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Modern GPUs are equipped with large amounts of high-bandwidth memory, enabling them to support mini-batch sizes of up to tens of thousands of training samples. However, most existing optimizers struggle to perform effectively at such a large batch size. 
As batch size increases, gradient noise decreases due to averaging over many samples, limiting the ability of first-order methods to escape sharp or suboptimal minima and reach the global minimum.
Meanwhile, second-order methods like the natural gradient with Kronecker-Factored Approximate Curvature (KFAC) often require excessively high damping to remain stable at large batch sizes. This high damping effectively ``washes out&quot; the curvature information that gives these methods their advantage, reducing their performance to that of simple gradient descent.
In this paper, we introduce Fisher-Orthogonal Projection (FOP), a novel technique that restores the effectiveness of the second-order method at very large batch sizes, enabling scalable training with improved generalization and faster convergence.
FOP constructs a variance-aware update direction by leveraging gradients from two sub-batches, enhancing the average gradient with a component of the gradient difference that is orthogonal to the average under the Fisher-metric. 
Through extensive benchmarks, we show that FOP accelerates convergence by $\times1.2–1.3$ over K-FAC and $\times1.5–1.7$ over SGD/AdamW at the same moderate batch sizes, while at extreme scales it achieves up to a $\times7.5$ speedup. 
Unlike other methods, FOP maintains small-batch accuracy when scaling to extremely large batch sizes. Moreover, it reduces Top-1 error by 2.3–3.3\% on long-tailed CIFAR benchmarks, demonstrating robust generalization under severe class imbalance. Our lightweight, geometry-aware use of intra-batch variance makes natural-gradient optimization practical on modern data-centre GPUs. FOP is open-source and pip-installable, which can be integrated into existing training code with a single line and no extra configuration.

AAAI 2026

Beyond the Mean: Fisher-Orthogonal Projection for Natural Gradient Descent in Large Batch Training

ml: information theory

ml: learning theory

ml: optimization

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ACL-IJCNLP 2021

The great event is jointly organized by the Association for Computational Linguistics (ACL) and Asian Federation of Natural Language Processing (AFNLP).

Modern GPUs are equipped with large amounts of high-bandwidth memory, enabling them to support mini-batch sizes of up to tens of thousands of training samples. However, most existing optimizers struggle to perform effectively at such a large batch size. 
As batch size increases, gradient noise decreases due to averaging over many samples, limiting the ability of first-order methods to escape sharp or suboptimal minima and reach the global minimum.
Meanwhile, second-order methods like the natural gradient with Kronecker-Factored Approximate Curvature (KFAC) often require excessively high damping to remain stable at large batch sizes. This high damping effectively ``washes out" the curvature information that gives these methods their advantage, reducing their performance to that of simple gradient descent.
In this paper, we introduce Fisher-Orthogonal Projection (FOP), a novel technique that restores the effectiveness of the second-order method at very large batch sizes, enabling scalable training with improved generalization and faster convergence.
FOP constructs a variance-aware update direction by leveraging gradients from two sub-batches, enhancing the average gradient with a component of the gradient difference that is orthogonal to the average under the Fisher-metric. 
Through extensive benchmarks, we show that FOP accelerates convergence by $\times1.2–1.3$ over K-FAC and $\times1.5–1.7$ over SGD/AdamW at the same moderate batch sizes, while at extreme scales it achieves up to a $\times7.5$ speedup. 
Unlike other methods, FOP maintains small-batch accuracy when scaling to extremely large batch sizes. Moreover, it reduces Top-1 error by 2.3–3.3\% on long-tailed CIFAR benchmarks, demonstrating robust generalization under severe class imbalance. Our lightweight, geometry-aware use of intra-batch variance makes natural-gradient optimization practical on modern data-centre GPUs. FOP is open-source and pip-installable, which can be integrated into existing training code with a single line and no extra configuration.

technical paper

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We are pleased to announce the Fortieth AAAI Conference on Artificial Intelligence (AAAI-26), which will be held in Singapore EXPO from January 20 to January 27, 2026.

Neural algorithmic reasoning, a term first coined by DeepMind, has recently emerged as a popular research direction. It aims to train neural networks to mimic the step-by-step behavior of classical rule-based algorithms. More specifically, the execution of such algorithms can be abstracted as a sequence of states, where each state represents the intermediate outcome after an execution step. The training objective is to generate state sequences that accurately replicate the underlying algorithmic process. A common framework for this task adopts an "encoder-processor-decoder" architecture, where the encoder learns representations of states, the processor simulates algorithmic steps, and the decoder reconstructs output states. While prior work has primarily focused on improving the processor, the role of the encoder in representation learning has received relatively little attention. Most existing approaches rely on simple MLP-based encoders, raising the question of whether such representations are sufficiently informative for supporting algorithmic reasoning.

This paper investigates how to improve encoder representations for neural algorithmic reasoning. We propose a reconstruction module that aims to recover the input state from its encoded representation. This auxiliary reconstruction task encourages the encoder to retain critical information about the input. We demonstrate that incorporating this task during training improves the performance of existing neural architectures on standard benchmarks. Furthermore, we observe that current encoders often underutilize the correlations among features within a state. To address this, we draw inspiration from self-supervised learning and design an enhanced variant of the auxiliary task that encourages the encoder to capture intra-state feature dependencies. Experimental results show that our method enables the encoder to learn richer representations, thereby enhancing the performance of existing processors on algorithmic reasoning tasks.

Richer Representations for Neural Algorithmic Reasoning via Auxiliary Reconstruction

Forecasting time series with extreme events is critical yet challenging due to their high variance, irregular dynamics, and sparse but high-impact nature. While existing methods excel in modeling dominant regular patterns, their performance degrades significantly during extreme events, constituting the primary source of forecasting errors in real-world applications. Although some approaches incorporate auxiliary signals to improve performance, they still fail to capture extreme events' complex temporal dynamics. To address these limitations, we propose M$^2$FMoE, an extreme-adaptive forecasting model that learns both regular and extreme patterns through multi-resolution and multi-view frequency modeling. It comprises three modules: (1) a multi-view frequency mixture-of-experts module assigns experts to distinct spectral bands in Fourier and Wavelet domains, with cross-view shared band splitter aligning frequency partitions and enabling inter-expert collaboration to capture both dominant and rare fluctuations; (2) a multi-resolution adaptive fusion module that hierarchically aggregates frequency features from coarse to fine resolutions, enhancing sensitivity to both short-term variations and sudden changes; (3) a temporal gating integration module that dynamically balances long-term trends and short-term frequency-aware features, improving adaptability to both regular and extreme temporal patterns. Experiments on real-world hydrological datasets with extreme patterns demonstrate that M$^2$FMoE outperforms state-of-the-art baselines without requiring extreme-event labels.

M2FMoE: Multi-Resolution Multi-View Frequency Mixture-of-Experts for Extreme-Adaptive Time Series Forecasting

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equations (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong assumptions about the structure of the kernel integral operator, assumptions which may limit expressivity. We present SVD-NO, a neural operator that explicitly parameterizes the kernel by its singular-value decomposition (SVD) and then carries out the integral directly in the low-rank basis. Two lightweight networks learn the left and right singular functions, a diagonal parameter matrix learns the singular values, and a Gram-matrix regularizer enforces orthonormality. As SVD-NO approximates the full kernel, it obtains a high degree of expressivity. Furthermore, due to its low-rank structure the computational complexity of applying the operator remains reasonable, leading to a practical system. In extensive evaluations on five diverse benchmark equations, SVD-NO achieves a new state of the art. In particular, SVD-NO provides greater performance gains on PDEs whose solutions are highly spatially variable. To facilitate reproducibility, an anonymized implementation is included in the supplementary material.

SVD-NO: Learning PDE Solution Operators with SVD Integral Kernels

Multi-robot systems in complex physical collaborations face a "shared brain dilemma": transmitting high-dimensional multimedia data (e.g., video streams at ~30MB/s) creates severe bandwidth bottlenecks and decision-making latency. To address this, we propose PIPHEN, an innovative distributed physical cognition-control framework. Its core idea is to replace "raw data communication" with "semantic communication" by performing "semantic distillation" at the robot edge, reconstructing high-dimensional perceptual data into compact, structured physical representations. This idea is primarily realized through two key components: (1) a novel Physical Interaction Prediction Network (PIPN), derived from large model knowledge distillation, to generate this representation; and (2) a Hamiltonian Energy Network (HEN) controller, based on energy conservation, to precisely translate this representation into coordinated actions. Experiments show that, compared to baseline methods, PIPHEN can compress the information representation to less than 5\% of the original data volume and reduce collaborative decision-making latency from 315ms to 76ms, while significantly improving task success rates. This work provides a fundamentally efficient paradigm for resolving the "shared brain dilemma" in resource-constrained multi-robot systems.

PIPHEN: Physical Interaction Prediction with Hamiltonian Energy Networks

Experience replay is a foundational technique in reinforcement learning that enhances learning stability by storing past experiences in a replay buffer and reusing them during training. Despite its practical success, its theoretical properties remain underexplored. In this paper, we present a theoretical framework that models experience replay using resampled $U$- and $V$-statistics, providing rigorous variance reduction guarantees. We apply this framework to policy evaluation tasks using the Least-Squares Temporal Difference (LSTD) algorithm and a Partial Differential Equation (PDE)-based model-free algorithm, demonstrating significant improvements in stability and efficiency, particularly in data-scarce scenarios. Beyond policy evaluation, we extend the framework to kernel ridge regression, showing that the experience replay-based method reduces the computational cost from the traditional $O(n^3)$ in time to as low as $O(n^2)$ in time while simultaneously reducing variance. Extensive numerical experiments validate our theoretical findings, demonstrating the broad applicability and effectiveness of experience replay in diverse machine learning tasks.

Variance Reduction via Resampling and Experience Replay

Process or step-wise supervision has played a crucial role in advancing complex multi-step reasoning capabilities of Large Language Models (LLMs). However, efficient, high-quality automated process annotation remains a significant challenge. To address this, we introduce **S**ingle-**P**ass **A**nnotation with **R**eference-Guided **E**valuation (*SPARE*), a novel structured framework that enables efficient per-step annotation by jointly aligning solution steps to reference solutions and determine its accuracy with explicit reasoning in single generation. We demonstrate *SPARE*'s effectiveness across four diverse datasets spanning mathematical reasoning (GSM8K, MATH), multi-hop question answering (MuSiQue-Ans), and spatial reasoning (SpaRP), showing consistent improvements in two applications: (1) training Process Reward Models (PRMs) for ranking and aggregating multiple generations, and (2) fine-tuning models via offline reinforcement learning for greedy decoding. On PROCESSBENCH, *SPARE* demonstrates data-efficient out-of-distribution generalization, using only ~16% of training samples compared to human-labeled and other synthetically trained baselines. Additionally, it achieves competitive performance with MCTS-based methods while offering 2.3x speedup in terms of total token count. Manual analysis reveals complementary precision-recall characteristics with MCTS approaches, suggesting potential for ensemble methods. These results establish *SPARE* as a practical and scalable solution for automatic process supervision in LLM reasoning.

SPARE: Single-Pass Annotation with Reference-Guided Evaluation for Automatic Process Supervision and Reward Modelling

Computing stable partitions in hedonic games is a challenging task because there exist games in which stable outcomes do not exist. Even more, these No-instances can often be leveraged to prove computational hardness results. We make this impression rigorous in a dynamic model of cardinal hedonic games by providing meta theorems. These imply hardness of deciding about the possible or necessary convergence of deviation dynamics based on the mere existence of No-instances. Our results hold for additively separable, fractional, and modified fractional hedonic games (ASHGs, FHGs, and MFHGs). Moreover, they encompass essentially all reasonable stability notions based on single-agent deviations. Second, we propose dynamics as a method to find individually rational and contractually individual stable (CIS) partitions in ASHGs. In particular, we find that CIS dynamics from the singleton partition possibly converge after a linear number of deviations but may require an exponential number of deviations in the worst case.

Deviation Dynamics in Cardinal Hedonic Games

Class integration test order (CITO) generation is essential for reducing the overhead of test stub construction—the primary cost in integration testing—and for ensuring system reliability in complex software systems. While reinforcement learning (RL) has demonstrated potential in automating CITO generation, existing methods suffer from unstable policy learning and limited robustness against structural perturbations and defect injection. These challenges stem from insufficient reward shaping and the absence of reliable oracles for validation. To address these limitations, we propose LM-CITO, a stability-aware RL framework that integrates Lyapunov-guided reward shaping with semantic validation via metamorphic testing (MT). Specifically, we design a Lyapunov energy function over class dependency graphs to promote monotonic structural convergence during training, and define metamorphic relations (MRs) to verify behavioral consistency under controlled perturbations. Extensive experiments on six real-world systems demonstrate that LM-CITO consistently produces more effective policies, yielding CITOs with significantly reduced stubbing costs compared to baseline models. Furthermore, MT verifies the capability of our MRs to detect diverse defects across 19 injected bug variants, confirming LM-CITO’s robustness under varied fault-induced perturbations. These results highlight the synergy of stability guidance and MR-based validation, offering an effective, principled solution for oracle-free RL in software testing.

Stability-Aware Reinforcement Learning for Robust Class Integration Test Order Generation

Marginal Fisher Analysis (MFA) is a classical dimensionality reduction (DR) method that leverages dual graphs to capture intra-class compactness and inter-class separability. However, MFA's reliance on high-quality labels limits its practical application. For another, existing unsupervised DR methods neglect data's local manifold relationship, resulting in poor discriminativeness. To address these limitations, we propose a novel DR method named \textbf{D}iscriminative \textbf{G}raph \textbf{E}mbedding \textbf{F}ramework (DGEF) via Label-Free Marginal Fisher Analysis. Our approach uses the adjacency matrix and cluster indicator matrix derived from centerless K-Means to construct intrinsic graph and penalty graph, which preserve the local manifold structure of the data. Additionally, we have derived the convertible relationship between centerless K-Means and Manifold learning and unified them within a graph embedding framework. By adopting the intrinsic graph and penalty graph, our DGEF avoids centroid initialization and ensures robustness and discriminativeness. This method achieves dimensionality reduction adaptively without relying on labeled data. Extensive experiments on benchmark datasets show that our approach outperforms conventional methods in clustering performance.

Discriminative Graph Embedding Framework via Label-Free Marginal Fisher Analysis

While knowledge distillation has seen widespread use in pre-training and instruction tuning, its application to aligning language models with human preferences remains underexplored, particularly in the more realistic cross-tokenizer setting. The incompatibility of tokenization schemes between teacher and student models has largely prevented fine-grained, white-box distillation of preference information. To address this gap, we propose Cross-Tokenizer Preference Distillation (CTPD), the first unified framework for transferring human-aligned behavior between models with heterogeneous tokenizers. CTPD introduces three key innovations: (1) Aligned Span Projection, which maps teacher and student tokens to shared character-level spans for precise supervision transfer; (2) a cross-tokenizer adaptation of Token-level Importance Sampling (TIS-DPO) for improved credit assignment; and (3) a Teacher-Anchored Reference, allowing the student to directly leverage the teacher’s preferences in a DPO-style objective. Our theoretical analysis grounds CTPD in importance sampling, and experiments across multiple benchmarks confirm its effectiveness, with significant performance gains over existing methods. These results establish CTPD as a practical and general solution for preference distillation across diverse tokenization schemes, opening the door to more accessible and efficient alignment of language models.

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Richer Representations for Neural Algorithmic Reasoning via Auxiliary Reconstruction

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