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.
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.
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.
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.
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.
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…
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 …
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.
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.
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.
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…
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.
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 …
Transformers are less sensitive to input perturbations compared to other models.
problem Understanding the inductive biases of transformers and distinguishing them from other architectures.
method Identified token-wise sensitivity as a metric to explain transformers' inductive biases across different data modalities.
result Transformers have lower sensitivity than MLPs, CNNs, ConvMixers, and LSTMs, across vision and language tasks.
A central goal of meta-learning is to find a learning rule that enables fast adaptation across a set of tasks, by learning the appropriate inductive bias for that set. Most meta-learning algorithms try to find a \textit{global} learning rule that encodes this inductive bias. However, a global learning rule represented …
Deep convolutional networks can be understood through kernel methods, providing insights into their inductive bias.
problem Understanding the functional space and inductive bias of deep convolutional networks.
method Using kernel methods to analyze simple hierarchical kernels with convolution and pooling layers.
result The RKHS consists of additive models of interaction terms between patches, and pooling layers encourage spatial similarities.
Improved Mamba model for long-range sequence tasks.
problem Mamba's poor performance on long-range sequential tasks.
method Proposed B2S6, combining block-wise selective dynamics and channel-specific bias.
result Empirically, B2S6 outperforms S4 and S4D on LRA tasks.
SGD-trained deep nets often generalize well due to a strong inductive bias towards low-error, low-complexity functions.
problem Understanding why overparameterized deep nets generalize well despite fitting training data perfectly.
method Empirical investigation of PSGD(f∣S) and PB(f∣S) for various architectures and datasets. result The probability of SGD-converging on a function consistent with training data correlates well with the Bayesian posterior probability of expressing that function.
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a useful constraint, both theoretically--to prove convergence and optimality guar…
COMET learns monotonic neural networks by incorporating counterexamples.
problem Enforcing monotonicity constraints in neural networks for real-world tasks.
method Counterexample-guided learning technique for ReLU neural networks.
result COMET achieves state-of-the-art results and improves model quality.
New measure quantifies task difficulty for machine learning models.
problem Quantifying the inherent difficulty of machine learning tasks.
method Inductive bias complexity measure.
result Tasks requiring generalization over many dimensions are more difficult.
Looped transformers outperform standard transformers in complex reasoning tasks due to a specific loss landscape geometry.
problem Understanding why looped transformers outperform standard transformers in complex reasoning tasks.
method Explained through loss landscape geometry, distinguishing between U-shaped and V-shaped valleys, and proposing SHIFT training strategy.
result Looped transformers' recursive architecture induces a River-V-Valley landscape, leading to better loss convergence and complex pattern learning.
State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties. A recent line of work has shown that in a certain over-parameterized regime, the learning dynamics of gradient descent are governed …
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.
A new method uses algebraic insights to create approximately equivariant networks without complex architectures.
problem Designing equivariant neural networks with complex architectures and high computational cost.
method Imposes the group's regular representation as an inductive bias via an auxiliary loss, adding no learnable parameters.
result Matches or outperforms specialized models in several cases, even for infinite groups.
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.
OMIC improves matrix completion with orthonormal side information and nuclear-norm regularization.
problem Matrix completion with improved interpretability and adaptability.
method OMIC combines orthonormal side information and nuclear-norm regularization, optimized by a converging algorithm.
result OMIC outperforms state-of-the-art methods in synthetic and real-world datasets.
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.
Lectures on deep learning from a learning theory perspective.
problem Understanding how deep learning architectures lead to inductive bias.
method Statistical learning theory and stochastic optimization.
result Gradient descent on linear diagonal networks can lead to various forms of implicit bias.
Study on NNs for forecasting time series with novel control variable combinations.
problem Forecast future time series with novel combinations of control variables.
method Modular NN architecture with inductive bias for independence of control variables.
result Modular NN architecture improves forecasting of dependent variables up to large horizons.
A new reinforcement learning method reduces action complexity for robust control.
problem Deep reinforcement learning's susceptibility to spurious correlations.
method Minimizing trajectory entropy to encourage simple, predictable actions.
result Trajectory Entropy Reinforcement Learning achieves superior performance and robustness.