More details on each of these datasets are given below. This data is referred to as "in-domain" because the validation data is generated using the same As for cache hits, they are also not counted as visits. Figure 9: MCTS-Guided decoding algorithm for Symbolic Regression with the pre-trained transformer model used for expansion and evaluation steps. MCTS algorithm (Figure 1) which can be used in a similar fashion but without sharing information with the pre-trained transformer. The approach involves fine-tuning an actor-critic-like model to adjust the pre-trained model on a group of symbolic regression instances.

Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's

More details on each of these datasets are given below. This data is referred to as "in-domain" because the validation data is generated using the same As for cache hits, they are also not counted as visits. Figure 9: MCTS-Guided decoding algorithm for Symbolic Regression with the pre-trained transformer model used for expansion and evaluation steps. MCTS algorithm (Figure 1) which can be used in a similar fashion but without sharing information with the pre-trained transformer. The approach involves fine-tuning an actor-critic-like model to adjust the pre-trained model on a group of symbolic regression instances.

Symbolic regression aims to discover mathematical equations that fit given numerical data. It has been applied in various fields of scientific research, such as producing human-readable expressions that explain physical phenomena. Recently, Neural symbolic regression (NSR) methods that involve Transformers pre-trained on large-scale synthetic datasets have gained attention. While these methods offer advantages such as short inference time, they suffer from low performance, particularly when the number of input variables is large. In this study, we hypothesized that this limitation stems from the memorization bias of Transformers in symbolic regression. We conducted a quantitative evaluation of this bias in Transformers using a synthetic dataset and found that Transformers rarely generate expressions not present in the training data. Additional theoretical analysis reveals that this bias arises from the Transformer's inability to construct expressions compositionally while verifying their numerical validity. We finally examined if tailoring test-time strategies can lead to reduced memorization bias and better performance. We empirically demonstrate that providing additional information to the model at test time can significantly mitigate memorization bias. On the other hand, we also find that reducing memorization bias does not necessarily correlate with improved performance. These findings contribute to a deeper understanding of the limitations of NSR approaches and offer a foundation for designing more robust, generalizable symbolic regression methods. Code is available at https://github.com/Shun-0922/Mem-Bias-NSR .

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained transformer-based models in generating equations as sequences, leveraging large-scale pre-training on synthetic datasets and offering notable advantages in terms of inference time over classical Genetic Programming (GP) methods. However, these models primarily rely on supervised pre-training goals borrowed from text generation and overlook equation discovery objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise.

Recently, a number of researchers have proposed spectral algorithms for learning models of dynamical systems — for example, Hidden Markov Models (HMMs), Partially Observable Markov Decision Processes (POMDPs), and Transformed Predictive State Representations (TPSRs). These algorithms are attractive since they are statistically consistent and not subject to local optima. However, they are batch methods: they need to store their entire training data set in memory at once and operate on it as a large matrix, and so they cannot scale to extremely large data sets (either many examples or many features per example). In turn, this restriction limits their ability to learn accurate models of complex systems. To overcome these limitations, we propose a new online spectral algorithm, which uses tricks such as incremental Singular Value Decomposition (SVD) and random projections to scale to much larger data sets and more complex systems than previous methods. We demonstrate the new method on an inertial measurement prediction task and a high-bandwidth video mapping task and we illustrate desirable behaviors such as "closing the loop," where the latent state representation changes suddenly as the learner recognizes that it has returned to a previously known place.

A central problem in artificial intelligence is that of planning to maximize future reward under uncertainty in a partially observable environment. In this paper we propose and demonstrate a novel algorithm which accurately learns a model of such an environment directly from sequences of action-observation pairs. We then close the loop from observations to actions by planning in the learned model and recovering a policy which is near-optimal in the original environment. Specifically, we present an efficient and statistically consistent spectral algorithm for learning the parameters of a Predictive State Representation (PSR). We demonstrate the algorithm by learning a model of a simulated high-dimensional, vision-based mobile robot planning task, and then perform approximate point-based planning in the learned PSR. Analysis of our results shows that the algorithm learns a state space which efficiently captures the essential features of the environment. This representation allows accurate prediction with a small number of parameters, and enables successful and efficient planning.