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Publications
Machine learning and information theory concepts towards an AI Mathematician
The current state of the art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms … (see more)of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities—which correspond to our intuition and habitual behaviors—but still lacks something important regarding system 2 abilities—which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example, by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.
Current model-based reinforcement learning (MBRL) agents struggle with long-term dependencies. This limits their ability to effectively solv… (see more)e tasks involving extended time gaps between actions and outcomes, or tasks demanding the recalling of distant observations to inform current actions. To improve temporal coherence, we integrate a new family of state space models (SSMs) in world models of MBRL agents to present a new method, Recall to Imagine (R2I). This integration aims to enhance both long-term memory and long-horizon credit assignment. Through a diverse set of illustrative tasks, we systematically demonstrate that R2I not only establishes a new state-of-the-art for challenging memory and credit assignment RL tasks, such as BSuite and POPGym, but also showcases superhuman performance in the complex memory domain of Memory Maze. At the same time, it upholds comparable performance in classic RL tasks, such as Atari and DMC, suggesting the generality of our method. We also show that R2I is faster than the state-of-the-art MBRL method, DreamerV3, resulting in faster wall-time convergence.
Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained … (see more)using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.
Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained … (see more)using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.
Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained … (see more)using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.
Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained … (see more)using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.
The Mediterranean Basin has historically been subject to alien plant invasions that threaten its unique biodiversity. This seasonally dry an… (see more)d densely populated region is undergoing severe climatic and socioeconomic changes, and it is unclear whether these changes will worsen or mitigate plant invasions. Predictions are often biased, as species may not be in equilibrium in the invaded environment, depending on their invasion stage and ecological characteristics. To address future predictions uncertainty, we identified invasion hotspots across multiple biased modelling scenarios and ecological characteristics of successful invaders. We selected 92 alien plant species widespread in Mediterranean Europe and compiled data on their distribution in the Mediterranean and worldwide. We combined these data with environmental and propagule pressure variables to model global and regional species niches, and map their current and future habitat suitability. We identified invasion hotspots, examined their potential future shifts, and compared the results of different modelling strategies. Finally, we generalised our findings by using linear models to determine the traits and biogeographic features of invaders most likely to benefit from global change. Currently, invasion hotspots are found near ports and coastlines throughout Mediterranean Europe. However, many species occupy only a small portion of the environmental conditions to which they are preadapted, suggesting that their invasion is still an ongoing process. Future conditions will lead to declines in many currently widespread aliens, which will tend to move to higher elevations and latitudes. Our trait models indicate that future climates will generally favour species with conservative ecological strategies that can cope with reduced water availability, such as those with short stature and low specific leaf area. Taken together, our results suggest that in future environments, these conservative aliens will move farther from the introduction areas and upslope, threatening mountain ecosystems that have been spared from invasions so far.
The Mediterranean Basin has historically been subject to alien plant invasions that threaten its unique biodiversity. This seasonally dry an… (see more)d densely populated region is undergoing severe climatic and socioeconomic changes, and it is unclear whether these changes will worsen or mitigate plant invasions. Predictions are often biased, as species may not be in equilibrium in the invaded environment, depending on their invasion stage and ecological characteristics. To address future predictions uncertainty, we identified invasion hotspots across multiple biased modelling scenarios and ecological characteristics of successful invaders. We selected 92 alien plant species widespread in Mediterranean Europe and compiled data on their distribution in the Mediterranean and worldwide. We combined these data with environmental and propagule pressure variables to model global and regional species niches, and map their current and future habitat suitability. We identified invasion hotspots, examined their potential future shifts, and compared the results of different modelling strategies. Finally, we generalised our findings by using linear models to determine the traits and biogeographic features of invaders most likely to benefit from global change. Currently, invasion hotspots are found near ports and coastlines throughout Mediterranean Europe. However, many species occupy only a small portion of the environmental conditions to which they are preadapted, suggesting that their invasion is still an ongoing process. Future conditions will lead to declines in many currently widespread aliens, which will tend to move to higher elevations and latitudes. Our trait models indicate that future climates will generally favour species with conservative ecological strategies that can cope with reduced water availability, such as those with short stature and low specific leaf area. Taken together, our results suggest that in future environments, these conservative aliens will move farther from the introduction areas and upslope, threatening mountain ecosystems that have been spared from invasions so far.
The Mediterranean Basin has historically been subject to alien plant invasions that threaten its unique biodiversity. This seasonally dry an… (see more)d densely populated region is undergoing severe climatic and socioeconomic changes, and it is unclear whether these changes will worsen or mitigate plant invasions. Predictions are often biased, as species may not be in equilibrium in the invaded environment, depending on their invasion stage and ecological characteristics. To address future predictions uncertainty, we identified invasion hotspots across multiple biased modelling scenarios and ecological characteristics of successful invaders. We selected 92 alien plant species widespread in Mediterranean Europe and compiled data on their distribution in the Mediterranean and worldwide. We combined these data with environmental and propagule pressure variables to model global and regional species niches, and map their current and future habitat suitability. We identified invasion hotspots, examined their potential future shifts, and compared the results of different modelling strategies. Finally, we generalised our findings by using linear models to determine the traits and biogeographic features of invaders most likely to benefit from global change. Currently, invasion hotspots are found near ports and coastlines throughout Mediterranean Europe. However, many species occupy only a small portion of the environmental conditions to which they are preadapted, suggesting that their invasion is still an ongoing process. Future conditions will lead to declines in many currently widespread aliens, which will tend to move to higher elevations and latitudes. Our trait models indicate that future climates will generally favour species with conservative ecological strategies that can cope with reduced water availability, such as those with short stature and low specific leaf area. Taken together, our results suggest that in future environments, these conservative aliens will move farther from the introduction areas and upslope, threatening mountain ecosystems that have been spared from invasions so far.
