Soft geometric bias improves physical dynamics predictions.
problem Learning physical dynamics with exact group equivariance can degrade performance.
method Object-centric world models using geometric algebra neural networks.
result Soft geometric inductive bias leads to better physical fidelity predictions.
New method stabilizes machine learning for physics-informed inverse problems.
problem Reconstructing physical quantities from PDE-compliant measurements.
method Physics-informed learning with smooth inductive bias.
result PDE operators stabilize variance and prevent overfitting in fixed dimensions.
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…
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.
Paper develops a framework to identify latent dynamics from high-dimensional data.
problem Identifying latent dynamics from high-dimensional time-series data.
method Combines physics inductive bias and learn-to-identify strategy.
result Meta-HyLaD framework effectively identifies hybrid latent dynamics.
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.
Kempe discusses NTK approach to machine learning problems.
problem Generally unsolvable machine learning problems.
method NTK approach focusing on kernel formulations.
result Practical applications like data distillation and adversarial robustness.
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.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
This paper tackles data-efficient nonlinear control in Hamiltonian systems using symplectic geometry.
problem Data-efficient nonlinear control in Hamiltonian systems.
method Combines symplectic geometry, recurrence on energy level sets, and chain policies to solve target reachability problems.
result Data requirements depend on geometric and recurrence properties of the Hamiltonian, not the state dimension.
MC-LSTM extends LSTM to conserve mass in neural networks.
problem Conservation laws in real-world systems.
method Extending LSTM's inductive bias to conserve mass.
result MC-LSTM sets new state-of-the-art for predicting peak flows.
We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true fo…
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.
The paper introduces a new σ-LSTM cell for volatility forecasting using stylized facts.
problem Lack of explainability and stylized knowledge in neural network volatility modeling.
method Introduces a new σ-LSTM cell with a stochastic processing layer, designed to incorporate stylized facts about volatility. result Shows good out-of-sample forecasting performance with the σ-LSTM cell. Novel method combines physics priors for energy-conserving dynamics.
problem Learning long-term dynamics of complex physical systems from noisy data.
method Variational Integrator Graph Networks integrating energy constraint, high-order symplectic integrators, and graph neural networks.
result Improves predictive performance across single and many-body problems.
Paper introduces LODE-GPs for modeling data following linear ODEs.
problem Modeling data from systems of linear ODEs.
method Symbolic construction of LODE-GPs using Smith normal form algorithms.
result Improves GP modeling of data from systems of linear ODEs.
Physics-enhanced NNs improve predictive accuracy in small data scenarios.
problem Predicting physical systems dynamics with limited data.
method Integrating physical principles (Hamiltonian/Lagrangian) and regularization term based on energy level into neural networks.
result Significant gains in predictive accuracy for small data cases.
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.
Study shows how large neural networks avoid overfitting through decoupling of feature learning and complexity growth.
problem Understanding inductive bias and generalization in large neural networks.
method Dynamical mean field theory applied to large two-layer networks.
result Training dynamics of large networks exhibit a separation of timescales, decoupling feature learning and overfitting.
In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate induct…
This paper explains the theoretical inductive bias of Isolation Forest.
problem Lack of theoretical foundation explaining Isolation Forest's success.
method Formulated the growth process of iForest as a random walk, derived expected depth function using transition probabilities.
result Established a theoretical understanding of iForest's effectiveness and parameter adaptability.
Improves transferability of representations from source to target domains with weights and invariant representations.
problem Label shift between source and target domains in unsupervised domain adaptation.
method Integrates weights and invariant representations to bound the target risk, highlighting the role of inductive bias.
result Empirical evidence shows that weak inductive bias makes adaptation more robust.
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
problem Understanding how neural networks learn and generalize on Boolean data.
method End-to-end analysis of depth-2 discrete fully connected networks and DNF formulas, using Monte Carlo learning.
result Predictable training dynamics and interpretable features emerge, linking inductive bias and generalization.
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.
Study reveals biases in gradient descent for GLNs, improving neural network performance.
problem Understanding and improving the inductive biases of deep neural networks.
method Derive infinite-time training limit of gated linear networks and generalize to other networks.
result Theoretical framework captures key inductive biases of ReLU networks.
We present experiments demonstrating that some other form of capacity control, different from network size, plays a central role in learning multilayer feed-forward networks. We argue, partially through analogy to matrix factorization, that this is an inductive bias that can help shed light on deep learning.
Novel approach uses inductive biases for semiconductor etching.
problem Significant violations of physics in etching process predictions.
method Introduced deep learning model with inductive biases.
result Fits measurements faster and follows physical behavior.
Study shows different trajectory prediction models generalize better under OoD conditions.
problem Comparing trajectory prediction models' robustness across different datasets.
method Training models on Argoverse 2 and testing on Waymo Open Motion, and vice versa, with various augmentation strategies.
result Smallest model with highest inductive bias performs best in OoD generalization.
In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework to systematically investigate bias and generalization in deep generative models …
Study reveals how neural network architectures bias their learning based on feature directions.
problem Understanding how neural network architectures bias their learning based on feature directions.
method Defined neural anisotropy directions (NADs) to encapsulate the directional inductive bias of architectures and provided an efficient method to identify them.
result NADs characterize the features used by CNNs to discriminate between different classes for the CIFAR-10 dataset.
New diagnostic tool for assessing approximate Bayesian inference.
problem Assessing the trustworthiness of approximate Bayesian inference.
method Reframe the problem in terms of incompatible conditional distributions and use Gibbs priors.
result The diagnostic tool can discover the inductive bias in various Bayesian models and approximations.
Machine learning methods adapt the parameters of a model, constrained to lie in a given model class, by using a fixed learning procedure based on data or active observations. Adaptation is done on a per-task basis, and retraining is needed when the system configuration changes. The resulting inefficiency in terms of da…
Basic binary relations such as equality and inequality are fundamental to relational data structures. Neural networks should learn such relations and generalise to new unseen data. We show in this study, however, that this generalisation fails with standard feed-forward networks on binary vectors. Even when trained wit…
Transformers capture combinatorial tasks with bounded error and logarithmic sample dependence.
problem Capturing complex combinatorial tasks with bounded error and sample efficiency.
method Formal definition of algorithmic capture, empirical analysis of infinite-width transformers, upper bounds on computational complexity.
result Transformers exhibit an inductive bias favoring simpler algorithmic procedures over higher complexity ones.
In this paper we introduce a new inductive bias for capsule networks and call networks that use this prior γ-capsule networks. Our inductive bias that is inspired by TE neurons of the inferior temporal cortex increases the adversarial robustness and the explainability of capsule networks. A theoretical framework with…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new class of learnable models--based on graph networks--which implement an inductive…
The dominant paradigm for relation prediction in knowledge graphs involves learning and operating on latent representations (i.e., embeddings) of entities and relations. However, these embedding-based methods do not explicitly capture the compositional logical rules underlying the knowledge graph, and they are limited …
Characterizes inductive bias in multi-channel linear CNNs with bounded weight norm.
problem Understanding the inductive bias in multi-channel linear convolutional networks.
method Function space characterization and empirical testing of gradient descent.
result The inductive bias depends on the number of output channels for multi-channel inputs but not for single-channel inputs.
Graph neural networks improve combinatorial optimization by leveraging inductive bias.
problem Combinatorial optimization problems often arise from related data distributions.
method Using graph neural networks to enhance or solve combinatorial tasks.
result Graph neural networks effectively encode combinatorial and relational input.
Centuries of development in natural sciences and mathematical modeling provide valuable domain expert knowledge that has yet to be explored for the development of machine learning models. When modeling complex physical systems, both domain knowledge and data provide necessary information about the system. In this paper…
Endowing robots with human-like physical reasoning abilities remains challenging. We argue that existing methods often disregard spatio-temporal relations and by using Graph Neural Networks (GNNs) that incorporate a relational inductive bias, we can shift the learning process towards exploiting relations. In this work,…
Transformers tend to learn more symmetric functions in sequence data.
problem Understanding inductive bias in Transformers with infinitely over-parameterized models.
method Analyzing Transformers in the Gaussian process limit, using representation theory of the symmetric group.
result Transformers are biased towards more permutation symmetric functions, and this can be quantitatively predicted.
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.
A new method for multi-task learning improves performance without weakening inductive bias.
problem Joint optimization of parameters for multiple tasks remains challenging.
method Maximum Roaming, a novel parameter partitioning method inspired by dropout.
result Maximum Roaming improves performance compared to recent multi-task learning formulations.
LANCA uses ANM to learn latent causal factors without supervision.
problem Learning latent causal factors without supervision.
method LANCA employs a deterministic Wasserstein Auto-Encoder coupled with a differentiable ANM Layer.
result LANCA outperforms baselines on physics and photorealistic environments.
ExpBERT uses natural language explanations to improve text interpretation.
problem Improving text interpretation for relation extraction tasks.
method Fine-tuning BERT on MultiNLI to interpret natural language explanations.
result ExpBERT matches a BERT baseline but requires less labeled data and improves performance.
Matrix SMD converges to unique solution minimizing Bregman divergence.
problem High-dimensional multi-output classification and matrix completion problems.
method Stochastic Mirror Descent with matrix parameters and matrix mirror functions.
result Matrix SMD converges exponentially to the unique solution minimizing Bregman divergence.
Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit models. The gradient-free algorithm, presented as a sequence of exactly solvable …