Artin groups have a special structure that helps prove a complex mathematical conjecture.
problem Proving the Farrell-Jones isomorphism conjecture for Artin groups.
method Identifying an inductive structure in Artin groups and applying it to the conjecture.
result The Farrell-Jones isomorphism conjecture is proven for certain Artin groups.
Noise affects the effectiveness of interpolating models, especially those with strong inductive biases.
problem The impact of noise on interpolating models with strong inductive biases.
method Analyzing linear and classification models with sparse ground truths, proving fast rates for interpolators.
result Strong inductive biases can lead to faster but noisier interpolators, contrary to intuition.
Strong inductive biases prevent harmless interpolation in overparameterized models.
problem Understanding the conditions under which overparameterized models can interpolate noise without overfitting.
method Theoretical analysis of high-dimensional kernel regression and deep neural networks, focusing on the role of inductive biases.
result The strength of an estimator's inductive bias determines whether interpolation is harmless or requires fitting noise for good generalization.
Machine learning refactors knowledge to improve learning efficiency.
problem Inductive program synthesis efficiency through knowledge restructuring.
method Introduces Knorf, a system that refactors knowledge bases using constraint optimization.
result Learning from refactored knowledge improves predictive accuracy fourfold and reduces learning time by half.
DEAL model predicts links for new nodes with only attribute info.
problem Predicting links for new nodes with only attribute info.
method DEAL model with two encoders and alignment mechanism.
result DEAL significantly outperforms existing methods on inductive link prediction.
NNLMs optimize poorly for word probabilities due to embedding space structure.
problem NNLMs assign suboptimal probabilities to some words.
method Analyzed the inductive bias of NNLMs and the structure of word embeddings.
result Words on the convex hull have bounded probability, affecting others.
GraIL predicts relations by reasoning over subgraphs, outperforming embeddings.
problem Relation prediction in knowledge graphs using latent representations is limited.
method Graph neural network with inductive bias to learn entity-independent relational semantics.
result GraIL outperforms existing rule-induction baselines in the inductive setting.
New approach relaxes inductive biases of physics-inspired NNs for better performance.
problem Challenges in applying physics-inspired NNs to real-world systems.
method Examined and relaxed inductive biases of Hamiltonian NNs, improving performance on non-conservative systems.
result Improved performance on practical, non-conservative systems by relaxing inductive biases.
Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form --- where form could be a tree, ring, chain, grid, etc. [Kemp & Tenenbaum (2008…
While current deep learning systems excel at tasks such as object classification, language processing, and gameplay, few can construct or modify a complex system such as a tower of blocks. We hypothesize that what these systems lack is a "relational inductive bias": a capacity for reasoning about inter-object relations…
Feed-forward nets fail to learn equality relations, but adding DR units helps.
problem Feed-forward neural networks struggle to learn equality relations reliably.
method Introduced differential rectifier (DR) units to create an inductive bias.
result DR units enable feed-forward nets to learn equality relations reliably.
Study shows mutual information can reward structure learning agents without expert systems.
problem Designing rewards for structure learning agents in natural language environments.
method Revisited Information Theory of unsupervised induction of phrase-structure grammars, using random sets of linguistic samples.
result Empirical evidence that simulated semantic structures can be distinguished from random ones by mutual information among their constituents.
Proposes a neural framework to select subsets efficiently across different models.
problem Lack of generalizability in subset selection methods for unseen architectures.
method Introduces a trainable subset selection framework, SubSelNet, that uses attention-based neural gadgets and subset samplers.
result SubSelNet generalizes across architectures and outperforms existing methods.
Enhances index selection for databases with task-specific inductive biases.
problem Challenges in traditional and automatic tuning strategies for database index set selection.
method Applies deep RL with task-specific inductive biases to index set selection, reformulating the problem as permutation learning.
result Improves index selection, achieving up to 40% smaller configurations with similar latency.
InGRA models for efficient Granger causality learning in multivariate time series.
problem Efficiently modeling Granger causality in large-scale multivariate time series data.
method Inductive GRanger causal modeling (InGRA) framework with prototypical Granger causal attention.
result InGRA detects common causal structures and infers Granger causal structures for new individuals.
Neural network learns causal graph structure from data.
problem Inferring causal graph structure from observational and interventional data.
method Supervised training of a neural network on synthetic graphs.
result Learned model generalizes to new graphs, robust to distribution shifts, and outperforms existing methods.
We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained b…
Unsupervised RNNGs perform similarly to supervised ones in language modeling and grammar induction.
problem Training RNNGs requires annotated data, which is costly.
method Amortized variational inference with a neural CRF parser.
result Unsupervised RNNGs achieve comparable performance to supervised ones.
New network learns image features inductively for disease classification.
problem Pre-processing image features limits network optimization.
method Inductive end-to-end learning with CNN and graph filters trained jointly.
result Significantly improved classification scores and higher stability.
Paper explores how knowledge distillation transfers inductive biases between models.
problem Transferring inductive biases between models for tasks with limited data.
method Knowledge distillation applied to models with different inductive biases (LSTMs vs. Transformers, CNNs vs. MLPs).
result Effect of inductive biases is transferred through knowledge distillation, impacting both performance and solution characteristics.
The paper explores methods to better estimate treatment effects by leveraging shared structure in potential outcomes.
problem Estimating treatment effects when outcomes may vary widely and existing methods often assume heterogeneity.
method Investigates and compares three learning strategies: regularization, reparametrization, and a multi-task architecture.
result All three approaches improve upon existing baselines, providing insights into their relative strengths.
Interpolated-MLPs control inductive bias for better performance in low-compute tasks.
problem Low-compute performance gap between MLPs and CNNs.
method Introduced Interpolated MLP (I-MLP) approach to control inductive bias incrementally.
result Continuous logarithmic relationship between inductive bias and performance in low-compute tasks.
New method quantifies inductive bias for machine learning tasks.
problem Quantifying the amount of inductive bias in machine learning models.
method Estimates inductive bias by modeling loss distribution of random hypotheses.
result Higher dimensional tasks require greater inductive bias.
Unified theory linking node embeddings and graph representations.
problem Clarifying the relationship between node embeddings and graph representations.
method Using invariant theory, the paper establishes a theoretical framework bridging node embeddings and structural graph representations.
result Proves equivalence between node embeddings and structural graph representations, showing they are interchangeable for various tasks.
New grammar model learns sentence structure with latent variables.
problem Grammar induction for sentences with complex dependencies.
method Compound probabilistic context-free grammar with latent variables, variational inference.
result Effective unsupervised parsing compared to state-of-the-art methods.
A new geometric method for clustering SPD data improves upon Euclidean and Riemannian approaches.
problem Skewed interpretations of SPD data in Euclidean analysis and computational inefficiency of Riemannian methods.
method Proposes a geometric method based on the Thompson metric for unsupervised clustering of SPD data.
result Demonstrates improved clustering results using inductive midrange centroid computation.
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.
A new method for document network embedding interprets and generalizes well.
problem Lack of interpretability and generalization to new documents in existing methods.
method Introduces Topic-Word Attention (TWA) and Inductive Document Network Embedding (IDNE) to generate document representations.
result Achieves state-of-the-art performance on various networks and produces meaningful representations.
Theoretical study on how model architecture affects contrastive learning performance.
problem Understanding the role of model architecture in self-supervised learning.
method Theoretical analysis of contrastive learning, focusing on model capacity and clustering structures.
result Contrastive representations have lower dimensionality than the number of clusters in the data distribution.
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interp…
One-layer transformers can't solve induction heads task efficiently.
problem Solving the induction heads task efficiently with one-layer transformers.
method Communication complexity argument showing exponential size requirement.
result No one-layer transformer can solve the induction heads task efficiently.
OTI extends OTP for inductive semi-supervised learning.
problem Inductive semi-supervised learning for out-of-sample data.
method Optimal transport-based approach extended to inductive tasks.
result OTI outperforms state-of-the-art methods in experiments.
TGAT learns node embeddings for evolving graphs, capturing both static and temporal features.
problem Learning node embeddings for dynamic graphs with evolving topological structures and temporal patterns.
method Temporal Graph Attention (TGAT) layer using self-attention and functional time encoding.
result TGAT model can inductively infer node embeddings for new and observed nodes as the graph evolves.
BPI models 2D patterns on multiple planes and 3D scene from a single image.
problem Understanding and editing images with multiple 2D planes and 3D scene from a single image.
method Box Program Induction (BPI) with neural networks and search-based algorithm.
result Holistic, structured scene representation enables 3D-aware image editing.
New method for embedding large networks without attributes, achieving state-of-the-art performance.
problem Learning embeddings from large-scale networks without domain-dependent attributes.
method Use predefined local encodings based on node degree frequencies at different distances.
result Inductive network embeddings generalize well across unseen or distant regions in the network.
Deep ResNets favor low bottleneck rank with proper hyperparameters.
problem Understanding the inductive bias of deep neural networks.
method Computed minimum-norm weights of a deep linear ResNet.
result Deep nonlinear ResNets have an inductive bias towards minimizing bottleneck rank.
Neural networks struggle with abstract patterns, new RBP structures improve performance.
problem Neural networks fail to learn abstract patterns based on identity rules.
method Proposed Relation Based Pattern (RBP) extensions to neural network structures.
result Neural networks with RBP structures achieve perfect performance on synthetic and real-world sequence prediction tasks.
The paper proposes a method to transfer knowledge across different settings using causal theory.
problem Learning transfer across similar but different settings.
method Bayesian perspective of causal theory induction, integrating instance-level associative learning and abstract-level structural causal knowledge.
result The proposed model achieved transfer behavior across trials and learning situations, unlike RL algorithms.
GTEA learns node representations in temporal interaction graphs.
problem Inductive representation learning on temporal interaction graphs.
method Integrates sequence model with time encoder and self-attention scheme for edge and node embeddings.
result GTEA learns comprehensive node representations capturing temporal and structural characteristics.
Paper proposes an inductive RGCN for few-shot link prediction in drug-repurposing.
problem Predicting rare interactions in drug-repurposing for novel diseases.
method Proposes an inductive RGCN to learn relation embeddings for few-shot learning.
result Significantly outperforms state-of-the-art models in few-shot learning tasks.
This research formalizes inductive generalization and proposes a new learning paradigm called Inductive Learning.
problem Generalization from easy to hard tasks, especially out-of-domain generalization.
method Formalizes inductive generalization, introduces Inductive Learning, and outlines steps to adapt techniques for learning model successors.
result A new learning paradigm (Inductive Learning) that emphasizes induction and universal properties of learning and computation.
Enhances MIL performance in scarce data scenarios using topological inductive biases.
problem Low performance of MIL in data-scarce scenarios.
method Incorporates topological inductive biases into MIL framework.
result Average performance improvements of 15.3% for synthetic datasets, 2.8% for benchmarks, and 5.5% for rare anemia classification.
Paper analyzes Bezier simplex fitting risks and optimal sampling.
problem Analyzing risks and optimal sampling for Bezier simplex fitting.
method Two fitting methods: inductive skeleton and all-at-once.
result Optimal subsample ratio for inductive skeleton fitting reduces risk.
We introduce several methods to define the self-inductance of a single loop as the regularization of divergent integrals which we obtain by applying Neumann (or Weber) formula for the mutual inductance of a pair of loops to the case when two loops are identical.
We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class contains the class of all geodesic metric spaces and all finitely generated groups…
Study shows gMPNNs struggle with OOD link prediction in larger test graphs.
problem Inductive out-of-distribution link prediction in larger test graphs.
method Theoretical analysis and development of a gMPNN with structural pairwise embeddings.
result Structural node embeddings from gMPNNs converge to random guessing as test graphs grow.
EMFs combine deep learning and probabilistic models for better density estimation.
problem Combining domain-specific knowledge with general-purpose deep learning.
method Alternating transformations with structured layers that embed domain-specific inductive biases.
result EMFs induce desirable properties like multimodality and hierarchical coupling.
RPPs improve deep learning models with soft equivariance constraints.
problem Balancing expressiveness and inductive biases in deep learning.
method Introducing Residual Pathway Priors (RPPs) to convert hard constraints into soft priors.
result RPPs enable models to learn structured solutions while retaining flexibility.