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Open problems in Graph learning

Quantization error propagation in recurrent states1 paper raises it · 1 addresses it
Low-precision recurrent states in linear attention degrade accuracy due to error accumulation over time and across dimensions.
- STEPQuant: When and Where Errors Matter in Delta-Rule Recurrent State Quantizationraises · addresses
Train-rollout discrepancy in low-precision RL1 paper raises it · 1 addresses it
Quantizing training and rollout paths independently in RL leads to mismatched behavior and reduced performance.
- TRACE: Rollout-Guided Quantization-Aware Training for FP4 Reinforcement Learning of MoE Language Modelsraises · addresses
Distribution shift in decoding-aware pruning1 paper raises it · 1 addresses it
Pruning guided by natural sequences fails to account for self-generated token distributions during decoding, hurting performance.
- SparseDecoding: Decoding-Aware Pruning for Accurate and Efficient LLM Inferenceraises · addresses
Lack of benchmarks for graph decision-making in System One models1 paper raises it · 1 addresses it
Existing benchmarks do not diagnose the unique challenges of graph-based decision tasks for non-language models.
- GraphDecisionBench: Benchmarking System One Models on Graph Tasksraises · addresses
Non-compositional sparse autoencoder features1 paper raises it · 1 addresses it
Sparse autoencoder features often exhibit higher-order interactions, limiting interpretability and control.
- Behavioral Compositionality of Sparse Autoencoder Representationsraises · addresses

Named by an AI from these papers' abstracts.

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Topics in this field

gradient descent · learning rate · neural networks221 papers43 this week
neural networks · neural network · arnold networks149 papers38 this week
graph learning · graph neural · graph neural networks263 papers36 this week
memory efficient · optimizers · low rank adaptation157 papers25 this week
bit quantization · quantization aware training · quantization aware152 papers20 this week
linear attention · softmax attention · transformer attention106 papers14 this week

Topics in this field

Active contributors · 90 days

Pietro LiòLocaLeJEPA: Maximum Entropy Representations under Geometric Priors8
Dan AlistarhWhat Matters for NVFP4 Training? A Comparative Study of Low-Precision Pretraining Recipes6
Rong-Hua LiToward Omni Multimodal Graph Foundation Model: A Topology-Driven Binding Approach6
Xunkai LiToward Omni Multimodal Graph Foundation Model: A Topology-Driven Binding Approach6
Rebekka BurkholzAC/DC on a Budget - Alternating Sparse Phases5
Haggai MaronGraph Metanetworks for Transformer Based Language Models5

Active contributors

Activity · 12 weeks

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arXiv cs.LGOct 17
Transformers as Adaptive Kernel Learners across Tasks for In-Context Learning
Zhaiming Shen, Alexander Cloninger, Rongjie Lai, Wenjing Liao
Transformers have emerged as a dominant architecture in modern machine learning, with in-context learning (ICL) enabling models to adapt to new tasks by conditioning on prompts, without any parameter updates. To understand the attention mechanism in transformer blocks, a growing line of theoretical work interprets ICL through the lens of classical statistical estimators. Recent works have established a connection between the attention mechanism and kernel methods, while the kernel function is usually assumed to be fixed. In practice, the query and key matrices in the attention mechanism are trained, which allows the attention mechanism to serve as an adaptive kernel method. In this work, we demonstrate that transformers can act as adaptive anisotropic kernel learners. Specifically, we study ICL for low-rank linear and multi-index nonlinear regressions, and conduct numerical simulations to show that the learned attention scores closely resemble the oracle kernels for these function classes. We then develop a general framework to analyze the generalization error of ICL by connecting transformers to the oracle kernel estimator for each function class. Our theory gives an explicit…
PDF arXiv
arXiv cs.CLOct 17
What Matters for NVFP4 Training? A Comparative Study of Low-Precision Pretraining Recipes
Anjulie Agrusa, Andrei Panferov, Elizabeth Wei, Keith Wyss, Paul Gibbons +5
Training large language models directly in 4-bit floating-point (FP) formats promises substantial improvements in throughput and energy efficiency. While some recipe design choices have been validated at scale, many promising approaches remain untested beyond small models and short token horizons, leaving open the question of which trends will hold. We present a systematic comparison of recent NVFP4 recipes at medium model scale, evaluating dense 8B and 30B-A3B MoE models trained for up to 1T tokens, with a focus on which ingredients are necessary for accuracy recovery. We propose a final recipe grounded in the principles behind established stable NVFP4 training at scale, incorporating state-of-the-art techniques such as unbiased gradient estimation with lower quantization error than stochastic rounding. To the best of our knowledge, this is the strongest FP4 training result demonstrated at this scale to date in loss gap to BF16. Through ablation studies, we find that: (i) each technique in the optimized recipe measurably improves loss trajectory, (ii) selective high-precision layers are necessary for recovering accuracy at scale, (iii) not all tensors in the backward pass…
PDF arXiv
arXiv cs.LGOct 16
Muon Operates Beyond the Edge of Stability
Niko Covic, Baraq Lipshitz, Alexander Padula, Stefan Visnjic
We study the Muon optimizer using sharpness and provide the first empirical evidence that the Flat Minima Hypothesis also applies to Muon. Further, we derive Muon's implicit preconditioner to analyze its potential Edge of Stability behavior. Experiments on CIFAR-10 show sharpness strongly correlates with generalization gap within each optimizer (Pearson $r = 0.45$-$0.69$, $p \leq 10^{-4}$), confirming the hypothesis holds for Muon similarly to Adam and SGD. However, Muon operates above the classical sharpness-based Adaptive Edge of Stability threshold that bounds diagonally-preconditioned optimizers like Adam and RMSprop, yet remains stable. Our findings suggest Muon operates in a fundamentally different regime than diagonally-adaptive methods. Defining the exact stability boundary for Muon remains an open question. All code is available at https://github.com/NikoCovic/DL-project.
PDF arXiv
arXiv cs.LGOct 16
Constructive Universal Approximation by Infinite-Dimensional Neural Networks via Gaussian-Weighted Ridgelet Transform
Sho Sonoda, Luca Galimberti, Yuanchao Xu, Isao Ishikawa, Masahiro Ikeda
Neural networks whose inputs are functions, as in operator learning, are usually shown to be universal by existence arguments, either by reduction to finite-dimensional networks or by Stone--Weierstrass-type density; these prove that approximants exist but say little about how the parameters depend on the target. We take a constructive route. We extend the ridgelet transform, an integral transform related to the Fourier, Radon, and wavelet transforms, to continuous maps on a separable infinite-dimensional Hilbert space, replacing the Lebesgue measure that is unavailable in infinite dimensions by Gaussian weights with a homogeneous mixture on the direction space. The resulting transform has a Plancherel identity and reconstruction formulas incorporating the frame operator, the correction induced by the weights, and it assigns to each target an explicit coefficient measure, one for every admissible analysis filter. From these representations we obtain uniform approximation on compact sets for all continuous non-polynomial activations of polynomial growth, including ReLU, and, by Monte Carlo sampling of the coefficient, finite-width networks with a dimension-free $O(N^{-1/2})$ error…
PDF arXiv
arXiv cs.LGOct 16
Inducing Fourier Geometry: A Smoothness Prior Imposes Approximate Translation Equivariance in Multimodal Stellar Embeddings
Ilay Kamai, Alex M. Bronstein, Hagai B. Perets
Learned representations often contain geometric structure induced by symmetries in the underlying data. We ask whether a known continuous parameter space can instead be used to \emph{induce} such structure when the corresponding symmetry is only approximate. We introduce a graph-Laplacian smoothness prior that encourages representations to vary smoothly over a physical parameter space without specifying a representation geometry; in the continuum limit it selects Laplacian eigenfunctions and therefore predicts the Fourier-like geometry associated with translation symmetry. On multimodal stellar representations spanning six astronomical surveys, the prior induces Toeplitz Gram structure and sinusoidal modes along stellar parameters, including in modalities whose native representations lack this geometry, while modality-specific residuals preserve structure outside the imposed coordinates. Of the exact-symmetry predictions, stationarity in a recoverable warped coordinate survives; diagnostics assuming exact quantization or asymptotic rates do not. The prior also improves downstream linear-probe performance and label efficiency, suggesting a general strategy: where a meaningful…
PDF arXiv
arXiv cs.AICodeOct 16▲ 7
A Conditional No-Hair Theorem for Transformers: How Language Models Forget Their Prompt
Shuyang Xiang
We ask how much an autoregressive transformer retains of its prompt after generating $t$ tokens. Consider two different prompts followed by the same continuation text, so that any difference in their hidden states comes from the prompt alone, and we find that the distance between their hidden states decays approximately as a power law $t^{-α}$, where $α=1$ is the rate at which a fixed prompt's share of uniform attention shrinks and smaller values mean longer memory. Trained models forget fast ($α\approx0.55$--$0.7$), untrained ones slowly ($α\approx0.2$--$0.5$). We prove that this offset is $O\big(P(\log t)^{L-1}/t\big)$ for a prompt of length $P$ and depth $L$. The bound holds for finite-depth pre-LN softmax transformers with bounded attention logits, under one additional condition: the pre-norm activations stay away from zero. The mechanism is geometric: the prompt's direct influence is diluted as the context grows, and \emph{relay} --- continuation tokens passing on what earlier tokens read from the prompt --- can only add logarithmic factors. This is what we call the \emph{conditional no-hair theorem}: given the text generated so far, the prompt's influence on the next token…
PDF arXiv Code

Papers

Topics in this field

gradient descent · learning rate · neural networks221 papers43 this week
neural networks · neural network · arnold networks149 papers38 this week
graph learning · graph neural · graph neural networks263 papers36 this week
memory efficient · optimizers · low rank adaptation157 papers25 this week
bit quantization · quantization aware training · quantization aware152 papers20 this week
linear attention · softmax attention · transformer attention106 papers14 this week

Active contributors · 90 days

Pietro LiòLocaLeJEPA: Maximum Entropy Representations under Geometric Priors8
Dan AlistarhWhat Matters for NVFP4 Training? A Comparative Study of Low-Precision Pretraining Recipes6
Rong-Hua LiToward Omni Multimodal Graph Foundation Model: A Topology-Driven Binding Approach6
Xunkai LiToward Omni Multimodal Graph Foundation Model: A Topology-Driven Binding Approach6
Rebekka BurkholzAC/DC on a Budget - Alternating Sparse Phases5
Haggai MaronGraph Metanetworks for Transformer Based Language Models5

Activity · 12 weeks

Coming with more sources: repos

Open problems in Graph learning

Quantization error propagation in recurrent states1 paper raises it · 1 addresses it
Low-precision recurrent states in linear attention degrade accuracy due to error accumulation over time and across dimensions.
- STEPQuant: When and Where Errors Matter in Delta-Rule Recurrent State Quantizationraises · addresses
Train-rollout discrepancy in low-precision RL1 paper raises it · 1 addresses it
Quantizing training and rollout paths independently in RL leads to mismatched behavior and reduced performance.
- TRACE: Rollout-Guided Quantization-Aware Training for FP4 Reinforcement Learning of MoE Language Modelsraises · addresses
Distribution shift in decoding-aware pruning1 paper raises it · 1 addresses it
Pruning guided by natural sequences fails to account for self-generated token distributions during decoding, hurting performance.
- SparseDecoding: Decoding-Aware Pruning for Accurate and Efficient LLM Inferenceraises · addresses
Lack of benchmarks for graph decision-making in System One models1 paper raises it · 1 addresses it
Existing benchmarks do not diagnose the unique challenges of graph-based decision tasks for non-language models.
- GraphDecisionBench: Benchmarking System One Models on Graph Tasksraises · addresses
Non-compositional sparse autoencoder features1 paper raises it · 1 addresses it
Sparse autoencoder features often exhibit higher-order interactions, limiting interpretability and control.
- Behavioral Compositionality of Sparse Autoencoder Representationsraises · addresses

Named by an AI from these papers' abstracts.

Recent papers

All in Research →

arXiv cs.LGOct 17
Transformers as Adaptive Kernel Learners across Tasks for In-Context Learning
Zhaiming Shen, Alexander Cloninger, Rongjie Lai, Wenjing Liao
Transformers have emerged as a dominant architecture in modern machine learning, with in-context learning (ICL) enabling models to adapt to new tasks by conditioning on prompts, without any parameter updates. To understand the attention mechanism in transformer blocks, a growing line of theoretical work interprets ICL through the lens of classical statistical estimators. Recent works have established a connection between the attention mechanism and kernel methods, while the kernel function is usually assumed to be fixed. In practice, the query and key matrices in the attention mechanism are trained, which allows the attention mechanism to serve as an adaptive kernel method. In this work, we demonstrate that transformers can act as adaptive anisotropic kernel learners. Specifically, we study ICL for low-rank linear and multi-index nonlinear regressions, and conduct numerical simulations to show that the learned attention scores closely resemble the oracle kernels for these function classes. We then develop a general framework to analyze the generalization error of ICL by connecting transformers to the oracle kernel estimator for each function class. Our theory gives an explicit…
PDF arXiv
arXiv cs.CLOct 17
What Matters for NVFP4 Training? A Comparative Study of Low-Precision Pretraining Recipes
Anjulie Agrusa, Andrei Panferov, Elizabeth Wei, Keith Wyss, Paul Gibbons +5
Training large language models directly in 4-bit floating-point (FP) formats promises substantial improvements in throughput and energy efficiency. While some recipe design choices have been validated at scale, many promising approaches remain untested beyond small models and short token horizons, leaving open the question of which trends will hold. We present a systematic comparison of recent NVFP4 recipes at medium model scale, evaluating dense 8B and 30B-A3B MoE models trained for up to 1T tokens, with a focus on which ingredients are necessary for accuracy recovery. We propose a final recipe grounded in the principles behind established stable NVFP4 training at scale, incorporating state-of-the-art techniques such as unbiased gradient estimation with lower quantization error than stochastic rounding. To the best of our knowledge, this is the strongest FP4 training result demonstrated at this scale to date in loss gap to BF16. Through ablation studies, we find that: (i) each technique in the optimized recipe measurably improves loss trajectory, (ii) selective high-precision layers are necessary for recovering accuracy at scale, (iii) not all tensors in the backward pass…
PDF arXiv
arXiv cs.LGOct 16
Muon Operates Beyond the Edge of Stability
Niko Covic, Baraq Lipshitz, Alexander Padula, Stefan Visnjic
We study the Muon optimizer using sharpness and provide the first empirical evidence that the Flat Minima Hypothesis also applies to Muon. Further, we derive Muon's implicit preconditioner to analyze its potential Edge of Stability behavior. Experiments on CIFAR-10 show sharpness strongly correlates with generalization gap within each optimizer (Pearson $r = 0.45$-$0.69$, $p \leq 10^{-4}$), confirming the hypothesis holds for Muon similarly to Adam and SGD. However, Muon operates above the classical sharpness-based Adaptive Edge of Stability threshold that bounds diagonally-preconditioned optimizers like Adam and RMSprop, yet remains stable. Our findings suggest Muon operates in a fundamentally different regime than diagonally-adaptive methods. Defining the exact stability boundary for Muon remains an open question. All code is available at https://github.com/NikoCovic/DL-project.
PDF arXiv
arXiv cs.LGOct 16
Constructive Universal Approximation by Infinite-Dimensional Neural Networks via Gaussian-Weighted Ridgelet Transform
Sho Sonoda, Luca Galimberti, Yuanchao Xu, Isao Ishikawa, Masahiro Ikeda
Neural networks whose inputs are functions, as in operator learning, are usually shown to be universal by existence arguments, either by reduction to finite-dimensional networks or by Stone--Weierstrass-type density; these prove that approximants exist but say little about how the parameters depend on the target. We take a constructive route. We extend the ridgelet transform, an integral transform related to the Fourier, Radon, and wavelet transforms, to continuous maps on a separable infinite-dimensional Hilbert space, replacing the Lebesgue measure that is unavailable in infinite dimensions by Gaussian weights with a homogeneous mixture on the direction space. The resulting transform has a Plancherel identity and reconstruction formulas incorporating the frame operator, the correction induced by the weights, and it assigns to each target an explicit coefficient measure, one for every admissible analysis filter. From these representations we obtain uniform approximation on compact sets for all continuous non-polynomial activations of polynomial growth, including ReLU, and, by Monte Carlo sampling of the coefficient, finite-width networks with a dimension-free $O(N^{-1/2})$ error…
PDF arXiv
arXiv cs.LGOct 16
Inducing Fourier Geometry: A Smoothness Prior Imposes Approximate Translation Equivariance in Multimodal Stellar Embeddings
Ilay Kamai, Alex M. Bronstein, Hagai B. Perets
Learned representations often contain geometric structure induced by symmetries in the underlying data. We ask whether a known continuous parameter space can instead be used to \emph{induce} such structure when the corresponding symmetry is only approximate. We introduce a graph-Laplacian smoothness prior that encourages representations to vary smoothly over a physical parameter space without specifying a representation geometry; in the continuum limit it selects Laplacian eigenfunctions and therefore predicts the Fourier-like geometry associated with translation symmetry. On multimodal stellar representations spanning six astronomical surveys, the prior induces Toeplitz Gram structure and sinusoidal modes along stellar parameters, including in modalities whose native representations lack this geometry, while modality-specific residuals preserve structure outside the imposed coordinates. Of the exact-symmetry predictions, stationarity in a recoverable warped coordinate survives; diagnostics assuming exact quantization or asymptotic rates do not. The prior also improves downstream linear-probe performance and label efficiency, suggesting a general strategy: where a meaningful…
PDF arXiv
arXiv cs.AICodeOct 16▲ 7
A Conditional No-Hair Theorem for Transformers: How Language Models Forget Their Prompt
Shuyang Xiang
We ask how much an autoregressive transformer retains of its prompt after generating $t$ tokens. Consider two different prompts followed by the same continuation text, so that any difference in their hidden states comes from the prompt alone, and we find that the distance between their hidden states decays approximately as a power law $t^{-α}$, where $α=1$ is the rate at which a fixed prompt's share of uniform attention shrinks and smaller values mean longer memory. Trained models forget fast ($α\approx0.55$--$0.7$), untrained ones slowly ($α\approx0.2$--$0.5$). We prove that this offset is $O\big(P(\log t)^{L-1}/t\big)$ for a prompt of length $P$ and depth $L$. The bound holds for finite-depth pre-LN softmax transformers with bounded attention logits, under one additional condition: the pre-norm activations stay away from zero. The mechanism is geometric: the prompt's direct influence is diluted as the context grows, and \emph{relay} --- continuation tokens passing on what earlier tokens read from the prompt --- can only add logarithmic factors. This is what we call the \emph{conditional no-hair theorem}: given the text generated so far, the prompt's influence on the next token…
PDF arXiv Code

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