VaSST uses soft symbolic trees for probabilistic symbolic regression.
problem Efficiently recover symbolic expressions from noisy data.
method Variational inference with soft symbolic trees.
result Superior performance in structural recovery and predictive accuracy.
Symbolic regression finds simple formulas for implied volatility.
problem Discovering accurate parametric representations for implied volatility.
method Symbolic regression to find analytic formulas from market data.
result Symbolic regression identifies compact parametrizations with competitive fitting performance.
Secure Multiparty Computation protects data privacy in Symbolic Regression.
problem Data privacy in Symbolic Regression models.
method Secure Multiparty Computation for vertical partitioning.
result Comparable performance to centralized model while preserving privacy.
Paper closes neural-symbolic learning loop with grammar model and back-search algorithm.
problem Slow convergence in neural-symbolic learning due to error propagation issues.
method Introduces grammar model as symbolic prior and back-search algorithm for efficient error propagation.
result Significantly outperforms RL methods in performance, converging speed, and data efficiency.
Bayesian symbolic regression automates model discovery from data.
problem Learning closed-form mathematical models from data using heuristic methods.
method Probabilistic approach to symbolic regression, connecting to information theory and statistical physics.
result Probabilistic approach provides model plausibility and performance guarantees.
Meta-learning symbolic default hyperparameters from dataset properties.
problem Empirical hyperparameter optimization is slow and requires manual configuration.
method Evolutionary algorithm to learn symbolic hyperparameter formulas from dataset properties.
result Meta-learning finds viable symbolic defaults for ML algorithms.
Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise that the statistical unit of interest is the symbol, and that inference is requ…
Symbolic regression improved by incorporating prior knowledge.
problem Insufficient guidance from training data alone for model accuracy.
method Multi-objective symbolic regression combining training data and prior constraints.
result Models that fit training data well and comply with prior knowledge.
Active learning improves SR by proposing experiments in data-limited settings.
problem Efficiently gathering data for symbolic regression with physical constraints.
method Query by committee using the Pareto frontier of equations, with physical constraints.
result Reduces data required for SR and achieves state-of-the-art results.
DEFINED improves wireless symbol detection with limited pilot data.
problem Efficient symbol detection over block-fading channels with scarce pilot data.
method In-context learning with decision feedback mechanism.
result Significant performance improvements, often needing only a single pilot pair.
R2T hybrid model improves robust regression for asymmetric noise.
problem Least-squares regression fails with asymmetric structured noise.
method Transformer encoder, compression NN, fixed symbolic equation.
result Median regression MSE of 6e-6 to 3.5e-5 on synthetic data.
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
Transformer models can solve complex math problems with less data.
problem Solving complex symbolic mathematics problems with limited data.
method Pretrain transformer models on language translation tasks and fine-tune for symbolic math.
result Pretrained transformer models achieve comparable accuracy to state-of-the-art models with less data.
Bayesian symbolic regression uncovers missing physics from data with uncertainty quantification.
problem Incomplete knowledge of physical laws from experimental data.
method Bayesian symbolic regression using Reversible Jump Markov Chain Monte Carlo.
result Uncertainty quantification in recovered model structures.
SE-RRMs solve structured problems like Sudoku and ARC-AGI by enforcing symbol equivariance.
problem Structured reasoning problems like Sudoku and ARC-AGI.
method Symbol-equivariant recurrent reasoning models enforcing permutation equivariance.
result SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize to larger and smaller instances.
OccamNet finds interpretable symbolic fits to data efficiently.
problem Complex neural models extrapolate poorly and are hard to interpret.
method Samples functions, biases towards better fits, and uses cross-entropy matching.
result Outperforms state-of-the-art symbolic regression methods on real-world datasets.
PySR method automates discovering equations from data in chaotic dynamics and epidemics.
problem Discovering equations from complex data in dynamical systems.
method Symbolic regression methods, focusing on PySR.
result PySR method efficiently infers equations from chaotic dynamics and epidemic models, matching original forms.
Symbolic LSTM improves time series forecasting by reducing hyperparameter sensitivity.
problem High sensitivity to hyperparameters and random initialization in numerical time series forecasting.
method Combining LSTM with a dimension-reducing symbolic representation.
result Symbolic representation alleviates forecasting problems and speeds up training.
Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.
problem Determining geometric data from boundary symbol of connection Laplacian.
method Analyze symbol of Dirichlet-to-Neumann operator associated with connection Laplacian.
result Geometric data on boundary and normal derivatives are determined by symbol.
Develops a Bayesian framework for symbolic regression of scientific expressions.
problem Lack of principled uncertainty quantification and interpretability in existing symbolic regression methods.
method Hierarchical Bayesian framework with tree-structured symbolic expressions and Markov chain Monte Carlo inference.
result Robust performance on various datasets, including single-atom catalysis.
Improved symbolic regression finds optimal formulas robust to noise.
problem Finding accurate formulas for noisy data.
method Exploits graph modularity, uses normalizing flows, and statistical hypothesis testing.
result Discoveres many formulas previously unattainable.
DEFINED uses decision feedback ICL to detect symbols with minimal pilot data.
problem Limited pilot data in wireless receivers.
method In-context learning with decision feedback mechanism.
result Small Transformer trained with DEFINED achieves significant performance improvements.
Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this propert…
S2KAN integrates symbolic primitives into neural network activations for improved interpretability.
problem Training activations in KANs often lack symbolic fidelity, leading to unintelligible models.
method Softly Symbolified Kolmogorov-Arnold Networks (S2KAN) integrates symbolic primitives into training with learnable gates and a Minimum Description Length objective.
result S2KAN discovers interpretable forms when symbolic terms suffice, gracefully degrading to dense splines when necessary.
ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.
Study shows how transformers classify symbols without naming them, proving a margin-versus-collision criterion.
problem How transformers classify symbols without naming them.
method Logistic classification analysis of transformer-kernel regime, colored collision graph.
result Decomposes learned predictor into ideal template-level classifier and finite-sample perturbation.
Improves neural network search in combinatorial spaces of mathematical symbols.
problem Early commitment and initialization bias limit exploration in neural network search.
method Entropy regularization and distribution initialization methods.
result Improves performance, increases sample efficiency, lowers solution complexity.
Generative Neuro-Symbolic model learns from raw data with rich conceptual representations.
problem Learning rich, general-purpose conceptual representations from raw perceptual inputs.
method Generative Neuro-Symbolic (GNS) model combining symbolic and neural network approaches.
result Model learns from raw data and generalizes to 4 unique tasks.
Develops experimental design for discovering missing physics in bioreactors.
problem Discovering missing physics in incomplete model structures of process systems.
method Combines universal differential equations and symbolic regression with sequential experimental design.
result Successfully recovered true model structure of a bioreactor using machine learning techniques.
Paper analyzes symbolic-dynamics inspired Markov modeling for time-series data.
problem Capturing temporal patterns in sequential data for statistical learning.
method Two-step process: discretization of continuous attributes and estimation of temporal memory.
result Effective Markov modeling depends on accurate discretization and memory estimation.
Neuro-symbolic traders suppress market prices, highlighting risks to stability.
problem Understanding and quantifying the influence of AI-generated financial models on markets.
method Developed virtual neuro-symbolic traders using deep generative models and tested them in a virtual market.
result Neuro-symbolic traders suppress market prices compared to historical data, indicating potential market instability.
We present the perceptor gradients algorithm -- a novel approach to learning symbolic representations based on the idea of decomposing an agent's policy into i) a perceptor network extracting symbols from raw observation data and ii) a task encoding program which maps the input symbols to output actions. We show that t…
This paper presents a technique for reduced-order Markov modeling for compact representation of time-series data. In this work, symbolic dynamics-based tools have been used to infer an approximate generative Markov model. The time-series data are first symbolized by partitioning the continuous measurement space of the …
Extraction of symbolic information from signals is an active field of research enabling numerous applications especially in the Musical Information Retrieval domain. This complex task, that is also related to other topics such as pitch extraction or instrument recognition, is a demanding subject that gave birth to nume…
Machine learning finds new natural laws from noisy data.
problem Discovery of natural laws relies on human inspiration.
method Recursive-LASSO-based symbolic regression (RLS) method.
result Data-driven formulation of natural laws from noisy data.
The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such r…
EPSTE: A geometric token and deep learning approach to estimating transfer entropy in neuroimaging time series
problem Inferring directed interactions between neural systems from EEG and MEG
method Reframing TE estimation as a learnable problem operating on structured symbolic representations
result EPSTE achieves near-perfect recovery of ground-truth directed structure and significantly lower absolute error than the baseline
Study evaluates clustering methods for Google Trends data.
problem Clustering high-dimensional, noisy time series data.
method Symbolic Aggregate Approximation (SAX), Enhanced SAX (eSAX), and Topological Data Analysis (TDA).
result TDA provides more balanced and meaningful groupings than SAX and eSAX.
Deep neural network generates symbolic equations from data.
problem Lack of insight into underlying mappings from traditional deep learning.
method Combines deep learning flexibility with symbolic solutions.
result Accurately generates governing equations for dynamical systems.
Zoetrope Genetic Programming improves symbolic regression performance.
problem Evolutionary symbolic regression for complex mathematical expressions.
method Zoetropic representation, repeated fusion operations, linear combination, crossover, mutation, selection.
result Zoetrope Genetic Programming achieves state-of-the-art performance and low computational time.
Extract symbolic models from deep learning with inductive biases.
problem Interpreting and discovering physical principles from deep neural networks.
method Introduce strong inductive biases in GNNs, encourage sparse latent representations, apply symbolic regression.
result Extracted symbolic equations from neural networks, including known force laws and new analytic formulas.
Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of symbolic regression. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. …
PandaAI: A practical agent for neuro-symbolic data analysis and decision-making in finance
problem Sequential decision-making in finance
method Leveraging LLMs for market regime modeling and constrained alpha generation
result PandaAI achieves higher Rank IC and lower maximum drawdown
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…
Research on style transfer and domain translation has clearly demonstrated the ability of deep learning-based algorithms to manipulate images in terms of artistic style. More recently, several attempts have been made to extend such approaches to music (both symbolic and audio) in order to enable transforming musical st…
Reinforcement learning and symbolic planning have both been used to build intelligent autonomous agents. Reinforcement learning relies on learning from interactions with real world, which often requires an unfeasibly large amount of experience. Symbolic planning relies on manually crafted symbolic knowledge, which may …
Efficient algorithm for identifying causal effects in linear models.
problem Determining causal effects from observational data under latent confounding.
method Symbolic computation and efficient algorithm for finding identifying formulas.
result Proves the existence of identifying formulas of a specified degree in quasi-polynomial time.
For an arbitrary Riemannian manifold X and Hermitian vector bundles E and F over X we define the notion of the normal symbol of a pseudodifferential operator P from E to F. The normal symbol of P is a certain smooth function from the cotangent bundle T∗X to the homomorphism bundle Hom(E,F) and dep…