potentially reducing the cost and labor associated with human-curated datasets. Moreover, the implications extend beyond efficiency. As AI systems start defining their own learning trajectories, they could uncover insights and strategies unforeseen by human designers. Challenges: Aligning Goals and Ensuring Safety While the framework offers immense promise, it raises critical questions about safety and alignment. Recursive self-improvement systems must remain aligned with human values and objectives. The research highlights two significant hurdles: Feedback Alignment: Ensuring that internal feedback mechanisms reflect the observer’s intended goals. Diversity and Coverage: Avoiding the collapse of generative diversity, where systems might overfit or narrow their learning scope. Maintaining alignment in a system that evolves autonomously is a non-trivial challenge. As the researchers note, "Feedback is what gives direction to learning; without it, the process is merely one of self-modification."​ Potential Applications The Boundless Socratic Learning framework could revolutionize fields requiring iterative problem-solving and creativity, such as: Mathematics: AI agents proving theorems or generating proofs for unsolved problems. Science: Designing experiments and hypotheses in closed-loop systems. Education: Personalized learning systems that adapt to and predict student needs over time. A practical example cited involves an AI generating and verifying mathematical proofs in a closed system, steadily building its capabilities until it achieves a major breakthrough​. Conclusion: Toward Open-Ended Intelligence The promise of Boundless Socratic Learning lies in its ability to catalyze a shift from human-supervised AI to systems that evolve and improve autonomously. While significant challenges remain, the introduction of this framework represents a step toward the long-term goal of open-ended intelligence, where AI is not just a tool but a partner in discovery. For those intrigued by the details, the full research paper can be accessed here. Google DeepMind researchers have unveiled a groundbreaking framework called Boundless Socratic Learning (BSL) , a paradigm shift in artificial intelligence aimed at enabling systems to self-improve through structured language-based interactions. This approach could mark a pivotal step toward the elusive goal of artificial superintelligence (ASI), where AI systems drive their own development with minimal human input. Boundless Socratic Learning (BSL) The Concept: Language Games and Self-Sustaining Learning At its core, Boundless Socratic Learning relies on "language games," structured interactions where AI agents create, evaluate, and refine their learning environments. These games not only serve as a source of data but also provide embedded feedback mechanisms, ensuring continuous adaptation and optimization. The process unfolds in three primary dimensions: Input/Output Learning: Agents iteratively improve their responses using in-system feedback, without relying on external datasets. Game Selection: The ability to choose or even design which "language games" to engage in further broadens the scope of learning. Code Self-Modification: A theoretical but tantalizing possibility where agents might refine their own programming. Input/Output Learning: Agents iteratively improve their responses using in-system feedback, without relying on external datasets. Input/Output Learning : Agents iteratively improve their responses using in-system feedback, without relying on external datasets. Input/Output Learning Game Selection: The ability to choose or even design which "language games" to engage in further broadens the scope of learning. Game Selection : The ability to choose or even design which "language games" to engage in further broadens the scope of learning. Game Selection Code Self-Modification: A theoretical but tantalizing possibility where agents might refine their own programming. Code Self-Modification : A theoretical but tantalizing possibility where agents might refine their own programming. Code Self-Modification The self-improvement potential here is limited primarily by compute resources and time, bypassing traditional constraints of data availability or human intervention. Why It Matters: A Blueprint for Autonomous AI Development The introduction of BSL addresses a long-standing challenge in AI development—how to extend learning and adaptability beyond the initial training phase. By enabling recursive learning processes within closed systems, DeepMind outlines a future where AI models can generate their own data, design their own tasks, and evaluate their performance without external input. This approach aligns with the broader ambition across AI labs to develop systems capable of autonomous self-training , potentially reducing the cost and labor associated with human-curated datasets. Moreover, the implications extend beyond efficiency. As AI systems start defining their own learning trajectories, they could uncover insights and strategies unforeseen by human designers. autonomous self-training Challenges: Aligning Goals and Ensuring Safety While the framework offers immense promise, it raises critical questions about safety and alignment. Recursive self-improvement systems must remain aligned with human values and objectives. The research highlights two significant hurdles: Feedback Alignment: Ensuring that internal feedback mechanisms reflect the observer’s intended goals. Feedback Alignment : Ensuring that internal feedback mechanisms reflect the observer’s intended goals. Feedback Alignment Diversity and Coverage: Avoiding the collapse of generative diversity, where systems might overfit or narrow their learning scope. Diversity and Coverage : Avoiding the collapse of generative diversity, where systems might overfit or narrow their learning scope. Diversity and Coverage Maintaining alignment in a system that evolves autonomously is a non-trivial challenge. As the researchers note, "Feedback is what gives direction to learning; without it, the process is merely one of self-modification."​ Potential Applications The Boundless Socratic Learning framework could revolutionize fields requiring iterative problem-solving and creativity, such as: Mathematics: AI agents proving theorems or generating proofs for unsolved problems. Mathematics : AI agents proving theorems or generating proofs for unsolved problems. Mathematics Science: Designing experiments and hypotheses in closed-loop systems. Science : Designing experiments and hypotheses in closed-loop systems. Science Education: Personalized learning systems that adapt to and predict student needs over time. Education : Personalized learning systems that adapt to and predict student needs over time. Education A practical example cited involves an AI generating and verifying mathematical proofs in a closed system, steadily building its capabilities until it achieves a major breakthrough​. Conclusion: Toward Open-Ended Intelligence The promise of Boundless Socratic Learning lies in its ability to catalyze a shift from human-supervised AI to systems that evolve and improve autonomously. While significant challenges remain, the introduction of this framework represents a step toward the long-term goal of open-ended intelligence, where AI is not just a tool but a partner in discovery. For those intrigued by the details, the full research paper can be accessed here . here

Boundless Socratic Learning: Google DeepMind's Vision for AI That Learns Without Limits

Table of Links Abstract and 1. Introduction Preliminaries


Proposed Approach
3.1 Notation
3.2 Nueral Networks on SPD Manifolds
3.3 MLR in Structure Spaces
3.4 Neural Networks on Grassmann Manifolds


Experiments


Conclusion and References A. Notations B. MLR in Structure Spaces C. Formulation of MLR from the Perspective of Distances to Hyperplanes D. Human Action Recognition E. Node Classification F. Limitations of our work G. Some Related Definitions H. Computation of Canonical Representation I. Proof of Proposition 3.2 J. Proof of Proposition 3.4 K. Proof of Proposition 3.5 L. Proof of Proposition 3.6 M. Proof of Proposition 3.11 N. Proof of Proposition 3.12 F LIMITATIONS OF OUR WORK Our SPD network GyroSpd++ relies on different Riemannian metrics across the layers, i.e., the convolutional layer is based on Affine-Invariant metrics while the MLR layer is based on LogEuclidean metrics. Although we have provided the experimental results demonstrating that GyroSpd++ achieves good performance on all the datasets compared to state-of-the-art methods, it is not clear if our design is optimal for the human action recognition task. When it comes to building a deep SPD architecture, it is useful to provide insights into Riemannian metrics one should use for each network block in order to obtain good performance on a target task. In our Grassmann network Gr-GCN++, the feature transformation and bias and nonlinearity operations are performed on Grassmann manifolds, while the aggregation operation is performed in tangent spaces. Previous works (Dai et al., 2021; Chen et al., 2022) on HNNs have shown that this hybrid method limits the modeling ability of networks. Therefore, it is desirable to develop GCNs where all the operations are formalized on Grassmann manifolds. Authors:
(1) Xuan Son Nguyen, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (xuan-son.nguyen@ensea.fr);
(2) Shuo Yang, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (son.nguyen@ensea.fr);
(3) Aymeric Histace, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (aymeric.histace@ensea.fr). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Preliminaries Proposed Approach
3.1 Notation
3.2 Nueral Networks on SPD Manifolds
3.3 MLR in Structure Spaces
3.4 Neural Networks on Grassmann Manifolds Experiments Conclusion and References Preliminaries Preliminaries Preliminaries Proposed Approach 3.1 Notation 3.2 Nueral Networks on SPD Manifolds 3.3 MLR in Structure Spaces 3.4 Neural Networks on Grassmann Manifolds Proposed Approach 3.1 Notation 3.1 Notation 3.2 Nueral Networks on SPD Manifolds 3.2 Nueral Networks on SPD Manifolds 3.3 MLR in Structure Spaces 3.3 MLR in Structure Spaces 3.4 Neural Networks on Grassmann Manifolds 3.4 Neural Networks on Grassmann Manifolds Experiments Experiments Experiments Conclusion and References Conclusion and References Conclusion and References A. Notations A. Notations B. MLR in Structure Spaces B. MLR in Structure Spaces C. Formulation of MLR from the Perspective of Distances to Hyperplanes C. Formulation of MLR from the Perspective of Distances to Hyperplanes D. Human Action Recognition D. Human Action Recognition E. Node Classification E. Node Classification F. Limitations of our work F. Limitations of our work G. Some Related Definitions G. Some Related Definitions H. Computation of Canonical Representation H. Computation of Canonical Representation I. Proof of Proposition 3.2 I. Proof of Proposition 3.2 J. Proof of Proposition 3.4 J. Proof of Proposition 3.4 K. Proof of Proposition 3.5 K. Proof of Proposition 3.5 L. Proof of Proposition 3.6 L. Proof of Proposition 3.6 M. Proof of Proposition 3.11 M. Proof of Proposition 3.11 N. Proof of Proposition 3.12 N. Proof of Proposition 3.12 F LIMITATIONS OF OUR WORK Our SPD network GyroSpd++ relies on different Riemannian metrics across the layers, i.e., the convolutional layer is based on Affine-Invariant metrics while the MLR layer is based on LogEuclidean metrics. Although we have provided the experimental results demonstrating that GyroSpd++ achieves good performance on all the datasets compared to state-of-the-art methods, it is not clear if our design is optimal for the human action recognition task. When it comes to building a deep SPD architecture, it is useful to provide insights into Riemannian metrics one should use for each network block in order to obtain good performance on a target task. In our Grassmann network Gr-GCN++, the feature transformation and bias and nonlinearity operations are performed on Grassmann manifolds, while the aggregation operation is performed in tangent spaces. Previous works (Dai et al., 2021; Chen et al., 2022) on HNNs have shown that this hybrid method limits the modeling ability of networks. Therefore, it is desirable to develop GCNs where all the operations are formalized on Grassmann manifolds. Authors: (1) Xuan Son Nguyen, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (xuan-son.nguyen@ensea.fr); (2) Shuo Yang, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (son.nguyen@ensea.fr); (3) Aymeric Histace, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (aymeric.histace@ensea.fr). Authors: Authors: (1) Xuan Son Nguyen, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (xuan-son.nguyen@ensea.fr); (2) Shuo Yang, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (son.nguyen@ensea.fr); (3) Aymeric Histace, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (aymeric.histace@ensea.fr). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv

The Limitations of GyroSpd++ and Gr-GCN++ in Human Action Recognition and Graph Embedding Tasks

Table of Links Abstract and 1 Introduction 2 Background & Problem Statement 2.1 How can we use MLLMs for Diffusion Synthesis that Synergizes both sides? 3 DreamLLM 3.1 End-to-End Interleaved generative Pretraining (I-GPT) 3.2 Model Training 4 Experiments and 4.1 Multimodal Comprehension 4.2 Text-Conditional Image Synthesis 4.3 Multimodal Joint Creation & Comprehension 5 Discussions 5.1 Synergy between creation & Comprehension? 5. 2 What is learned by DreamLLM? 6 Related Works 7 Conclusions and References A Additional Experiments B Additional Qualitative Examples C Implementation Details D Additional Related Works E Limitations, Failure Cases & Future Works E LIMITATIONS, FAILURE CASES & FUTURE WORKS Limitations While DREAMLLM has made significant strides toward the development of versatile, creative, and foundational MLLMs, it still has several limitations. Model scale. The primary constraint pertains to the scale of the LLMs utilized. Current evaluations mainly employ 7B LLMs as the base model, and despite the impressive results garnered, the potential benefits of larger model sizes, such as 65B or 130B (Kaplan et al., 2020), are worth future exploration. Training data. The second challenge relates to the quality and quantity of training data (Jia et al., 2021). As the model size and capabilities scale up, a corresponding increase in data is crucial. However, the procurement and refinement of high-quality training data present substantial logistical and financial hurdles. For instance, the open-source interleaved dataset MMC4 contains a significant amount of noise in the form of text and images, like commercial advertisements. This noise could adversely affect the model’s output language and image style. Prompt sensitivity. The sensitivity of LLMs to human prompts is a known issue (Wei et al., 2022b; Wang et al., 2023b; Zhou et al., 2023), a challenge that extends to MLLMs. For instance, MLLMs’ propensity for detailed responses necessitates tailored prompting to elicit concise and short answers, which is particularly useful when addressing Visual Question Answering (VQA) tasks. Failure Cases The main failure cases of DREAMLLM are observed for multiple image-based content creations. For instance, when presented with two images and a composite instruction such as “A and B”, DREAMLLM sometimes generates a single subject that amalgamates the characteristics of A and B. This output aligns more closely with the directive “A like B”. This phenomenon is not unique to DREAMLLM, but is also observed in specialized compositional generation methodologies, such as Structure Diffusion (Feng et al., 2023; Chefer et al., 2023). This recurring issue may be attributed to the inherent complexity of compositional generation tasks, compounded by the severe scarcity of data specific to this domain. Future Works As a simple and general multimodal learning framework, our future work aims to enhance the DREAMLLM framework by integrating fine-grained visual comprehension via methods like precise referring instruction tuning (Zhao et al., 2023a). We also plan to expand beyond visual and linguistic content comprehension and generation. Several promising research directions include: • Exploring applications of in-context generation capabilities of DREAMLLM to complex tasks such as image-to-image translation (Isola et al., 2017; Zhang et al., 2023c; Zhang & Agrawala, 2023). • Utilizing DREAMLLM’s context consistency feature for geometry-preserving tasks, including 3D content creation (Poole et al., 2023; Qi et al., 2023b; Liu et al., 2023b), representation learning (Dong et al., 2023; Qi et al., 2023a; Zhang et al., 2023a;e), scene comprehension (Zhang et al., 2023b; Hong et al., 2023), and embodied artificial inteligence (Ichter et al., 2022). • Striving to achieve a unified multimodal zero-shot generalist by extending the scope to various modalities using techniques such as ImageBind (Girdhar et al., 2023) and exploring content creation models in other modalities like audio (Kong et al., 2021). This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors:
(1) Runpei Dong, Xi’an Jiaotong University and Internship at MEGVII;
(2) Chunrui Han, MEGVII Technology;
(3) Yuang Peng, Tsinghua University and Internship at MEGVII;
(4) Zekun Qi, Xi’an Jiaotong University and Internship at MEGVII;
(5) Zheng Ge, MEGVII Technology;
(6) Jinrong Yang, HUST and Internship at MEGVII;
(7) Liang Zhao, MEGVII Technology;
(8) Jianjian Sun, MEGVII Technology;
(9) Hongyu Zhou, MEGVII Technology;
(10) Haoran Wei, MEGVII Technology;
(11) Xiangwen Kong, MEGVII Technology;
(12) Xiangyu Zhang, MEGVII Technology and a Project leader;
(13) Kaisheng Ma, Tsinghua University and a Corresponding author;
(14) Li Yi, Tsinghua University, a Corresponding authors and Project leader. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background & Problem Statement 2 Background & Problem Statement 2.1 How can we use MLLMs for Diffusion Synthesis that Synergizes both sides? 2.1 How can we use MLLMs for Diffusion Synthesis that Synergizes both sides? 3 DreamLLM 3 DreamLLM 3.1 End-to-End Interleaved generative Pretraining (I-GPT) 3.1 End-to-End Interleaved generative Pretraining (I-GPT) 3.2 Model Training 3.2 Model Training 4 Experiments and 4.1 Multimodal Comprehension 4 Experiments and 4.1 Multimodal Comprehension 4.2 Text-Conditional Image Synthesis 4.2 Text-Conditional Image Synthesis 4.3 Multimodal Joint Creation & Comprehension 4.3 Multimodal Joint Creation & Comprehension 5 Discussions 5.1 Synergy between creation & Comprehension? 5.1 Synergy between creation & Comprehension? 5. 2 What is learned by DreamLLM? 5. 2 What is learned by DreamLLM? 6 Related Works 6 Related Works 7 Conclusions and References 7 Conclusions and References A Additional Experiments A Additional Experiments B Additional Qualitative Examples B Additional Qualitative Examples C Implementation Details C Implementation Details D Additional Related Works D Additional Related Works E Limitations, Failure Cases & Future Works E Limitations, Failure Cases & Future Works E LIMITATIONS, FAILURE CASES & FUTURE WORKS Limitations While DREAMLLM has made significant strides toward the development of versatile, creative, and foundational MLLMs, it still has several limitations. Limitations Model scale. The primary constraint pertains to the scale of the LLMs utilized. Current evaluations mainly employ 7B LLMs as the base model, and despite the impressive results garnered, the potential benefits of larger model sizes, such as 65B or 130B (Kaplan et al., 2020), are worth future exploration. Model scale. Training data. The second challenge relates to the quality and quantity of training data (Jia et al., 2021). As the model size and capabilities scale up, a corresponding increase in data is crucial. However, the procurement and refinement of high-quality training data present substantial logistical and financial hurdles. For instance, the open-source interleaved dataset MMC4 contains a significant amount of noise in the form of text and images, like commercial advertisements. This noise could adversely affect the model’s output language and image style. Training data. Prompt sensitivity. The sensitivity of LLMs to human prompts is a known issue (Wei et al., 2022b; Wang et al., 2023b; Zhou et al., 2023), a challenge that extends to MLLMs. For instance, MLLMs’ propensity for detailed responses necessitates tailored prompting to elicit concise and short answers, which is particularly useful when addressing Visual Question Answering (VQA) tasks. Prompt sensitivity. Failure Cases The main failure cases of DREAMLLM are observed for multiple image-based content creations. For instance, when presented with two images and a composite instruction such as “A and B”, DREAMLLM sometimes generates a single subject that amalgamates the characteristics of A and B. This output aligns more closely with the directive “A like B”. Failure Cases This phenomenon is not unique to DREAMLLM, but is also observed in specialized compositional generation methodologies, such as Structure Diffusion (Feng et al., 2023; Chefer et al., 2023). This recurring issue may be attributed to the inherent complexity of compositional generation tasks, compounded by the severe scarcity of data specific to this domain. Future Works As a simple and general multimodal learning framework, our future work aims to enhance the DREAMLLM framework by integrating fine-grained visual comprehension via methods like precise referring instruction tuning (Zhao et al., 2023a). We also plan to expand beyond visual and linguistic content comprehension and generation. Several promising research directions include: Future Works • Exploring applications of in-context generation capabilities of DREAMLLM to complex tasks such as image-to-image translation (Isola et al., 2017; Zhang et al., 2023c; Zhang & Agrawala, 2023). • Utilizing DREAMLLM’s context consistency feature for geometry-preserving tasks, including 3D content creation (Poole et al., 2023; Qi et al., 2023b; Liu et al., 2023b), representation learning (Dong et al., 2023; Qi et al., 2023a; Zhang et al., 2023a;e), scene comprehension (Zhang et al., 2023b; Hong et al., 2023), and embodied artificial inteligence (Ichter et al., 2022). • Striving to achieve a unified multimodal zero-shot generalist by extending the scope to various modalities using techniques such as ImageBind (Girdhar et al., 2023) and exploring content creation models in other modalities like audio (Kong et al., 2021). This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv Authors: (1) Runpei Dong, Xi’an Jiaotong University and Internship at MEGVII; (2) Chunrui Han, MEGVII Technology; (3) Yuang Peng, Tsinghua University and Internship at MEGVII; (4) Zekun Qi, Xi’an Jiaotong University and Internship at MEGVII; (5) Zheng Ge, MEGVII Technology; (6) Jinrong Yang, HUST and Internship at MEGVII; (7) Liang Zhao, MEGVII Technology; (8) Jianjian Sun, MEGVII Technology; (9) Hongyu Zhou, MEGVII Technology; (10) Haoran Wei, MEGVII Technology; (11) Xiangwen Kong, MEGVII Technology; (12) Xiangyu Zhang, MEGVII Technology and a Project leader; (13) Kaisheng Ma, Tsinghua University and a Corresponding author; (14) Li Yi, Tsinghua University, a Corresponding authors and Project leader. Authors: Authors: (1) Runpei Dong, Xi’an Jiaotong University and Internship at MEGVII; (2) Chunrui Han, MEGVII Technology; (3) Yuang Peng, Tsinghua University and Internship at MEGVII; (4) Zekun Qi, Xi’an Jiaotong University and Internship at MEGVII; (5) Zheng Ge, MEGVII Technology; (6) Jinrong Yang, HUST and Internship at MEGVII; (7) Liang Zhao, MEGVII Technology; (8) Jianjian Sun, MEGVII Technology; (9) Hongyu Zhou, MEGVII Technology; (10) Haoran Wei, MEGVII Technology; (11) Xiangwen Kong, MEGVII Technology; (12) Xiangyu Zhang, MEGVII Technology and a Project leader; (13) Kaisheng Ma, Tsinghua University and a Corresponding author; (14) Li Yi, Tsinghua University, a Corresponding authors and Project leader.

The Limitations and Failure Cases of DreamLLM: How Far Can it Go?

Avoid These 7 Leadership Mistakes That Will Limit Your Team’s Growth

These days, most companies offer public APIs you can access with a special token generated straight from their dashboard. Similarly, many online projects provide public endpoints to fetch data. The problem? If you send too many requests, you'll hit a rate limiter wall. Discover how to circumvent API rate limiting! Dive into the world of API rate limit measures—learn what they are, how they work, and the tricks to get around them! 🥷 What's API Rate Limiting? API rate limiting is a handy technique used by web services to control the number of requests a client can make to their public endpoints within a specified time frame. ⌛ To better understand how this works, imagine you're at a theme park on a sunny Saturday. ☀️ The park offers a refill station for soda cups, but there’s a catch: you can only refill one cup every 10 minutes🥤. Why? To prevent chaos and ensure everyone gets a drink without hogging the fountain. That’s exactly how API rate limiting works! 💡 Think of an API rate limit as a speed limit for your data requests—keeping things in check. 🛑 It controls how often users can make requests to a server within a specific timeframe. Wait… But Why Do Web Services Even Limit Their APIs? The answer is straightforward: web services limit their APIs to ensure fair usage, prevent abuse, avoid security issues like DDoS attacks, and maintain the overall performance and stability of their services. 🦸‍♂️ Most companies, social media platforms, and online services provide access to a subset of their data through public endpoints. (Is that really the best way to access their data? 🤔 Not quite! For more insights, check out our article on web scraping vs API). To access those endpoints, all you need to do is sign up, create an API key, and use it to authenticate yourself against their public endpoints, as detailed in their documentation. 🔑 Sounds easy, right? 😄 Sure, but there are other factors at play, just like API rate limiting! But why is that complex mechanism really necessary? ❓❓❓ Imagine a few users start bombarding the servers with hundreds of thousands of requests per second. The servers would struggle to handle the load, causing slowdowns for all users. Companies definitely want to avoid that, even for free public endpoints! 🚫 Users typically aren’t fans of downtime or slow services—especially if they’re paying for access to those APIs 💸. To prevent that, web services implement API rate limit measures to restrict the number of requests a specific user can make within a given timeframe. ⏰ You can usually find these API rate-limiting policies in the provider's documentation. Here are some useful pages for popular web services with public APIs: GitHub API rate limiting policies
OpenAI rate limiting policies
Zoom API rate limits What Happens When You Ignore API Rate Limits For a rate limiter to work, the system needs to count all the incoming requests from a user. But how does it know it’s the same user spamming those requests? 🔍 By keeping an eye on the user’s API key or IP address (or both). That’s how the server can track who’s hitting up the web service! Now, keep in mind that API rate limit measures vary wildly from provider to provider. Some cap you at X requests per Y seconds with the same API key, while others slap on additional limits for requests from the same IP. There are even services that consider things like endpoint-specific quotas! Regardless of the implementation, if you hit that limit, expect a “429 Too Many Requests” error response. Basically the server's way of saying, “Whoa there, slow down! Give others a chance too!” 😅 Hitting an API rate limit can range from a simple 429 error to a full-blown IP ban. (⚠️ Pro tip: Follow our guide on how to avoid an IP ban!) And trust me, getting banned is no fun—it can bring your entire automation operation or services relying on those endpoints to a screeching halt. 😱 API Rate Limit Exceeded: What to Do? How to circumvent API rate limiting? Explore the most effective ways! Pay More It’s sad, but like most problems in life, you can just buy your way out of API rate limits 💰. Companies profit by capping requests based on your plan tier. The more you pay, the more requests you can fire off—plain and simple. But let’s be real… while this isn't exactly the most ethical or infinitely scalable solution, it makes sense from a business perspective. It’s like paying for extra luggage on a flight—you want more room, you gotta cough up more cash. ✈️ Create More API Keys Some providers track your incoming requests by looking at the API key you use to authenticate. Since each API key has a limit on the number of requests it can produce in a given timeframe, the magic trick here seems obvious: create multiple API keys! 🎩 ✨ Paying more for a plan is like scaling vertically, but the idea is to scale horizontally instead—creating multiple keys with different purposes and running them concurrently. Sounds foolproof, right? Well, not so fast… Providers know that trick and have countermeasures in place: They can link each API key to an account, so the rate limit might count all requests from your account, not just individual keys.


They could cap the number of API keys you can create. Want more keys? Pay more!


They may also use IP-based rate limiting, preventing multiple keys from bypassing the limit. So yeah, the game is rigged! 😔 Use Proxies A proxy server acts like a middleman between you and the web service’s endpoints. It receives your requests, routes them to the target server, grabs the response, and sends it back to you. This way, the web server sees the requests coming from the proxy's IP, not your IP. 🕵️‍♂️ This mechanism lets you cloak your identity behind the proxy’s server. Considering that top-tier proxy providers offer networks of millions of proxy IPs, that's basically unlimited firepower! When providers enforce IP-based rate limits, proxies are your go-to solution for bypassing API rate limiting. ⚡ Want to integrate proxies into your OS, browser, HTTP client, or scripts? Piece of cake! 🍰 Just a few clicks or a couple of lines of code, depending on your setup. For more guidance, follow our integration guides. If you’re looking for the best proxy provider on the market, look no further than Bright Data. Check out our proxy offerings or watch the video below to find the perfect fit for your needs—and your wallet: https://www.youtube.com/watch?v=VuIl5J2nR3U&embedable=true Final Thoughts Now you know how to circumvent API rate limiting like a pro. Web services cap your requests to nudge you toward higher-priced tiers, but there’s a trick up your sleeve: proxy servers! Need to avoid blocks when hitting public APIs? Bright Data’s suite of tools has got your back! Join the mission to make the Internet accessible for all. 🌐 Until next time, keep surfing the Web with freedom! These days, most companies offer public APIs you can access with a special token generated straight from their dashboard. Similarly, many online projects provide public endpoints to fetch data. The problem? If you send too many requests, you'll hit a rate limiter wall. Discover how to circumvent API rate limiting! Dive into the world of API rate limit measures—learn what they are, how they work, and the tricks to get around them! 🥷 What's API Rate Limiting? API rate limiting is a handy technique used by web services to control the number of requests a client can make to their public endpoints within a specified time frame. ⌛ API rate limiting To better understand how this works, imagine you're at a theme park on a sunny Saturday. ☀️ The park offers a refill station for soda cups, but there’s a catch: you can only refill one cup every 10 minutes🥤. Why? To prevent chaos and ensure everyone gets a drink without hogging the fountain. That’s exactly how API rate limiting works! 💡 Think of an API rate limit as a speed limit for your data requests—keeping things in check. 🛑 It controls how often users can make requests to a server within a specific timeframe. Wait… But Why Do Web Services Even Limit Their APIs? The answer is straightforward: web services limit their APIs to ensure fair usage, prevent abuse, avoid security issues like DDoS attacks , and maintain the overall performance and stability of their services. 🦸‍♂️ DDoS attacks Most companies, social media platforms, and online services provide access to a subset of their data through public endpoints. (Is that really the best way to access their data? 🤔 Not quite! For more insights, check out our article on web scraping vs API ). web scraping vs API To access those endpoints, all you need to do is sign up, create an API key , and use it to authenticate yourself against their public endpoints, as detailed in their documentation. 🔑 API key Sounds easy, right? 😄 Sure, but there are other factors at play, just like API rate limiting ! But why is that complex mechanism really necessary? ❓❓❓ API rate limiting Imagine a few users start bombarding the servers with hundreds of thousands of requests per second. The servers would struggle to handle the load, causing slowdowns for all users. Companies definitely want to avoid that, even for free public endpoints! 🚫 Users typically aren’t fans of downtime or slow services—especially if they’re paying for access to those APIs 💸. To prevent that, web services implement API rate limit measures to restrict the number of requests a specific user can make within a given timeframe. ⏰ You can usually find these API rate-limiting policies in the provider's documentation. Here are some useful pages for popular web services with public APIs: GitHub API rate limiting policies OpenAI rate limiting policies Zoom API rate limits GitHub API rate limiting policies GitHub API rate limiting policies OpenAI rate limiting policies OpenAI rate limiting policies Zoom API rate limits Zoom API rate limits What Happens When You Ignore API Rate Limits For a rate limiter to work, the system needs to count all the incoming requests from a user. But how does it know it’s the same user spamming those requests? 🔍 By keeping an eye on the user’s API key or IP address (or both). That’s how the server can track who’s hitting up the web service! API key IP address Now, keep in mind that API rate limit measures vary wildly from provider to provider. Some cap you at X requests per Y seconds with the same API key, while others slap on additional limits for requests from the same IP. There are even services that consider things like endpoint-specific quotas! Regardless of the implementation, if you hit that limit, expect a “ 429 Too Many Requests ” error response. 429 Too Many Requests Basically the server's way of saying, “Whoa there, slow down! Give others a chance too!” 😅 Hitting an API rate limit can range from a simple 429 error to a full-blown IP ban. (⚠️ Pro tip : Follow our guide on how to avoid an IP ban !) And trust me, getting banned is no fun—it can bring your entire automation operation or services relying on those endpoints to a screeching halt. 😱 Pro tip how to avoid an IP ban API Rate Limit Exceeded: What to Do? How to circumvent API rate limiting? Explore the most effective ways! Pay More It’s sad, but like most problems in life, you can just buy your way out of API rate limits 💰. Companies profit by capping requests based on your plan tier. The more you pay, the more requests you can fire off—plain and simple. But let’s be real… while this isn't exactly the most ethical or infinitely scalable solution, it makes sense from a business perspective. It’s like paying for extra luggage on a flight—you want more room, you gotta cough up more cash. ✈️ Create More API Keys Some providers track your incoming requests by looking at the API key you use to authenticate. Since each API key has a limit on the number of requests it can produce in a given timeframe, the magic trick here seems obvious: create multiple API keys! 🎩 ✨ Paying more for a plan is like scaling vertically, but the idea is to scale horizontally instead—creating multiple keys with different purposes and running them concurrently. Sounds foolproof, right? Well, not so fast… Providers know that trick and have countermeasures in place: They can link each API key to an account, so the rate limit might count all requests from your account, not just individual keys. They could cap the number of API keys you can create. Want more keys? Pay more! They may also use IP-based rate limiting, preventing multiple keys from bypassing the limit. They can link each API key to an account, so the rate limit might count all requests from your account, not just individual keys. They can link each API key to an account, so the rate limit might count all requests from your account, not just individual keys. They could cap the number of API keys you can create. Want more keys? Pay more! They could cap the number of API keys you can create. Want more keys? Pay more! They may also use IP-based rate limiting, preventing multiple keys from bypassing the limit. They may also use IP-based rate limiting, preventing multiple keys from bypassing the limit. So yeah, the game is rigged! 😔 Use Proxies A proxy server acts like a middleman between you and the web service’s endpoints. It receives your requests, routes them to the target server, grabs the response, and sends it back to you. This way, the web server sees the requests coming from the proxy's IP, not your IP. 🕵️‍♂️ proxy server This mechanism lets you cloak your identity behind the proxy’s server. Considering that top-tier proxy providers offer networks of millions of proxy IPs, that's basically unlimited firepower! top-tier proxy providers millions When providers enforce IP-based rate limits, proxies are your go-to solution for bypassing API rate limiting. ⚡ Want to integrate proxies into your OS, browser, HTTP client, or scripts? Piece of cake! 🍰 Just a few clicks or a couple of lines of code, depending on your setup. For more guidance, follow our integration guides . integration guides If you’re looking for the best proxy provider on the market, look no further than Bright Data. Check out our proxy offerings or watch the video below to find the perfect fit for your needs—and your wallet: proxy offerings https://www.youtube.com/watch?v=VuIl5J2nR3U&embedable=true https://www.youtube.com/watch?v=VuIl5J2nR3U&embedable=true Final Thoughts Now you know how to circumvent API rate limiting like a pro. Web services cap your requests to nudge you toward higher-priced tiers, but there’s a trick up your sleeve: proxy servers! Need to avoid blocks when hitting public APIs? Bright Data ’s suite of tools has got your back! Join the mission to make the Internet accessible for all. 🌐 Bright Data Until next time, keep surfing the Web with freedom!

How to Circumvent API Rate Limiting

Jak obejít omezení rychlosti API

Cómo evitar la limitación de velocidad de la API

API レート制限を回避する方法

როგორ ავიცილოთ API სიჩქარის შეზღუდვა

API ылдамдыгын чектөөнү кантип айланып өтсө болот

Tsela ya go Efoga go Lekanyetša Seelo sa API

د API نرخ محدودولو څرنګوالی

Imaynatataq API Tasa Limitación nisqamanta muyuy

Как обойти ограничение скорости API

Hur man kringgår API-hastighetsbegränsning

Jinsi ya Kuzuia Kikomo cha Kiwango cha API

Paano Iwasan ang Paglilimita sa Rate ng API

Authors:
(1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work;
(2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work;
(3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University;
(4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Table of Links Abstract and 1 Introduction 2 Calculating the Stochastic Wave Vector Dark Matter Signal 2.1 The Dark Photon Field 2.2 The Detector Signal 3 Statistical Analysis and 3.1 Signal Likelihood 3.2 Projected Exclusions 4 Application to Accelerometer Studies 4.1 Recasting Generalised Limits onto B − L Dark Matter 5 Future Directions 6 Conclusions, Acknowledgments, and References A Equipartition between Longitudinal and Transverse Modes B Derivation of Marginal Likelihood with Stochastic Field Amplitude C Covariance Matrix D The Case of the Gradient of a Scalar 4.1 Recasting Generalised Limits onto B − L Dark Matter To recast our limits on β shown in Fig. 4 into one on the parameter of interest for this model, the gauge coupling strength gB−L, we must define four quantities. Firstly, we must make clear what the quantity A is for this experiment, which will depend on both the model and the signal of interest for this sensor. Secondly, we must choose an observation time, Tobs. Thirdly, we must elaborate on what the concrete noise profile, σ(ω), for this type of experiment is. Lastly, and least importantly following from our discussion above, we must choose a latitude for the experiment. Once these are known, Eq. (2.8) can be re-arranged for gB−L, giving us our model- and experiment-specific 90% CL limit. For B − L coupled dark photon dark matter, the relevant signal is a differential acceleration. This is given by Eq. (2.6) in the time domain, with a now concrete choice for A, Here, gB−L is the gauge coupling strength of the model, ∆ij is the differential B −L charge per nucleon between materials i and j, given by For our observation time, we take Tobs = 10T⊕ to be firmly in the regime where the three peaks can be resolved. For light cavities, which may only be able to remain coherent over the scale of hours rather than days, such a runtime is optimistic. However, since our aim here is merely to showcase how our method can be used concretely and compare to the works of Refs. [36, 38], we do not see this as an issue. Our strategy is general and can be applied to any axial sensor and vector-like DM model, and we have settled on this configuration only for the sake of argument; other sensor technologies, such a magnetically levitated sensors, do not have this issue. Moreover, multiple cavities or data-stacking techniques can be employed to mitigate this issue. Our choices for all of the above parameters except for the laser power, which we expand on below, are summarised in Table 1. These are in keeping with the choices made in Refs. [36, 38]. The choice of where to tune the laser power is critical to give us competitive limits for a wide range of dark matter masses. We have found that we can achieve excellent limits for low dark matter masses, which are of most relevance to our work, by tuning the laser power such that the back-action and shot-noise components are minimised at low We note that this choice of power tuning is different from the strategies usually employed in other studies. Typically, the laser power is tuned so that the measurement-added noise is either minimised on resonance or, as LIGO implements it, well above resonance [88]. However, we found that both of these choices detriments the limit that we can draw at low masses, increasing the background at low frequencies beyond the thermal noise floor. For these other strategies to be beneficial at both the respective frequency targets and at low frequencies, the thermal noise would have to be significantly lower than that achieved with our choice of sensor mass, quality factor, and bath temperature. In the treatment of our backgrounds, we have neglected seismic noise, which can become important at frequencies below ∼ 10 Hz. Since we require the use of two materials to measure the differential acceleration peculiar to B − L DM, we can envision constructing two sensors: one with a moveable mirror made of material i and another of material j. By subtracting their signals, we both isolate the differential acceleration signature and remove backgrounds common to both—this includes the seismic noise component [63] We show our limits in Fig. 5 for three choices of resonance frequency: 1 Hz, 10 Hz and 100 Hz. For all but the last of these frequencies, we are able to exclude new regions of the UDLM B − L parameter space, best excluded by the fifth-force satellite experiment MICROSCOPE [89] and torsion-balance experiment E¨ot-Wash [90]. This showcases the power of such sensors in searching for this DM candidate, as was first pointed out in Ref. [63]. In a single-peak analysis focusing solely on the Compton peak, our limits would be weakened by approximately a factor of 2, as can be seen from Fig. 4. This difference becomes more dramatic for sensors located closer to the equator. We note that σ(ω), though mostly slowly varying in the frequency width ∆ω = ω⊕, does exhibit a large gradient around the resonance frequency of the cavity. In the neighbourhood of this frequency, our assumption that σ(ω) does not vary greatly in the above range is incorrect, and a more careful analysis in which all three peaks take on different noise levels would have to be conducted for more representative limits. However, we do not expect that our limits would differ greatly from our calculation and, at any rate, would still smoothly join to the regimes on either side of the resonance frequency, where our assumption holds. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Authors: Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Calculating the Stochastic Wave Vector Dark Matter Signal 2.1 The Dark Photon Field 2.1 The Dark Photon Field 2.2 The Detector Signal 2.2 The Detector Signal 3 Statistical Analysis and 3.1 Signal Likelihood 3 Statistical Analysis and 3.1 Signal Likelihood 3.2 Projected Exclusions 3.2 Projected Exclusions 4 Application to Accelerometer Studies 4 Application to Accelerometer Studies 4.1 Recasting Generalised Limits onto B − L Dark Matter 4.1 Recasting Generalised Limits onto B − L Dark Matter 5 Future Directions 5 Future Directions 6 Conclusions, Acknowledgments, and References 6 Conclusions, Acknowledgments, and References A Equipartition between Longitudinal and Transverse Modes A Equipartition between Longitudinal and Transverse Modes B Derivation of Marginal Likelihood with Stochastic Field Amplitude B Derivation of Marginal Likelihood with Stochastic Field Amplitude C Covariance Matrix C Covariance Matrix D The Case of the Gradient of a Scalar D The Case of the Gradient of a Scalar 4.1 Recasting Generalised Limits onto B − L Dark Matter To recast our limits on β shown in Fig. 4 into one on the parameter of interest for this model, the gauge coupling strength gB−L, we must define four quantities. Firstly, we must make clear what the quantity A is for this experiment, which will depend on both the model and the signal of interest for this sensor. Secondly, we must choose an observation time, Tobs. Thirdly, we must elaborate on what the concrete noise profile, σ(ω), for this type of experiment is. Lastly, and least importantly following from our discussion above, we must choose a latitude for the experiment. Once these are known, Eq. (2.8) can be re-arranged for gB−L, giving us our model- and experiment-specific 90% CL limit. For B − L coupled dark photon dark matter, the relevant signal is a differential acceleration. This is given by Eq. (2.6) in the time domain, with a now concrete choice for A, Here, gB−L is the gauge coupling strength of the model, ∆ij is the differential B −L charge per nucleon between materials i and j, given by For our observation time, we take Tobs = 10T⊕ to be firmly in the regime where the three peaks can be resolved. For light cavities, which may only be able to remain coherent over the scale of hours rather than days, such a runtime is optimistic. However, since our aim here is merely to showcase how our method can be used concretely and compare to the works of Refs. [36, 38], we do not see this as an issue. Our strategy is general and can be applied to any axial sensor and vector-like DM model, and we have settled on this configuration only for the sake of argument; other sensor technologies, such a magnetically levitated sensors, do not have this issue. Moreover, multiple cavities or data-stacking techniques can be employed to mitigate this issue. Our choices for all of the above parameters except for the laser power, which we expand on below, are summarised in Table 1. These are in keeping with the choices made in Refs. [36, 38]. The choice of where to tune the laser power is critical to give us competitive limits for a wide range of dark matter masses. We have found that we can achieve excellent limits for low dark matter masses, which are of most relevance to our work, by tuning the laser power such that the back-action and shot-noise components are minimised at low We note that this choice of power tuning is different from the strategies usually employed in other studies. Typically, the laser power is tuned so that the measurement-added noise is either minimised on resonance or, as LIGO implements it, well above resonance [88]. However, we found that both of these choices detriments the limit that we can draw at low masses, increasing the background at low frequencies beyond the thermal noise floor. For these other strategies to be beneficial at both the respective frequency targets and at low frequencies, the thermal noise would have to be significantly lower than that achieved with our choice of sensor mass, quality factor, and bath temperature. In the treatment of our backgrounds, we have neglected seismic noise, which can become important at frequencies below ∼ 10 Hz. Since we require the use of two materials to measure the differential acceleration peculiar to B − L DM, we can envision constructing two sensors: one with a moveable mirror made of material i and another of material j. By subtracting their signals, we both isolate the differential acceleration signature and remove backgrounds common to both—this includes the seismic noise component [63] We show our limits in Fig. 5 for three choices of resonance frequency: 1 Hz, 10 Hz and 100 Hz. For all but the last of these frequencies, we are able to exclude new regions of the UDLM B − L parameter space, best excluded by the fifth-force satellite experiment MICROSCOPE [89] and torsion-balance experiment E¨ot-Wash [90]. This showcases the power of such sensors in searching for this DM candidate, as was first pointed out in Ref. [63]. In a single-peak analysis focusing solely on the Compton peak, our limits would be weakened by approximately a factor of 2, as can be seen from Fig. 4. This difference becomes more dramatic for sensors located closer to the equator. We note that σ(ω), though mostly slowly varying in the frequency width ∆ω = ω⊕, does exhibit a large gradient around the resonance frequency of the cavity. In the neighbourhood of this frequency, our assumption that σ(ω) does not vary greatly in the above range is incorrect, and a more careful analysis in which all three peaks take on different noise levels would have to be conducted for more representative limits. However, we do not expect that our limits would differ greatly from our calculation and, at any rate, would still smoothly join to the regimes on either side of the resonance frequency, where our assumption holds. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Recasting Three-Peak Exclusion Limits on B − L Dark Matter via Accelerometer Studies

Authors:
(1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work;
(2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work;
(3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University;
(4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Table of Links Abstract and 1 Introduction 2 Calculating the Stochastic Wave Vector Dark Matter Signal 2.1 The Dark Photon Field 2.2 The Detector Signal 3 Statistical Analysis and 3.1 Signal Likelihood 3.2 Projected Exclusions 4 Application to Accelerometer Studies 4.1 Recasting Generalised Limits onto B − L Dark Matter 5 Future Directions 6 Conclusions, Acknowledgments, and References A Equipartition between Longitudinal and Transverse Modes B Derivation of Marginal Likelihood with Stochastic Field Amplitude C Covariance Matrix D The Case of the Gradient of a Scalar 3 Statistical Analysis We now consider the projected exclusion limits that a generic experiment would be able to set using our three-peak analysis. To do this, we use a series of likelihood-ratio tests. 3.1 Signal Likelihood For our likelihood, we follow a hybrid frequentist-Bayesian approach, defining a marginalized likelihood in which all nuisance parameters are integrated out. In our case, these are the random Rayleigh parameters, α, and random uniform DM phases, φ. Such a hybrid approach has already been used in the context of ultralight bosonic dark matter [42, 79]. Our work differs from Ref. [79] since they focused on an axion-like signal as opposed to that from vector DM. It goes beyond Ref. [42] since they did not consider the peaks arising from the rotation of the Earth in their analysis. The full likelihood over all frequency space is then given by the product of the likelihoods in each frequency bin, where pi represents the excess power density in the ith frequency bin, p is the full data vector, and the product runs over all Nbins frequency bins. Ultimately, since our signal only manifests in three bins, it suffices for us to consider only those bins that could potentially contain a signal, and we may ignore all other bins. We can express the likelihood in this way because each bin is statistically uncorrelated, as we show in Appendix C. This is in contrast with the analysis performed in Ref. [45], where a similar study was conducted in the case of the gradient of a scalar in the time domain. There, a complicated covariance matrix had to be computed to account for correlations in the signal at different times. In Fourier space, these covariances disappear. The power of performing this analysis in the frequency domain is thus not only that the signal is contained within a small number of bins, but also that these bins are statistically independent, which allows us to treat the statistics in a significantly simpler way. Crucially, once the latitude of the experiment, ϕ, is fixed, the likelihood depends on the product of all experimental variables via the dimensionless parameter β. This means that we can set a more holistic limit that is independent of the specifics of an experiment. Once the form of A (which depends on both the experiment and the DM model), the observation time Tobs, and the noise profile σ are known, the ensuing limit on β can be recast to one on the model parameters of interest. This makes our analysis, both the results and overall logic, as generally useful as possible. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Authors: Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Calculating the Stochastic Wave Vector Dark Matter Signal 2.1 The Dark Photon Field 2.1 The Dark Photon Field 2.2 The Detector Signal 2.2 The Detector Signal 3 Statistical Analysis and 3.1 Signal Likelihood 3 Statistical Analysis and 3.1 Signal Likelihood 3.2 Projected Exclusions 3.2 Projected Exclusions 4 Application to Accelerometer Studies 4 Application to Accelerometer Studies 4.1 Recasting Generalised Limits onto B − L Dark Matter 4.1 Recasting Generalised Limits onto B − L Dark Matter 5 Future Directions 5 Future Directions 6 Conclusions, Acknowledgments, and References 6 Conclusions, Acknowledgments, and References A Equipartition between Longitudinal and Transverse Modes A Equipartition between Longitudinal and Transverse Modes B Derivation of Marginal Likelihood with Stochastic Field Amplitude B Derivation of Marginal Likelihood with Stochastic Field Amplitude C Covariance Matrix C Covariance Matrix D The Case of the Gradient of a Scalar D The Case of the Gradient of a Scalar 3 Statistical Analysis We now consider the projected exclusion limits that a generic experiment would be able to set using our three-peak analysis. To do this, we use a series of likelihood-ratio tests. 3.1 Signal Likelihood For our likelihood, we follow a hybrid frequentist-Bayesian approach, defining a marginalized likelihood in which all nuisance parameters are integrated out. In our case, these are the random Rayleigh parameters, α, and random uniform DM phases, φ. Such a hybrid approach has already been used in the context of ultralight bosonic dark matter [42, 79]. Our work differs from Ref. [79] since they focused on an axion-like signal as opposed to that from vector DM. It goes beyond Ref. [42] since they did not consider the peaks arising from the rotation of the Earth in their analysis. The full likelihood over all frequency space is then given by the product of the likelihoods in each frequency bin, where pi represents the excess power density in the i th frequency bin, p is the full data vector, and the product runs over all Nbins frequency bins. Ultimately, since our signal only manifests in three bins, it suffices for us to consider only those bins that could potentially contain a signal, and we may ignore all other bins. We can express the likelihood in this way because each bin is statistically uncorrelated, as we show in Appendix C. This is in contrast with the analysis performed in Ref. [45], where a similar study was conducted in the case of the gradient of a scalar in the time domain. There, a complicated covariance matrix had to be computed to account for correlations in the signal at different times. In Fourier space, these covariances disappear. The power of performing this analysis in the frequency domain is thus not only that the signal is contained within a small number of bins, but also that these bins are statistically independent, which allows us to treat the statistics in a significantly simpler way. th Crucially, once the latitude of the experiment, ϕ, is fixed, the likelihood depends on the product of all experimental variables via the dimensionless parameter β. This means that we can set a more holistic limit that is independent of the specifics of an experiment. Once the form of A (which depends on both the experiment and the DM model), the observation time Tobs, and the noise profile σ are known, the ensuing limit on β can be recast to one on the model parameters of interest. This makes our analysis, both the results and overall logic, as generally useful as possible. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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