Perceptor Gradients learns symbolic representations from raw data.
problem Learning transferable symbolic representations from raw data.
method Decomposes policy into perceptor network and task encoding program.
result Efficiently learns symbolic representations for control tasks.
Symbolic neural network for analyzing and patching complex systems.
problem Analyzing and verifying complex neural networks.
method Symbolic representation of piecewise-linear neural networks for efficient computation.
result Demonstrated applications in weakest preconditions, strongest postconditions, and patching.
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.
ABBA creates a new symbolic time series representation based on Brownian bridge.
problem Representing time series data in a compact, symbolic form.
method Adaptive polygonal chain approximation followed by mean-based clustering.
result ABBA outperforms other representations in preserving time series shape information.
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…
Neural networks learn symbolic structure to perform compositional tasks.
problem How neural networks perform well on compositional tasks without explicit representations.
method ROLE analysis to uncover symbolic structure in recurrent neural networks.
result Neural networks converge to solutions that implicitly represent symbolic structure.
SGE learns symbolic node representations from relational data.
problem Mining insights from complex, real-world systems.
method SGE uses frequent pattern mining on a node's neighborhood to learn symbolic node representations.
result SGE outperforms shallow node embedding methods on a venue classification task.
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.
The Kashaev invariants of 3-manifolds are based on 6j-symbols from the representation theory of the Weyl algebra, a Hopf algebra corresponding to the Borel subalgebra of $U_q(sl(2,\C))$. In this paper, we show that Kashaev's 6j-symbols are intertwining operators of local representations of quantum Teichmüller space…
Graph networks learn symbolic physics laws from simulations.
problem Learning interpretable physics laws from simulations.
method Inductive biases on graph networks for symbolic regression.
result Graph networks can learn symbolic laws of physics.
Many real-world domains can be expressed as graphs and, more generally, as multi-relational knowledge graphs. Though reasoning and learning with knowledge graphs has traditionally been addressed by symbolic approaches, recent methods in (deep) representation learning has shown promising results for specialized tasks su…
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.
In this paper we use fractal geometry to investigate boundary aspects of the first homology group for finite coverings of the modular surface. We obtain a complete description of algebraically invisible parts of this homology group. More precisely, we first show that for any modular subgroup the geodesic forward dynami…
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.
The paper connects knot homology, quantum 6j-symbols, and complements of knots.
problem Investigating the relationship between knot homology, quantum 6j-symbols, and knot complements.
method Developed a grading rule for HOMFLY-PT and Kauffman homology, found relationships between A-polynomials, and conjectured closed-form expressions for quantum 6j-symbols and knot complements.
result Closed-form expressions for SO(N) quantum 6j-symbols and conjectured expressions for (a,t)-deformed F_K for knot complements.
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.
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…
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.
Efficiently searches through Gaussian process kernels using symbolic representation and Bayesian optimization.
problem Manual selection of kernels in Gaussian processes is complex and computationally expensive.
method Proposes a novel method using symbolic representation and Bayesian optimization to search through a structured kernel space.
result Empirically shows a computationally more efficient way of searching through a discrete kernel space.
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
The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. The research focus has mostly been on improving the accuracy and efficiency of classifiers, while their interpretability has been somewhat neglected. Classifier interpretabil…
CSML learns causal structures for few-shot learning.
problem Spurious correlations limit deep learning generalization.
method CSML combines perception, causal induction, and reasoning modules.
result CSML achieves superior few-shot learning across tasks.
Explores tensor products in hyperdimensional computing.
problem Understanding tensor products in hyperdimensional computing.
method Generalized results from graph embeddings to vector symbolic architectures and hyperdimensional computing.
result Tensor product is the most general and expressive representation with errorless unbinding and detection.
New neural KB representation speeds up reasoning with large symbolic knowledge bases.
problem Efficiently reasoning with large symbolic knowledge bases.
method Sparse-matrix reified knowledge base, enabling fully differentiable, scalable neural modules.
result Competitive performance on KB completion and semantic parsing benchmarks.
The Interaction-Transformation (IT) is a new representation for Symbolic Regression that restricts the search space into simpler, but expressive, function forms. This representation has the advantage of creating a smoother search space unlike the space generated by Expression Trees, the common representation used in Ge…
PG-IM uses neural-symbolic programs to manipulate images.
problem Creating holistic image representations and manipulations.
method PG-IM detects patterns, induces symbolic programs, and manipulates images using a neural network.
result PG-IM learns from a single image and achieves superior performance.
We generalize the colored Alexander invariant of knots to an invariant of graphs, and we construct a face model for this invariant by using the corresponding 6j-symbol, which comes from the non-integral representations of the quantum group U_q(sl_2). We call it the SL(2, C) quantum 6j-symbol, and show its relation to t…
Framework learns portable representations for diverse tasks.
problem Creating task-independent abstract representations for diverse environments.
method Autonomously learns portable representations in egocentric space.
result Portable representations enable task-independent planning and transfer.
QABBA improves time series storage efficiency while preserving shape information.
problem Efficient storage and shape preservation of time series data.
method Quantized symbolic time series approximation (QABBA) using ABBA technique.
result QABBA achieves a new state-of-the-art on Monash regression dataset.
Neural-symbolic model improves link prediction in knowledge graphs.
problem Effective relational learning and reasoning for AI systems.
method Neural-symbolic graph neural network that learns over all paths in knowledge graphs.
result Neural-symbolic model outperforms path-based approaches in link prediction.
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.
Symbolic Data Analysis is based on special descriptions of data - symbolic objects (SO). Such descriptions preserve more detailed information about units and their clusters than the usual representations with mean values. A special kind of symbolic object is a representation with frequency or probability distributions …
In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of t…
Hybrid model learns novel handwritten characters better than neural or symbolic models alone.
problem Generating novel yet structured concepts.
method Neuro-symbolic model combining neural networks and probabilistic programs.
result Hybrid model outperforms alternative models in learning and generalizing novel handwritten characters.
Paper proposes a bijective approach for signal/symbol translation using variational auto-encoders.
problem Extracting symbolic information from signals, especially in music, is challenging and non-generic.
method Turned into a density estimation task, using two variational auto-encoders with additive constraint.
result Bijective signal/symbol translation achieved, allowing both signal-to-symbol and symbol-to-signal inference.
Enhances speech quality in noisy environments using symbolic sequential modeling.
problem Improving speech quality in noisy conditions.
method Incorporates symbolic sequential modeling into speech enhancement framework.
result Significant improvement in speech quality metrics (PESQ, STOI) on TIMIT dataset.
The paper extends Lie bracket to noncommutative geometry using differential operators.
problem Generalizing Lie bracket to noncommutative geometry.
method Antisymmetrizing compositions of vector fields and treating symbols of differential operators.
result Provided necessary and sufficient conditions for jet modules to represent differential operators.
Paper introduces a new symbol map for differential symmetry breaking operators.
problem Generalizing the symbol map to non-abelian settings.
method Introduces and studies the truncated symbol map Symb0(D). result Classified and constructed differential intertwining operators and homomorphisms.
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.
We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or resonant) weights, this procedure gives rise to a quantization, which is intrinsi…
PDE-NetGen converts physical equations to neural networks for various scientific problems.
problem Bridging physics and deep learning for efficient neural network architectures.
method Combines symbolic calculus and neural network generation to translate PDEs into NN architectures.
result Generates compact, computationally-efficient physics-informed NN architectures.
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 …
A neural network learns relational representations from raw data.
problem Learning reusable representations from raw pixel data.
method Explicitly relational neural network architecture trained on visual relational tasks.
result The architecture outperforms baselines on unseen tasks.
Co-eye combines multiple symbolic representations to improve time series classification accuracy.
problem Challenges in time series classification due to domain diversity.
method Inspired by compound eyes, Co-eye uses multiple symbolic representations and hyper-parameterised lenses to classify time series data.
result Co-eye outperforms state-of-the-art techniques in accuracy and robustness across various domains.
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is ma…
This paper introduces lattice representations for efficient discrete learning.
problem Efficient learning of discrete representations in Euclidean space.
method Lattice quantization and novel algorithms for efficient learning.
result New mathematical result linking training and inference expressions.
In this paper, we consider the problem of event classification with multi-variate time series data consisting of heterogeneous (continuous and categorical) variables. The complex temporal dependencies between the variables combined with sparsity of the data makes the event classification problem particularly challengin…
Researchers extend pseudodifferential calculus on filtered manifolds using fixed point algebras.
problem Defining operators with varying orders on filtered manifolds.
method Using generalized fixed point algebras and nilpotent Lie groups, they construct a new calculus.
result They establish a new calculus that reflects the behavior of differential operators on filtered manifolds.