Theoretical study on AI models' resilience to data contamination during recursive training.
problem Data contamination in recursive training of generative AI models.
method General framework with minimal assumptions on real data distribution and flexible generative models.
result Contaminated recursive training converges with a rate equal to the minimum of baseline model's rate and contamination fraction.
Greedy training of recursive partitioning estimators faces a computational barrier when the true function doesn't satisfy a specific property.
problem Computational inefficiency of greedy training for recursive partitioning estimators.
method Analysis of greedy training for sparse regression functions over binary features.
result Greedy training requires exponential samples when the true function doesn't satisfy a specific property (MSP), but only logarithmic samples when it does.
Recursive training of generative models can lead to model collapse, and the recursion converges to a unique limiting distribution.
problem Model collapse in recursive training of generative models
method Recursive training on their own outputs
result Recursive training converges to a unique limiting distribution
Recursive neural networks have widely been used by researchers to handle applications with recursively or hierarchically structured data. However, embedded control flow deep learning frameworks such as TensorFlow, Theano, Caffe2, and MXNet fail to efficiently represent and execute such neural networks, due to lack of s…
Study uses reinforcement learning to optimize portfolios under recursive utility.
problem Improving portfolio allocation using risk-sensitive objectives.
method Approximated certainty equivalent via Monte Carlo, trained actor-critic algorithms (PPO, A2C).
result Recursive-utility agent outperforms discounted baseline in Sharpe ratio, max drawdown, and cumulative return.
Model collapse occurs quickly for synthetic data generated by previous models.
problem Model quality degrades over recursive training on synthetic data.
method Theoretical and experimental evaluations of discrete and Gaussian distributions under near ML estimation.
result Model collapse for discrete distributions is approximately linearly dependent on the number of times a word occurs in the original corpus, and for Gaussian models, the standard deviation reduces to zero roughly at n iterations.
Proposes a strategy to train models with minimal labeled data.
problem Scarce and expensive labeled data for medical tasks.
method Recursive training strategy to use image-level annotations for pixel-level segmentation.
result Improved segmentation of intracranial hemorrhage in CT scans.
The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
Paper tackles model collapse in recursive generative models using a weighted training scheme.
problem Model collapse in recursive generative models trained on synthetic data.
method Iteratively trains models on real and synthetic data, evaluates weighted training schemes.
result Optimal weighting scheme for synthetic data follows a unified expression, revealing a trade-off with model performance.
The paper investigates model collapse in language models from a probabilistic perspective.
problem Understanding and preventing model collapse in language model training.
method Investigates recursive parametric model training from a probabilistic standpoint, characterizing conditions for model collapse and proposing mitigation strategies.
result Progressively increasing sample size is necessary to prevent model collapse, with a superlinear growth rate required in the asymptotic regime.
A new method optimizes diffusion models with recursive likelihood ratios.
problem Efficiently aligning pre-trained diffusion models for specific applications.
method Recursive Likelihood Ratio (RLR) optimizer for Half-Order (HO) fine-tuning.
result The RLR method achieves unbiased and lower-variance gradients, improving model performance.
Benchmarking recursive collapse claims with a new framework under false-positive control.
problem Evaluating recursive systems for failure patterns and warning claims.
method Developed Loopzero framework for testing recursive failures, specified claim boundaries in Lean, evaluated under FP constraint, and compared with standard detectors.
result No standard detectors or Loopzero's pre-registered quantile detector achieved the required operating point under the false-positive contract.
Improved disentanglement of data factors using recursive training.
problem Current unsupervised disentanglement methods are inconsistent and fail to achieve levels of disentanglement seen in supervised approaches.
method Introduced PBT for VAEs, used UDR for heuristic scoring, and developed recursive rPU-VAE approach.
result Recursive training leads to robust disentanglement of data factors across multiple datasets.
New ODE solvers improve training efficiency and accuracy.
problem Training Neural ODEs requires efficient and accurate gradient calculation.
method Presented algebraically reversible ODE solvers that are time and memory efficient, calculate exact gradients, and are numerically stable.
result Reversible solvers strictly improve upon previous architectures in efficiency and accuracy.
A new algorithm SRG-DQN reduces variance in deep Q-learning.
problem Inaccurate estimation of anchor points in SVRG for deep Q-learning.
method Introduces recursive gradient variance reduction for stochastic gradient updates.
result Demonstrates improved efficiency and effectiveness of SRG-DQN on reinforcement learning tasks.
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…
The decremented learning algorithms are required in machine learning, to prune redundant nodes and remove obsolete inline training samples. In this paper, an efficient decremented learning algorithm to prune redundant nodes is deduced from the incremental learning algorithm 1 proposed in [9] for added nodes, and two de…
We introduce Recurrent Predictive State Policy (RPSP) networks, a recurrent architecture that brings insights from predictive state representations to reinforcement learning in partially observable environments. Predictive state policy networks consist of a recursive filter, which keeps track of a belief about the stat…
Theoretical study shows AI models can recover from contaminated training data.
problem Data contamination in AI training can degrade model performance.
method Theoretical analysis and experiments on various data types.
result Models converge to true distribution under mild conditions, with rate dependent on real data fraction.
This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. Recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples. This study examines Ridge Support Vector Models, subsequently devising a recursion-…
Recursive KalmanNet generalizes well in noisy, out-of-distribution scenarios.
problem Generalization in noisy, out-of-distribution scenarios.
method Recurrent neural network guided by a Kalman filter.
result Recursive KalmanNet performs well in scenarios with different temporal dynamics from training data.
SciRE-Solver accelerates DMs sampling by recursively calculating the score function derivative.
problem Slow iterative process of diffusion models due to estimating the score function derivative.
method Recursive Difference (RD) method combined with truncated Taylor expansion of score-integrand.
result SciRE-Solver achieves state-of-the-art FIDs with significantly fewer score function evaluations.
Paper defines Farey Recursive Functions and explores their properties.
problem Understanding recursive functions on rationals.
method Defined and studied Farey Recursive Functions using Farey graph.
result Farey Recursive Functions naturally connect to 2-bridge knots and links.
The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.
problem Computing volumes for physical gravity models.
method Topological recursion and physical two-dimensional gravity models.
result Derivation of Virasoro constraints and cut-and-join equations for generalized Mirzakhani's recursions.
ORFit trains models on streaming data with one pass, minimizing memory and computational costs.
problem Training large models on a stream of data without retraining on previous data.
method Orthogonal Recursive Fitting (ORFit) using orthogonal gradient descent and recursive least-squares.
result ORFit updates parameters orthogonally to past gradients, leading to efficient memory and computational usage.
Training deep neural networks on large-scale datasets requires significant hardware resources whose costs (even on cloud platforms) put them out of reach of smaller organizations, groups, and individuals. Backpropagation, the workhorse for training these networks, is an inherently sequential process that is difficult t…
New framework for DNN training guarantees convergence to global minimum.
problem Training deep neural networks to converge to global minimum.
method Reformulated minimization problem with recursive algorithmic framework, using bounded style assumptions.
result Convergence to an ε-(global) minimum with O(1/ε^3) gradient computations.
Tab-TRM uses recursive model for insurance pricing on tabular data.
problem Insurance pricing on tabular data.
method Adapts recursive latent reasoning to insurance modeling using a compact, parameter-efficient network.
result Improves insurance pricing accuracy using iterative refinement of latent tokens.
XR-Transformer accelerates XMC by recursively fine-tuning on multi-resolution objectives.
problem Efficiently classifying texts with large label sets.
method Recursive multi-resolution fine-tuning of transformers.
result XR-Transformer achieves 20x faster training time and 54% Precision@1 on Amazon-3M.
New recursion formula for non-orientable surfaces resolves divergences.
problem Computing volumes of moduli spaces for non-orientable surfaces.
method Generalization of Mirzakhani's recursion to non-orientable surfaces, handling divergences with integral kernels.
result Regularized volumes can be computed with a cutoff on crosscap size.
Harer and Zagier proved a recursion to enumerate gluings of a 2d-gon that result in an orientable genus g surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is t…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs to larger datasets, several sparse approximations based on so-called inducing p…
Breaking symmetry in training data is key for generalization in feature learning kernels.
problem Grokking in algebraic tasks, where models perform well on training but fail on unseen data.
method Used Recursive Feature Machine (RFM) with AGOP to learn task-relevant features, breaking symmetry in training data.
result Generalization occurs only when symmetry in the training set is broken, and RFM generalizes by recovering underlying invariance group action.
This paper studies recursive ensembles driven by Fibonacci updates, improving learning dynamics.
problem Improving learning dynamics in recursive ensemble learning.
method Develops second-order recursive architectures with Fibonacci-type update flows.
result Establishes global convergence conditions and generalization bounds for recursive ensembles.
The article improves prediction by aggregating Kalman recursions online.
problem Improving expert aggregation in prediction models.
method Using exponential weights and state-space models to aggregate Kalman recursions.
result New algorithms outperform existing methods in Kalman recursion expert aggregation.
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.
Solves a recursion for Gromov-Witten invariants of the unknot.
problem Determining Gromov-Witten invariants for a specific Lagrangian brane.
method Uses a skein-theoretic recursion and geometric solutions.
result Solves the recursion to find the expected hook-content formula.
We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive observations of covariates, treatment, and the outcome of the treatment. The standa…
New recursion found for hyperbolic sphere volumes.
problem Volume calculation of hyperbolic sphere moduli spaces.
method Proved a non-linear recursive relation.
result Generalized Zograf's result for conical points and geodesic boundaries.
Humans are capable of attributing latent mental contents such as beliefs or intentions to others. The social skill is critical in daily life for reasoning about the potential consequences of others' behaviors so as to plan ahead. It is known that humans use such reasoning ability recursively by considering what others …
This work generalizes a formula linking Seiberg-Witten prepotential and topological recursion.
problem Analyzing the relationship between Seiberg-Witten curves and topological recursion.
method Analytical approach using Seiberg-Witten family of curves.
result A generalized formula relating Seiberg-Witten prepotential to the genus zero part of topological recursion on a Seiberg-Witten curve.
LASER compresses recursive model activations by exploiting their low-dimensional structure.
problem Understanding and optimizing the geometric structure of recursive reasoning trajectories.
method Dynamic low-rank basis tracking via matrix-free subspace tracking with a fidelity-triggered reset mechanism.
result Recursive activations occupy a linear, low-dimensional subspace that can be compressed efficiently.
We describe a method for recursively calculating Gromov-Witten invariants of all blowups of the projective plane. This recursive formula is different from the recursive formulas due to Göttsche and Pandharipande in the zero genus case, and Caporaso and Harris in the case of no blowups. We use tropical curves and a recu…
Topological recursion recovers a specific partition function for colored knots.
problem Recovering the extended Ooguri-Vafa partition function for colored HOMFLY-PT polynomials of torus knots.
method Applying topological recursion to the spectral curve of colored HOMFLY-PT polynomials of torus knots.
result Topological recursion reproduces the n-point functions of the extended Ooguri-Vafa partition function.
We derive the Do and Norbury recursion formula for the one-loop mean of an irregular spectral curve from a variant of replica method by Brezín and Hikami. We express this recursion in special times in which all terms W1(g) of the genus expansion of the one-loop mean are polynomials. We find a generalization of th…
This paper concerns the recursive utility maximization problem under partial information. We first transform our problem under partial information into the one under full information. When the generator of the recursive utility is concave, we adopt the variational formulation of the recursive utility which leads to a s…
This work presents an explicit-implicit procedure to compute a model predictive control (MPC) law with guarantees on recursive feasibility and asymptotic stability. The approach combines an offline-trained fully-connected neural network with an online primal active set solver. The neural network provides a control inpu…
We derive a recursion relation for hyperbolic string vertices and apply it to string field theory.
problem Deriving a recursion relation for hyperbolic string vertices and its implications for string field theory.
method Using systolic volumes and a modified Mirzakhani's recursion, we construct a higher-order vertex determination for hyperbolic string field theory.
result The higher order vertices in hyperbolic string field theory are determined by the cubic vertex iteratively for any background.