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How does latent variable modeling work in machine learning? | Latent variable modeling defines a probabilistic model with a latent hidden variable and a visible variable, allowing for the expression of a rich distribution over the visible variables. | A classic idea in machine learning is to define a probabilistic model with a latent hidden variable z and a visible variable y , where y is given to our learning algorithm. |
What do the variables x, y, and z represent in the context of modeling math problems? | In modeling math problems, x denotes a problem statement, y is the ground truth answer or proof, and z represents a free form thought process that leads to the proof. | For example, we can model the distribution over math problems and solutions by letting x denote a problem statement, y be ground truth answer or proof, and z as a free form thought process that leads to the proof. |
What is the target objective to optimize in latent variable modeling? | The target objective to optimize is the log loss, which has been effective in pretraining. | This view also suggests the benefits of using the log loss log P y mid x as the target objective to optimize, as the log loss objective has been so effective in pretraining. |
What was the focus of the research conducted by Cobbe et al. in 2021? | Cobbe et al. focused on training a generator with supervised learning on human-written solutions and verifiers that predict the correctness of candidate solutions. | Cobbe et al. train a generator with supervised learning on human written solutions and verifiers that predict the correctness of a candidate solution they can then search over these solutions. |
What property does CoT possess regarding compute usage? | CoT allows the model to use a variable amount of compute depending on the hardness of the problem. | In fact, CoT has a nice property that it allows the model to use a variable amount of compute depending on the hardness of the problem. |
What is the purpose of marginalizing over the latent variable in probabilistic modeling? | Marginalizing over the latent variable helps express a rich distribution over the visible variables. | Marginalizing summing over the possible values of the latent variable allows us to express a rich distribution over the visible variables, P y sum_ z sim P z P y mid z. |
How can the distribution over math problems and solutions be modeled? | The distribution can be modeled by letting x denote a problem statement, y be the ground truth answer or proof, and z as the free form thought process leading to the proof. | For example, we can model the distribution over math problems and solutions by letting x denote a problem statement, y be ground truth answer or proof, and z as a free form thought process that leads to the proof. |
What objective is suggested for optimization in the latent variable perspective? | The log loss log P y mid x is suggested as the target objective to optimize. | This view also suggests the benefits of using the log loss log P y mid x as the target objective to optimize, as the log loss objective has been so effective in pretraining. |
Who introduced the AQUA RAT dataset and what was its focus? | The AQUA RAT dataset was introduced by Ling, et al. 2017 and focused on generating intermediate steps before generating short answers for math problems. | The strategy of generating intermediate steps before generating short answers, particularly for math problems, was explored by Ling, et al. 2017, who introduced the AQUA RAT dataset. |
What property does CoT have regarding compute usage? | CoT allows the model to use a variable amount of compute depending on the hardness of the problem. | In fact, CoT has a nice property that it allows the model to use a variable amount of compute depending on the hardness of the problem. |
What is the role of the latent variable in probabilistic modeling? | The latent variable z helps to define a probabilistic model with a rich distribution over the visible variable y. | Latent Variable Modeling A classic idea in machine learning is to define a probabilistic model with a latent hidden variable z and a visible variable y , where y is given to our learning algorithm. |
How can we model the distribution over math problems using variables? | We can model the distribution by letting x denote a problem statement, y as the ground truth answer or proof, and z as the thought process leading to the proof. | For example, we can model the distribution over math problems and solutions by letting x denote a problem statement, y be ground truth answer or proof, and z as a free form thought process that leads to the proof. |
What is the target objective suggested for optimization in latent variable modeling? | The suggested target objective to optimize is the log loss log P y mid x. | This view also suggests the benefits of using the log loss log P y mid x as the target objective to optimize, as the log loss objective has been so effective in pretraining. |
What datasets were mentioned in relation to generating intermediate steps for math problems? | The AQUA RAT dataset and the Grade School Math GSM dataset were mentioned in relation to generating intermediate steps. | The strategy of generating intermediate steps before generating short answers, particularly for math problems, was explored by Ling, et al. 2017, who introduced the AQUA RAT dataset, and then expanded by Cobbe et al. 2021, who introduced the Grade School Math GSM dataset. |
What early methods were used to improve CoT reasoning? | Early methods for improving CoT reasoning included supervised learning on human-written reasoning traces or model-written traces filtered for answer correctness. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness. |
How can prompting enhance the performance of instruction-tuned models? | Prompting can enhance the performance of instruction-tuned models by encouraging them to think step by step or by using more complex prompts that make them reflect on related knowledge first. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What recent advancements have been made in improving CoT reasoning capabilities? | Recent advancements in improving CoT reasoning capabilities include reinforcement learning on datasets of problems with automatically checkable solutions, such as STEM problems and coding tasks. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests. |
What was the significance of the o1 preview and R1 tech report in the context of CoT reasoning? | The o1 preview and R1 tech report were significant as they demonstrated that a simple recipe using a policy gradient algorithm could lead to strong performance in CoT reasoning. | This approach rose to prominence with the announcement of o1 preview, o3, and the R1 tech report DeepSeek AI, 2025, which showed that a simple recipe where a policy gradient algorithm could lead to strong performance. |
What types of tasks were highlighted as suitable for reinforcement learning in the context of CoT reasoning? | Tasks highlighted as suitable for reinforcement learning in the context of CoT reasoning include STEM problems with short answers and coding tasks that can be checked with unit tests. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests. |
What early methods were used to improve CoT reasoning? | Early methods involved supervised learning on human-written reasoning traces or model-written traces filtered for answer correctness. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness. |
How can math performance of instruction-tuned models be boosted? | Math performance can be significantly boosted by appropriately prompting the models, using techniques like 'think step by step' or more complex prompting. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step. |
What is a recent method to improve CoT reasoning capabilities? | A recent method involves doing reinforcement learning on a dataset of problems with automatically checkable solutions, like STEM problems or coding tasks. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions. |
What announcement highlighted a successful approach to CoT reasoning? | The announcement of o1 preview, o3, and the R1 tech report by DeepSeek AI in 2025 highlighted a successful approach using a policy gradient algorithm. | This approach rose to prominence with the announcement of o1 preview, o3, and the R1 tech report DeepSeek AI, 2025. |
What methods were used to improve CoT reasoning in early work? | Early work on improving CoT reasoning involved supervised learning on human written reasoning traces or model written traces filtered for answer correctness. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness. |
How can the math performance of instruction-tuned models be boosted? | The math performance of instruction-tuned models can be significantly boosted by prompting them appropriately, such as using think step by step or more complex prompting to encourage the model to reflect on related knowledge first. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What recent findings have improved CoT reasoning capabilities? | Recent findings indicate that CoT reasoning capabilities can be significantly improved by doing reinforcement learning on datasets of problems with automatically checkable solutions. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests. |
What did the announcement of o1 preview, o3, and the R1 tech report reveal? | The announcement of o1 preview, o3, and the R1 tech report revealed that a simple recipe using a policy gradient algorithm could lead to strong performance. | This approach rose to prominence with the announcement of o1 preview, o3, and the R1 tech report DeepSeek AI, 2025 , which showed that a simple recipe where a policy gradient algorithm could lead to strong performance. |
What effect does thinking time have on larger models in math problem-solving? | Larger models benefit more from thinking time when solving math problems, leading to a higher success rate. | Chain of thought prompting leads to higher success rate of solving math problems. Larger models benefit more from thinking time. |
What was the early method used to improve Chain of Thought reasoning? | The early method involved supervised learning on human written reasoning traces or model written traces filtered for answer correctness. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness. |
How can the math performance of instruction tuned models be boosted? | Math performance can be boosted by prompting models appropriately, such as using 'think step by step' or more complex prompting to encourage reflection on related knowledge. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What recent work has shown improvements in CoT reasoning capabilities? | Recent work has shown that CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests. |
What did the announcement of the o1 preview, o3, and the R1 tech report demonstrate? | The announcement demonstrated that a simple recipe using a policy gradient algorithm could lead to strong performance in solving problems. | This approach rose to prominence with the announcement of o1 preview, o3, and the R1 tech report DeepSeek AI, 2025, which showed that a simple recipe where a policy gradient algorithm could lead to strong performance. |
What is the effect of thinking time on larger models? | Larger models benefit more from thinking time, which leads to a higher success rate in solving math problems. | Chain of thought prompting leads to higher success rate of solving math problems. Larger models benefit more from thinking time. |
What early methods were used to improve Chain of Thought (CoT) reasoning? | Early work on improving CoT reasoning involved supervised learning on human-written reasoning traces or model-written traces filtered for answer correctness. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness. |
How can math performance of instruction-tuned models be improved? | The math performance of instruction-tuned models can be significantly boosted by prompting them appropriately, such as using 'think step by step' or more complex prompting to encourage reflection on related knowledge first. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What approach was found to improve CoT reasoning capabilities significantly? | CoT reasoning capabilities can be significantly improved by using reinforcement learning on a dataset of problems with automatically checkable solutions. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions. |
What are the two main approaches for improving the decoding process at test time? | The two main approaches for improving the decoding process at test time are parallel sampling and sequential revision. | Two main approaches for improving the decoding process are parallel sampling and sequential revision. |
What was one early method used to improve CoT reasoning? | One early method used to improve CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness. |
How can math performance of instruction tuned models be significantly boosted? | The math performance of instruction tuned models can be significantly boosted by prompting them appropriately, such as using 'think step by step' methods or more complex prompting to reflect on related knowledge first. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What type of dataset was found to improve CoT reasoning capabilities through reinforcement learning? | Reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers or coding tasks that can be checked with unit tests, was found to improve CoT reasoning capabilities. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests. |
What announcement highlighted a simple recipe that could lead to strong performance in CoT reasoning? | The announcement of o1 preview, o3, and the R1 tech report by DeepSeek AI in 2025 highlighted a simple recipe where a policy gradient algorithm could lead to strong performance. | This approach rose to prominence with the announcement of o1 preview, o3, and the R1 tech report DeepSeek AI, 2025, which showed that a simple recipe where a policy gradient algorithm could lead to strong performance. |
What methods were used to improve CoT reasoning? | Supervised learning on human written reasoning traces and model written traces filtered for answer correctness were used to improve CoT reasoning. Additionally, reinforcement learning on datasets with automatically checkable solutions also contributed to its enhancement. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness, where the latter can be seen as a rudimentary form of reinforcement learning RL . Later work found that the CoT reasoning capabilities can be significantly ... |
How can math performance of instruction tuned models be boosted? | Math performance of instruction tuned models can be significantly boosted by using appropriate prompting techniques, like 'think step by step' or more complex prompting to encourage reflection on related knowledge. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What was a notable finding from the later work on CoT reasoning? | A notable finding was that CoT reasoning capabilities can be significantly improved through reinforcement learning on datasets with problems that have automatically checkable solutions. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions. |
What is the fundamental intent of test time compute? | The fundamental intent of test time compute is to adaptively modify the model's output distribution at test time to select better samples and alter the model's predictions towards a more desired distribution. | The fundamental intent of test time compute is to adaptively modify the model s output distribution at test time. |
What early methods were used to improve Chain of Thought (CoT) reasoning? | Early methods involved supervised learning on human-written reasoning traces or model-written traces filtered for answer correctness, along with rudimentary reinforcement learning. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness, where the latter can be seen as a rudimentary form of reinforcement learning RL. |
How can math performance of instruction-tuned models be boosted? | The math performance of instruction-tuned models can be significantly boosted by prompting them appropriately, such as using 'think step by step' methods or more complex prompting to encourage reflection on related knowledge. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What is one method found to improve CoT reasoning capabilities? | One method to significantly improve CoT reasoning capabilities is through reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems and coding tasks. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests. |
What did the announcement of the o1 preview and R1 tech report reveal? | The announcement revealed that a simple recipe using a policy gradient algorithm could lead to strong performance in CoT reasoning tasks. | This approach rose to prominence with the announcement of o1 preview, o3, and the R1 tech report DeepSeek AI, 2025, which showed that a simple recipe where a policy gradient algorithm could lead to strong performance. |
What are two main approaches for improving the decoding process at test time? | The two main approaches for improving the decoding process at test time are parallel sampling and sequential revision. | Two main approaches for improving the decoding process are parallel sampling and sequential revision. |
What methods have been used to improve CoT reasoning? | Methods to improve CoT reasoning include supervised learning on human written reasoning traces and model written traces filtered for answer correctness, and reinforcement learning on datasets with automatically checkable solutions. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness, where the latter can be seen as a rudimentary form of reinforcement learning RL. Later work found that the CoT reasoning capabilities can be significantly i... |
How can math performance of instruction-tuned models be boosted? | The math performance of instruction-tuned models can be significantly boosted by using appropriate prompting techniques, such as think step by step prompting or more complex prompting that encourages reflection on related knowledge. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What is a notable feature of larger models in the context of problem-solving? | Larger models benefit more from thinking time when solving problems, which contributes to higher success rates. | Chain of thought prompting leads to higher success rate of solving math problems. Larger models benefit more from thinking time. |
What are the two main approaches for improving the decoding process at test time? | The two main approaches for improving the decoding process at test time are parallel sampling and sequential revision. | Two main approaches for improving the decoding process are parallel sampling and sequential revision. |
What is the fundamental intent of test time compute? | The fundamental intent of test time compute is to adaptively modify the model's output distribution at test time. | The fundamental intent of test time compute is to adaptively modify the model s output distribution at test time. |
What early methods were used to improve CoT reasoning? | Early methods included supervised learning on human written reasoning traces or model written traces filtered for answer correctness, which can be seen as a rudimentary form of reinforcement learning. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness, where the latter can be seen as a rudimentary form of reinforcement learning RL. |
How can math performance of instruction tuned models be boosted? | Math performance of instruction tuned models can be significantly boosted by prompting them appropriately, such as using 'think step by step' or more complex prompting to encourage reflection on related knowledge. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What did later work reveal about improving CoT reasoning capabilities? | Later work revealed that CoT reasoning capabilities can be significantly improved by reinforcing learning on datasets of problems with automatically checkable solutions, like STEM problems or coding tasks. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests Zelikman et al. 2022, Wang et al., 2023, Liu e... |
What decoding methods are used to improve test time performance? | Two main decoding methods for improving test time performance are parallel sampling and sequential revision, where parallel sampling generates multiple outputs simultaneously and provides guidance per step. | Two main approaches for improving the decoding process are parallel sampling and sequential revision. |
How does sequential revision improve a model's responses? | Sequential revision improves a model's responses by adapting them iteratively based on previous outputs and encouraging the model to reflect on and correct its mistakes. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What is a limitation of relying on a model's intrinsic self-correction capability? | A limitation of relying on a model's intrinsic self-correction capability is that it may not lead to improvement without external feedback. | The revision process may have to rely on a fine tuned model, as naively relying on the model s intrinsic capability of self correction without external feedback may not lead to improvement. |
What are the characteristics of parallel sampling? | Parallel sampling is characterized as simple, intuitive, and easier to implement, but it is limited by the model's capability to achieve the correct solution in one attempt. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. |
What risks are associated with sequential revision? | The risks associated with sequential revision include the possibility of modifying correct predictions to be incorrect and the potential introduction of other types of hallucinations. | Sequential explicitly asks the model to reflect on mistakes but it is slower and requires extra care during implementation as it does run the risk of correct predictions being modified to be incorrect or introducing other types of hallucinations. |
How does sequential revision work in model response adaptation? | Sequential revision adapts the model's responses iteratively based on the output in the previous step, asking the model to reflect on its existing response and correct mistakes. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What is a potential drawback of relying on a model's intrinsic capability for self-correction? | A potential drawback is that naively relying on the model's intrinsic capability of self-correction without external feedback may not lead to improvement. | The revision process may have to rely on a fine tuned model, as naively relying on the model s intrinsic capability of self correction without external feedback may not lead to improvement. |
What is the main advantage of parallel sampling? | The main advantage of parallel sampling is that it is simple, intuitive, and easier to implement. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. |
What did Snell et al. 2024 demonstrate about sequential and parallel compute? | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, whereas harder questions often perform best with an optimal ratio of sequential to parallel compute. | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, whereas harder questions often perform best with an optimal ratio of sequential to parallel compute. |
How does sequential revision adapt the model's responses? | Sequential revision adapts the model's responses iteratively based on the output in the previous step. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What are the advantages of parallel sampling compared to sequential revision? | Parallel sampling is simple, intuitive, and easier to implement. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. |
What did Snell et al. 2024 demonstrate about easier and harder questions? | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, while harder questions often perform best with an optimal ratio of sequential to parallel compute. | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, whereas harder questions often perform best with an optimal ratio of sequential to parallel compute. |
How does sequential revision adapt the model's responses? | Sequential revision adapts the model's responses iteratively based on the output from the previous step, allowing the model to reflect on its existing response and correct mistakes. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What is a potential drawback of relying on the model's intrinsic capability of self-correction? | A potential drawback is that naively relying on the model's intrinsic capability of self-correction without external feedback may not lead to improvement. | The revision process may have to rely on a fine tuned model, as naively relying on the model s intrinsic capability of self correction without external feedback may not lead to improvement. |
What advantages does parallel sampling offer? | Parallel sampling is simple, intuitive, and easier to implement, but it depends on the model's ability to achieve the correct solution in one go. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. |
What findings did Snell et al. 2024 present regarding question difficulty and computational methods? | Snell et al. 2024 found that easier questions benefit from purely sequential test time compute, while harder questions often perform best with an optimal ratio of sequential to parallel compute. | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, whereas harder questions often perform best with an optimal ratio of sequential to parallel compute. |
What early work was done to improve Chain of Thought reasoning? | Early work on improving Chain of Thought reasoning included doing supervised learning on human-written reasoning traces and model-written traces filtered for answer correctness, which resembled a basic form of reinforcement learning. | Early work on improving CoT reasoning involved doing supervised learning on human written reasoning traces or model written traces filtered for answer correctness, where the latter can be seen as a rudimentary form of reinforcement learning RL. |
How can math performance of instruction-tuned models be boosted? | Math performance of instruction-tuned models can be significantly boosted by using appropriate prompting techniques, such as prompting to think step-by-step or employing more complex prompting to encourage reflection on related knowledge. | Some other work found that one could significantly boost math performance of instruction tuned models by prompting them appropriately, with think step by step Kojima et al. 2022 or more complex prompting to encourage the model to reflect on related knowledge first Yasunaga et al. 2023. |
What methods were found to significantly improve CoT reasoning capabilities? | CoT reasoning capabilities can be significantly improved by using reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers or coding tasks that can be checked with unit tests. | Later work found that the CoT reasoning capabilities can be significantly improved by doing reinforcement learning on a dataset of problems with automatically checkable solutions, such as STEM problems with short answers, or coding tasks that can be checked with unit tests Zelikman et al. 2022, Wang et al., 2023, Liu e... |
What is the fundamental intent of test time compute? | The fundamental intent of test time compute is to adaptively modify the model's output distribution at test time. | The fundamental intent of test time compute is to adaptively modify the model s output distribution at test time. |
What are the two main approaches to improving the decoding process? | The two main approaches for improving the decoding process are parallel sampling and sequential revision. | Two main approaches for improving the decoding process are parallel sampling and sequential revision. |
How does the sequential revision method adapt the model's responses? | The sequential revision method adapts the model's responses iteratively based on the output in the previous step, asking the model to reflect on its existing response and correct mistakes. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What is the main advantage of parallel sampling compared to sequential methods? | The main advantage of parallel sampling is that it is simple, intuitive, and easier to implement. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. |
How do easier and harder questions perform in relation to sequential and parallel compute? | Easier questions benefit from purely sequential test time compute, while harder questions often perform best with an optimal ratio of sequential to parallel compute. | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, whereas harder questions often perform best with an optimal ratio of sequential to parallel compute. |
How does sequential revision adapt the model's responses? | Sequential revision adapts the model's responses iteratively based on the output in the previous step, asking the model to reflect and correct its mistakes. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What are the benefits and drawbacks of parallel sampling? | Parallel sampling is simple, intuitive, and easier to implement, but it is limited by the model's capability to achieve the correct solution in one go. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. |
How do sequential and parallel methods complement each other? | Sequential and parallel methods can be used together, with easier questions benefiting from sequential compute and harder questions performing best with a mix of both methods. | These two methods can be used together. Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, whereas harder questions often perform best with an optimal ratio of sequential to parallel compute. |
How does sequential revision adapt the model's responses? | Sequential revision adapts the model's responses iteratively based on the output in the previous step. | Sequential revision adapts the model s responses iteratively based on the output in the previous step. |
What is a potential drawback of relying on a model's intrinsic capability of self-correction? | A potential drawback is that it may not lead to improvement without external feedback. | The revision process may have to rely on a fine tuned model, as naively relying on the model s intrinsic capability of self correction without external feedback may not lead to improvement. |
What is the advantage of parallel sampling compared to sequential revision? | The advantage of parallel sampling is that it is simple, intuitive, and easier to implement. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. |
What did Snell et al. 2024 demonstrate regarding easier and harder questions? | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, while harder questions perform best with a mixture of sequential and parallel compute. | Snell et al. 2024 showed that easier questions benefit from purely sequential test time compute, whereas harder questions often perform best with an optimal ratio of sequential to parallel compute. |
How does sequential revision adapt the model's responses? | Sequential revision adapts the model's responses iteratively based on the output in the previous step, allowing the model to reflect on its existing response and correct mistakes. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What are the limitations of relying on a model's intrinsic capability of self-correction? | Relying naively on the model's intrinsic capability of self-correction without external feedback may not lead to improvement. | The revision process may have to rely on a fine tuned model, as naively relying on the model s intrinsic capability of self correction without external feedback may not lead to improvement. |
What is the fundamental difference between parallel sampling and sequential revision? | The fundamental difference is that parallel sampling is simpler and easier to implement, while sequential revision explicitly asks the model to reflect on mistakes but is slower and requires more careful implementation. | Parallel sampling is simple, intuitive and easier to implement, but bounded by the model capability of whether it can achieve the correct solution in one go. Sequential explicitly asks the model to reflect on mistakes but it is slower and requires extra care during implementation. |
What does the Best of N algorithm do? | The Best of N algorithm collects N independent samples and chooses the highest ranking sample according to a scoring function. | Best of N is the simplest such algorithm one just collects N independent samples and chooses the highest ranking sample according to some scoring function. |
How does sequential revision adapt model responses? | Sequential revision adapts model responses iteratively by asking the model to reflect on its existing response and correct mistakes based on the output from the previous step. | Sequential revision adapts the model s responses iteratively based on the output in the previous step, asking the model to intentionally reflect its existing response and correct mistakes. |
What are the limitations of relying on the model's intrinsic capability of self-correction? | Relying naively on the model's intrinsic capability of self-correction without external feedback may not lead to improvement. | The revision process may have to rely on a fine tuned model, as naively relying on the model s intrinsic capability of self correction without external feedback may not lead to improvement. |
What is beam search in the context of parallel sampling? | Beam search is a more sophisticated search algorithm that maintains a set of promising partial sequences and alternates between extending them and pruning the less promising ones. | Beam search is a more sophisticated search algorithm that makes the search process more adaptive, spending more sampling computation on more promising parts of the solution space. |
What improvement did Xie et al. achieve on benchmarks using the Codex model? | Xie et al. achieved a 5-6% improvement on few shot GSM8k, AQuA and StrategyQA benchmarks with the Codex model. | These experiments by Xie et al. achieved 5 6 improvement on few shot GSM8k, AQuA and StrategyQA benchmarks with the Codex model. |
How does the process reward model (PRM) function during beam search according to Wu et al.? | According to Wu et al., the PRM determines how much each node should be expanded at each depth during beam search, based on softmax normalized reward scores. | Reward balanced search short for REBASE Wu et al. 2025 separately trained a process reward model PRM to determine how much each node should be expanded at each depth during beam search, according to the softmax normalized reward scores. |
What is the purpose of the RATIONALYST model trained by Jiang et al.? | The RATIONALYST model trained by Jiang et al. is designed for beam search guidance on synthetic rationales conditioned on a large amount of unlabelled data. | Jiang et al. 2024 trained their PRM, named RATIONALYST , for beam search guidance on synthetic rationales conditioned on a large amount of unlabelled data. |
What method does RATIONALYST use to filter good rationales? | RATIONALYST filters good rationales based on whether they help reduce the negative log probability of true answer tokens by a threshold. | Good rationales are filtered based on whether they help reduce the neg log prob of true answer tokens by a threshold, when comparing the difference between when the rationales is included in the context vs not. |
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