Paper characterizes optimal language model alignment methods.
problem Aligning language models to maximize reward while keeping them close to the original model.
method KL-constrained reinforcement learning and best-of-N methods.
result Optimal KL-constrained RL solution has a large deviation principle rate function.
We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be me…
This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail, for gradient flow applied to strictly decreasing loss functions (with similar re…
Study analyzes Hotelling-type tensor deflation for spiked tensors, providing insights into signal and noise.
problem Characterizing singular values and alignments in Hotelling-type tensor deflation.
method Asymptotic study of Hotelling-type tensor deflation in large dimensional regime using random tensor theory.
result Characterization of singular values and alignments at each step of the deflation procedure.
New method aligns diffusion models for inference-time properties without retraining.
problem Aligning pre-trained diffusion models for desired inference-time properties.
method Variationally stable Doob's matching for provable guidance estimation.
result Consistent estimator of guidance with non-asymptotic convergence guarantees.
This work optimizes alignment and uniformity of features on a hypersphere for better downstream performance.
problem Improving the performance of contrastive representation learning.
method Identifying and optimizing alignment and uniformity of features on a hypersphere.
result Directly optimizing alignment and uniformity leads to comparable or better performance than contrastive learning.
Solves wave equation on non-flat harmonic manifolds using Abel transform and Fourier analysis.
problem Wave equation on non-flat harmonic manifolds with specific curvature conditions.
method Explicit representation using inverse dual Abel transform and Fourier transform.
result Shows asymptotic Huygens principle and equidistribution of energy.
Pair Hidden Markov Models (PHMMs) are probabilistic models used for pairwise sequence alignment, a quintessential problem in bioinformatics. PHMMs include three types of hidden states: match, insertion and deletion. Most previous studies have used one or two hidden states for each PHMM state type. However, few studies …
Unified framework for aligning LLMs from human feedback.
problem Lack of strong theoretical justification for RLHF and inability to compare methods.
method Reframed alignment as distribution learning from pairwise preferences, proposing three principled objectives.
result Proposed objectives achieve strong non-asymptotic convergence to target LM.
New mass inequalities and proofs for causal variational principles.
problem Proving new mass inequalities for causal variational principles.
method Proved a new inequality for minimizers of causal variational principles and applied it to prove the positive mass theorem.
result Introduced a positive quasilocal mass and proved new mass inequalities.
We consider the relative canonical line bundle KX/T and a relatively ample line bundle (L,e−φ) over the total space X→T of fibration over the Teichmüller space by Riemann surfaces. We consider the case when the induced metric $\sqrt{-1}\partial\bar{\partial}φ|_{\…
In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and center of mass. Our assumption on the asymptotics is less stringent than any previo…
New theory explains contrastive learning via overlapping augmented views.
problem Lack of theoretical understanding of contrastive learning.
method Augmentation overlap perspective to improve downstream performance.
result Asymptotically closed bounds for downstream performance under weaker assumptions.
New method groups similar functional covariates for better modeling.
problem Analyzing functional covariates with similar shapes.
method Coefficient shape alignment regularization approach.
result True grouping structure can be accurately identified under certain conditions.
DTS improves inference-time alignment of diffusion models with less compute.
problem Inference-time alignment of diffusion models suffers from inaccurate value estimation and inefficient reuse of past computations.
method Diffusion Tree Sampling (DTS) uses a tree-based approach to propagate terminal rewards and iteratively refine value estimates.
result DTS produces asymptotically exact samples and matches the FID of best-performing baselines with up to 10x less compute.
The paper investigates Goodhart's law and its impact on goal alignment.
problem The adverse effects of optimizing a measure when it diverges from the true goal.
method Formal analysis of Goodhart's law, focusing on the tail distribution of discrepancies.
result Goodhart's law depends on the tail distribution of discrepancies between the true goal and the optimized measure.
The paper studies 1-equivariant harmonic map flow behavior from R² to S².
problem Examining the long-term dynamics of 1-equivariant harmonic map flow.
method Constructing and analyzing global solutions for the flow equation.
result Global solutions exhibit trichotomy in long-time asymptotic behavior.
One gradient step improves neural network feature learning by aligning weights with the teacher model.
problem Improving feature learning in neural networks through gradient descent.
method First gradient descent step on the first-layer parameters of a two-layer neural network.
result The first gradient update contains a rank-1 spike, leading to alignment with the teacher model.
EAST aligns neural network classifiers with user-defined evaluation metrics.
problem Mismatch between neural network training and evaluation metrics leads to suboptimal performance.
method EAST uses dynamic thresholding, soft-set confusion matrix, and annealing to align neural network predictions with target evaluation metrics.
result EAST improves alignment between training objectives and evaluation metrics, outperforming existing methods.
We analyze why some models resist unlearning using linear stability theory.
problem Understanding and predicting when machine learning models resist unlearning.
method Linear stability theory applied to machine learning models, focusing on data coherence and optimization dynamics.
result Data coherence and signal-to-noise ratio (SNR) influence unlearning resistance; lower SNR makes unlearning easier.
Study analyzes accuracy of tensor deflation in noisy conditions.
problem Analyzing accuracy of tensor deflation in noisy conditions.
method Asymptotic study of Hotelling-type tensor deflation in large tensor dimensions.
result Characterization of estimated singular values and singular vector alignments.
Response time improves alignment with diverse human preferences.
problem Standard aggregation of feedback ignores heterogeneity and anonymity.
method Augmenting feedback with response time data and modeling decisions with DDM.
result Estimator of heterogeneous preferences converges to true average preference.
Proposes a method to compare noisy high-dimensional datasets with low-dimensional manifolds.
problem Comparing distributions on manifolds in noisy high-dimensional datasets.
method Linking low-rank structure to manifold geometry, developing a scale-invariant distance measure.
result Superior robustness and statistical power compared to existing methods.
Method tackles uncertainty in reward models for LLMs from heterogeneous human feedback.
problem Uncertainty in reward models for LLMs from heterogeneous human feedback.
method Heterogeneous preference framework and alternating gradient descent algorithm.
result Established theoretical guarantees for estimator convergence and asymptotic distribution.
OmniMatch algorithm perfectly matches graphs without edge correlation.
problem Graph matching in the absence of edge correlation.
method OmniMatch algorithm for seeded multiple graph matching.
result OmniMatch aligns O(sα) unseeded vertices across multiple networks efficiently and perfectly. This paper surveys scalable automated alignment methods for LLMs.
problem Scalability issues in traditional human-annotated alignment methods for LLMs.
method Categorizes and discusses various automated alignment methods.
result Emerging automated alignment methods are effective and scalable.
Optimal feature learning strength improves generalization in deep networks.
problem Understanding how feature learning strength affects generalization in practical settings.
method Empirical studies and theoretical analysis of gradient flow dynamics in two-layer ReLU nets.
result Optimal feature learning strength yields substantial generalization gains, contrary to the prevailing intuition.
Inference-aware meta-alignment of LLMs reduces computational cost.
problem Aligning LLMs to diverse human preferences is challenging due to conflicting criteria.
method IAMA trains a base model to be aligned to multiple tasks via different inference-time alignment algorithms, using non-linear GRPO for optimization.
result IAMA enables effective alignment of LLMs to multiple criteria with limited computational budget.
Conformal Alignment ensures trustworthy outputs from foundation models.
problem Ensuring outputs from foundation models align with human values in high-stakes tasks.
method A framework that trains an alignment predictor using reference data to select trustworthy outputs.
result Conformal Alignment accurately identifies trustworthy outputs via lightweight training over moderate reference data.
Dual active learning improves RLHF by selecting optimal conversations and teachers.
problem Efficiently aligning LLMs with human preferences using RLHF from feedback.
method Offline RL for conversation and teacher selection, dual active reward learning, pessimistic RL.
result The proposed algorithm achieves minimal generalized variance and outperforms state-of-the-arts.
Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties arising from models estimated with finite, noisy data. We propose a robust adaptive …
The paper develops a theory for random forests, separating variance components and providing methods for estimating prediction intervals.
problem Understanding the variance and uncertainty in random forest predictions.
method Design-based theory, Monte Carlo averaging, PASR resampling.
result The floor of prediction uncertainty is positive and persists even without observation overlap, providing conservative prediction intervals.
This work optimizes signal estimation for sparse MRA with collision-free signals.
problem Recovering an unknown signal from repeated observations under cyclic isometries with high noise.
method Investigates minimax optimality for collision-free signals in the MRA model.
result The minimax optimal rate of estimation is \( \sigma^2/\sqrt{n} \) for sparse MRA.
Adapts viscosity method for free boundary minimal surfaces.
problem Finding min-max free boundary minimal surfaces.
method Adapting Rivière's viscosity method to free boundary conditions.
result Min-max value is sum of branched minimal immersions.
GNA optimally identifies the best arm with small gaps.
problem Best arm identification in fixed-budget settings.
method Generalized Neyman Allocation (GNA) for asymptotically locally minimax optimal BAI.
result GNA's worst-case bounds match the lower and upper bounds in the small-gap regime.
LPL optimizes embeddings to align local neighborhoods, improving cross-lingual word alignment.
problem Aligning embeddings across different datasets and languages.
method Locality Preserving Loss (LPL) optimizes model to project embeddings while maintaining local neighborhoods and aligning them.
result LPL-based alignment leads to better and consistent accuracy, especially in small training set settings.
Extends reinforcement learning alignment to scalar rewards, improving math reasoning.
problem Designing reinforcement learning algorithms for general LLM alignment.
method Introduces f-GRPO and f-HAL, estimating f-divergences between reward-aligned and unaligned distributions.
result Improves math reasoning RLVR tasks and mitigates reward hacking.
The paper proposes a learning-theoretic perspective on representation alignment.
problem Understanding how AI models' representations become aligned as they scale.
method Reviewing and connecting different notions of alignment, focusing on stitching.
result Relating properties of stitching to kernel alignment of representations.
SIGL learns scalable graphons from graphs.
problem Estimating graphons from graphs of varying sizes.
method Combines INRs and GNNs for scalable graphon estimation.
result SIGL learns consistent graphons at arbitrary resolutions.
Survey of alignment techniques for large language models.
problem Ensuring large language models align with human values.
method Analysis of diverse alignment methods and training paradigms.
result Preference-based methods offer more flexibility for nuanced alignment.
The paper addresses rigid alignment of noisy patches, providing a polynomial time algorithm and convergence conditions.
problem Finding a rigid alignment of overlapping local views (patches) that minimizes alignment error in a noisy setting.
method Characterizes non-degeneracy based on kernel and positivity of a matrix, provides polynomial time algorithm for testing non-degeneracy, and uses Riemannian gradient descent for alignment.
result The algorithm converges locally linearly to a non-degenerate perfect alignment under certain conditions.
We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S2, \begin{align*} u_t & = Δu + |\nabla u|^2 u \quad \text{in } Ω\times(0,T) \\ u &= \varphi \quad \text{on } \partial Ω\times(0,T) \\ u(\cdot,0) &= u_0 \quad \text{in } Ω, \end{align*} where Ω is a bounded, smooth do…
Study connects database alignment and planted matching using Gaussian features.
problem Identify matching between correlated user features in anonymized databases.
method Derived results for database alignment and planted matching, showing connections and thresholds.
result Performance thresholds for database alignment converge to planted matching when feature dimensionality is sufficiently high.
Bayesian framework proves thresholds for multi-graph alignment feasibility.
problem Determining when multi-graph alignment is statistically possible.
method Developed a Bayesian estimation framework over metric spaces.
result Identified thresholds for Gaussian and sparse Erdős-Rényi models.
SMAI framework tests and integrates single-cell data alignability.
problem Lack of a rigorous statistical test for alignability and distortion during alignment.
method Spectral manifold alignment and inference (SMAI) framework.
result SMAI outperforms existing methods in alignability testing and integration.
New method aligns brain data across individuals for better brain decoding.
problem Inter-individual variability in brain response patterns limits decoder generalization.
method SpectralOT method that embeds cortical geometry into Laplace-Beltrami eigenmodes.
result SpectralOT strikes balance between aligning functional features and preserving anatomical structure.
Method aligns multilingual news for better stock return prediction.
problem Losing nuances in multilingual news translations.
method Optimal transport for sentence alignment.
result Aligned sentences correlate better with stock returns.
This paper studies aligning knowledge graphs from different sources or languages. Most existing methods train supervised methods for the alignment, which usually require a large number of aligned knowledge triplets. However, such a large number of aligned knowledge triplets may not be available or are expensive to obta…