AAAI 2026 Papers

AAAI Conference on Artificial Intelligence

Decision breakdown

4,436papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Other / unlabeled
    4,436100.0%

Top 10 topics (click to filter)

No topic data yet.

Trends for all 207 research topics

Browse all papers

TabFlash: Efficient Table Understanding with Progressive Question Conditioning and Token Focusing

Jongha Kim, Minseong Bae, Sanghyeok Lee, Jinsung Yoon, Hyunwoo J Kim

Expand abstract

Table images present unique challenges for effective and efficient understanding due to the need for question-specific focus and the presence of redundant background regions. Existing Multimodal Large Language Model (MLLM) approaches often overlook these characteristics, resulting in uninformative and redundant visual representations. To address these issues, we aim to generate visual features that are both informative and compact for improved table understanding. We first propose progressive question conditioning, which injects the question into Vision Transformer layers with gradually increasing frequency, considering each layer’s capacity to handle additional information, to generate question-aware visual features. To reduce redundancy, we introduce a pruning strategy that discards background tokens, thereby improving efficiency. To mitigate information loss from pruning, we further propose token focusing, a training strategy that encourages the model to concentrate essential information in the retained tokens. By combining these approaches, we present TabFlash, an efficient and effective MLLM for table understanding. TabFlash achieves state-of-the-art performance, outperforming both open-source and proprietary MLLMs, while requiring 27% less FLOPs and 30% less memory usage compared to the second-best MLLM.

Technical
BD-Net: Has Depth-Wise Convolution Ever Been Applied in Binary Neural Networks?

Doyoung Kim, Jin-Seop Lee, Noo-ri Kim, Sungjoon Lee, Jee-Hyong Lee

Expand abstract

Recent advances in model compression have highlighted the potential of low-bit precision techniques, with Binary Neural Networks (BNNs) attracting attention for their extreme efficiency. However, extreme quantization in BNNs limits representational capacity and destabilizes training, posing significant challenges for lightweight architectures with depth-wise convolutions. To address this, we propose a 1.58-bit convolution to enhance expressiveness and a pre-BN residual connection to stabilize optimization by improving the Hessian condition number. These innovations enable, to the best of our knowledge, the first successful binarization of depth-wise convolutions in BNNs. Our method achieves 33M OPs on ImageNet with MobileNet V1, establishing a new state-of-the-art in BNNs by outperforming prior methods with comparable OPs. Moreover, it consistently outperforms existing methods across various datasets, including CIFAR-10, CIFAR-100, STL-10, Tiny ImageNet, and Oxford Flowers 102, with accuracy improvements of up to 9.3 percentage points.

Technical
Step-by-step Layered Design Generation

Faizan Farooq Khan, Joseph K J, Koustava Goswami, Mohamed Elhoseiny, Balaji Vasan Srinivasan

Expand abstract

Design generation, in its essence, is a step-by-step process where designers progressively refine and enhance their work through careful modifications. Despite this fundamental characteristic, existing approaches mainly treat design synthesis as a single-step generation problem, significantly underestimating the inherent complexity of the creative process. To bridge this gap, we propose a novel problem setting called Step-by-step Layered Design Generation, that tasks a machine learning model to generate a design, adhering to a sequence of instructions from a designer. Leveraging the recent advancements in Multi-modal LLMs, we propose SLEDGE: Step-by-step LayEred Design GEnerator to model each update to a design as an atomic layered change over its previous state, while being grounded on the instruction.To complement our new problem setting, we introduce a new evaluation suite, including a dataset and a benchmark. Our exhaustive experimental analysis and comparison with state-of-the-art approaches adapted to our new setup bring out the efficacy of our approach. We hope our work will attract attention to this pragmatic and under-explored research area.

Technical
GLANCE: Global Actions in a Nutshell for Counterfactual Explainability

Loukas Kavouras, Eleni Psaroudaki, Konstantinos Tsopelas, Dimitrios Rontogiannis, Nikolaos Theologitis, Dimitris Sacharidis, Giorgos Giannopoulos, Dimitrios Tomaras, Kleopatra Markou, Dimitrios Gunopulos, Dimitris Fotakis, Ioannis Emiris

Expand abstract

The widespread deployment of machine learning systems in critical real-world decision-making applications has highlighted the urgent need for counterfactual explainability methods that operate effectively. Global counterfactual explanations, expressed as actions to offer recourse, aim to provide succinct explanations and insights applicable to large population subgroups. High effectiveness, measured by the fraction of the population that is provided recourse, ensures that the actions benefit as many individuals as possible. Keeping the cost of actions low ensures the proposed recourse actions remain practical and actionable. Limiting the number of actions that provide global counterfactuals is essential to maximize interpretability. The primary challenge, therefore, is to balance these trade-offs—maximizing effectiveness, minimizing cost, while maintaining a small number of actions. We introduce GLANCE, a versatile and adaptive algorithm that employs a novel agglomerative approach, jointly considering both the feature space and the space of counterfactual actions, thereby accounting for the distribution of points in a way that aligns with the model's structure. This design enables the careful balancing of the trade-offs among the three key objectives, with the size objective functioning as a tunable parameter to keep the actions few and easy to interpret. Our extensive experimental evaluation demonstrates that GLANCE consistently shows greater robustness and performance compared to existing methods across various datasets and models.

Technical
Detecting the Future: All-at-Once Event Sequence Forecasting with Horizon Matching

Ivan Karpukhin, Andrey Savchenko

Expand abstract

Long-horizon events forecasting is a crucial task across various domains, including retail, finance, healthcare, and social networks. Traditional models for event sequences often extend to forecasting on horizon using an autoregressive (recursive) multi-step strategy, which has limited effectiveness due to typical convergence to constant or repetitive outputs. To address this limitation, we introduce DEF, a novel approach for simultaneous forecasting of multiple future events on a horizon with high accuracy and diversity. Our method optimally aligns predictions with ground truth events during training by using a novel matching-based loss function. We establish a new state-of-the-art in long-horizon event prediction, achieving up to a 50% relative improvement over existing temporal point processes and event prediction models. Furthermore, we achieve state-of-the-art performance in next-event prediction tasks while demonstrating high computational efficiency during inference.

Technical
Policy Zooming: Adaptive Discretization-based Infinite-Horizon Average-Reward Reinforcement Learning

Avik Kar, Rahul Singh

Expand abstract

We study infinite-horizon average-reward reinforcement learning for continuous space Lipschitz Markov decision processes (MDPs) in which an agent can play policies from a given set Φ. The proposed algorithms efficiently explore the policy space by “zooming” into the “promising regions” of Φ, thereby achieving adaptivity gains in the performance. We upper bound the regret as O ̃(T^(1-d_(eff.)^(-1) ) ), where d_(eff.) = d_z^Φ+2 for our model-free algorithm PZRL-MF and d_(eff.) = 2d_S + d_z^Φ+ 3 for our model-based algorithm PZRL-MB. Here, d_S is the dimension of the state space, and d_z^Φ is the zooming dimension given a set of policies Φ. d_z^Φ is an alternative measure of the complexity of the problem, and it depends on the underlying MDP as well as on Φ. Hence, the proposed algorithms exhibit low regret in case the problem instance is benign and/or the agent competes against a low-complexity Φ (that has a small d_z^Φ). When specialized to the case of finite-dimensional policy space, we obtain that d_(eff.) scales as the dimension of this space under mild technical conditions; and also obtain d_(eff.) = 2, or equivalently O ̃(√T) regret for PZRL-MF, under a curvature condition on the average reward function that is commonly used in the multi-armed bandit (MAB) literature.

Technical
HiCL: Hippocampal-Inspired Continual Learning

Kushal Kapoor, Wyatt Mackey, Yiannis Aloimonos, Xiaomin Lin

Expand abstract

We propose HiCL, a novel hippocampal-inspired dual-memory continual learning architecture designed to mitigate catastrophic forgetting by using elements inspired by the hippocampal circuitry. Our system encodes inputs through a grid-cell-like layer, followed by sparse pattern separation using a dentate gyrus-inspired module with top-k sparsity. Episodic memory traces are maintained in a CA3-like autoassociative memory. Task-specific processing is dynamically managed via a DG-gated mixture-of-experts mechanism, wherein inputs are routed to experts based on cosine similarity between their normalized sparse DG representations and learned task-specific DG prototypes computed through online exponential moving averages. This biologically grounded yet mathematically principled gating strategy enables differentiable, scalable task-routing without relying on a separate gating network, and enhances the model's adaptability and efficiency in learning multiple sequential tasks. Cortical outputs are consolidated using Elastic Weight Consolidation weighted by inter-task similarity. Crucially, we incorporate prioritized replay of stored patterns to reinforce essential past experiences. Evaluations on standard continual learning benchmarks demonstrate the effectiveness of our architecture in reducing task interference, achieving near state-of-the-art results in continual learning tasks at lower computational costs.

Technical
GEM: A Scale-Aware and Distribution-Sensitive Sparse Fine-Tuning Framework for Effective Downstream Adaptation

Sungmin Kang, Jisoo Kim, Salman Avestimehr, Sunwoo Lee

Expand abstract

Parameter-efficient fine-tuning (PEFT) has become a popular way to adapt large pre-trained models to new tasks. Most PEFT methods update only a small subset of parameters while freezing the rest, avoiding redundant computation. As they maximize the absolute size of the updates without regard to the parameters’ original scale, the resulting changes in model behavior can be minimal. In contrast, we maximize updates relative to each parameter’s scale, yielding more meaningful downstream adaptation. We propose Gradient-to-Weight Ratio and Entropy-guided Masking (GEM), a parameter scale-aware, distribution-sensitive sparse fine-tuning framework. GEM prioritizes parameters whose updates are significant in proportion to their initial pre-trained values. It also adaptively determines how many parameters to tune at each layer based on the entropy of parameter values, thereby making the most effective use of the computational budget in PEFT. Our empirical study demonstrates the efficacy of GEM on both general-domain tasks (GLUE and SuperGLUE) and domain-specific tasks (GSM8k and MBPP), achieving up to a 1.6% improvement in fine-tuning accuracy over full fine-tuning while updating only 0.1% of model parameters.

Technical
Understanding and Enhancing Differentiable Architecture Search from Information Bottleneck Perspective

Haidong Kang, Lianbo Ma, Pengjun Chen, Qiang He, Bo Yi

Expand abstract

Performance collapse is an intractable issue of Differentiable Architecture Search (DAS), where severe performance degradation of DAS happens when it trains on different search spaces or datasets. We theoretically analyze the issue from the information bottleneck (IB) perspective, and disclose that a solution to overcome this problem is to seek the bifurcation point of IB tradeoff between compression and prediction of the supernet. To this end, we propose a simple yet highly effective method, namely, Batch Entropy-decay Regularization (BER), to guide the learning of DAS, which restricts compression in DAS by imposing a penalty on the architecture parameters. Comprehensive theoretical analyses demonstrate that BER is able to completely resolve DAS's performance collapse issue. Compared with a number of state-of-the-art DAS variants, BER shows its overwhelmingly better performance on 7 search spaces (i.e., NAS-Bench-201, DARTS, S1-S4, MobileNet-like) and 5 popular datasets (i.e., CIFAR-10, CIFAR-100, ImageNet1k, PASCAL VOC 2007, and MS COCO 2017).

Technical
Sparse Additive Model Pruning for Order-Based Causal Structure Learning

Kentaro Kanamori, Hirofumi Suzuki, Takuya Takagi

Expand abstract

Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based approach that first estimates a topological order of the underlying DAG and then prunes spurious edges from the fully-connected DAG induced by the estimated topological order. Previous studies often focus on the former ordering step because it can dramatically reduce the search space of DAGs. In practice, the latter pruning step is equally crucial for ensuring both computational efficiency and estimation accuracy. Most existing methods employ a pruning technique based on generalized additive models and hypothesis testing, commonly known as CAM-pruning. However, this approach can be a computational bottleneck as it requires repeatedly fitting additive models for all variables. Furthermore, it may harm estimation quality due to multiple testing. To address these issues, we introduce a new pruning method based on sparse additive models, which enables direct pruning of redundant edges without relying on hypothesis testing. We propose an efficient algorithm for learning sparse additive models by combining the randomized tree embedding technique with group-wise sparse regression. Experimental results on both synthetic and real datasets demonstrated that our method is significantly faster than existing pruning methods while maintaining comparable or superior accuracy.

Technical
Quantum Transformer for Molecular Learning: Multi-Configuration Ground-State Energy Prediction

Yuichi Kamata, Quoc Hoan Tran, Yasuhiro Endo, Hirotaka Oshima

Expand abstract

The Transformer model, renowned for its powerful attention mechanism, has achieved state-of-the-art performance in various artificial intelligence tasks but faces challenges with quantum data. With a growing focus on leveraging quantum machine learning for quantum data, particularly in quantum chemistry, we propose the Molecular Quantum Transformer (MQT) for modeling interactions in molecular quantum systems. By utilizing quantum circuits to implement the attention mechanism on the molecular configurations, MQT can efficiently calculate ground-state energies for all configurations. Numerical demonstrations show that in calculating ground-state energies for H2, LiH, BeH2, and H4, MQT outperforms the classical Transformer, highlighting the promise of quantum effects in Transformer structures. Furthermore, its pretraining capability on diverse molecular data facilitates the efficient learning of new molecules, extending its applicability to complex molecular systems with minimal additional effort. Our method offers an alternative to existing quantum algorithms for estimating ground-state energies, opening new avenues in quantum chemistry and materials science.

Technical
HALO: Hardware-Aware Quantization with Low Critical-Path-Delay Weights for LLM Acceleration

Rohan Juneja, Shivam Aggarwal, Safeen Huda, Tulika Mitra, Li-Shiuan Peh

Expand abstract

Quantization is critical for efficiently deploying large language models (LLMs). Yet conventional methods remain hardware-agnostic, limited to bit-width constraints, and do not account for intrinsic circuit characteristics such as the timing behaviors and energy profiles of Multiply-Accumulate (MAC) units. This disconnect from circuit-level behavior limits the ability to exploit available timing margins and energy-saving opportunities, reducing the overall efficiency of deployment on modern accelerators. To address these limitations, we propose HALO, a versatile framework for Hardware-Aware Post-Training Quantization (PTQ). Unlike traditional methods, HALO explicitly incorporates detailed hardware characteristics, including critical-path timing and power consumption, into its quantization approach. HALO strategically selects weights with low critical-path-delays enabling higher operational frequencies and dynamic frequency scaling without disrupting the architecture's dataflow. Remarkably, HALO achieves these improvements with only a few dynamic voltage and frequency scaling (DVFS) adjustments, ensuring simplicity and practicality in deployment. Additionally, by reducing switching activity within the MAC units, HALO effectively lowers energy consumption. Evaluations on accelerators such as Tensor Processing Units (TPUs) and Graphics Processing Units (GPUs) demonstrate that HALO significantly enhances inference efficiency, achieving average performance improvements of 270% and energy savings of 51% over baseline quantization methods, all with minimal impact on accuracy.

Technical
EvoMoE: Expert Evolution in Mixture of Experts for Multimodal Large Language Models

Linglin Jing, Yuting Gao, Zhigang Wang, Wang Lan, Yiwen Tang, Weiyun Wang, Wenhai Wang, Qingpei Guo

Expand abstract

Recent advancements have shown that the Mixture of Experts (MoE) approach significantly enhances the capacity of large language models (LLMs) and improves performance on downstream tasks. Building on these promising results, multi-modal large language models (MLLMs) have increasingly adopted MoE techniques. However, existing multi-modal MoE tuning methods typically face two key challenges: expert uniformity and router rigidity. Expert uniformity occurs because MoE experts are often initialized by simply replicating the FFN parameters from LLMs, leading to homogenized expert functions and weakening the intended diversification of the MoE architecture. Meanwhile, router rigidity stems from the prevalent use of static linear routers for expert selection, which fail to distinguish between visual and textual tokens, resulting in similar expert distributions for image and text. To address these limitations, we propose EvoMoE, an innovative MoE tuning framework. EvoMoE introduces a meticulously designed expert initialization strategy that progressively evolves multiple robust experts from a single trainable expert, a process termed expert evolution that specifically targets severe expert homogenization. Furthermore, we introduce the Dynamic Token-aware Router (DTR), a novel routing mechanism that allocates input tokens to appropriate experts based on their modality and intrinsic token values. This dynamic routing is facilitated by hypernetworks, which dynamically generate routing weights tailored for each individual token. Extensive experiments demonstrate that EvoMoE significantly outperforms other sparse MLLMs across a variety of multi-modal benchmarks, including MME, MMBench, TextVQA, and POPE. Our results highlight the effectiveness of EvoMoE in enhancing the performance of MLLMs by addressing the critical issues of expert uniformity and router rigidity.

Technical
Signal Enhancement via Multi-view Dynamic Representation and Alignment-aware Fusion

Zikun Jin, Yuhua Qian, Xinyan Liang, Jiaqian Zhang, Jinpeng Yuan, Shen Hu, Haijun Geng, Honghong Cheng

Expand abstract

Robust signal enhancement under non-stationary and low SNR conditions remains challenging, as methods based on the short-time Fourier transform (STFT) with fixed resolution struggle to represent complex and time–frequency structures. While leveraging the fractional domain as an auxiliary view offers flexibility in modeling time-frequency structures, existing methods typically adopt fixed transform orders and overlook alignment between views, hindering effective integration of complementary representations and leaving frequency domain misalignment unresolved. Therefore, we propose FracFusion, a novel framework that integrates a learnable short-time fractional Fourier Transform (STFrFT) module to generate dynamic auxiliary views, combined with two stage alignment-aware fusion modules: Pearson Channel Fusion for correlation-guided consistency and Efficient Align Fusion for fine-grained, frequency aligned interaction. Experiments on speech and electromagnetic (EM) datasets show that FracFusion consistently outperforms state-of-the-art baselines across diverse noise levels and signal types, demonstrating robust adaptability across domains.

Technical
SMIDT: High-Performance Inference Framework for MoE Models with Dynamic Top-K Routing

Zewen Jin, Shen Fu, Chengjie Tang, Youhui Bai, Shengnan Wang, Jiaan Zhu, Chizheng Fang, Ping Gong, Cheng Li

Expand abstract

To accelerate Mixture-of-Experts (MoE) inference, the hybrid parallelism paradigm is first applying pipeline parallelism (PP) to vertically divide the model into stages, with each stage further divided horizontally using tensor or expert parallelism. On the algorithm side, dynamic Top-K routing reduces computation by activating fewer experts per token on average. In this paper, we explore the application of dynamic Top-K routing to PP-enabled MoE inference, aiming to fully unleash their combined potential. We identify key performance bottlenecks arising from Top-K value variation across layers, which conflicts with PP's typically uniform stage partitioning, as well as opportunities to optimize memory usage through their integration. To address these challenges, we present SMIDT, an efficient MoE inference framework tailored for dynamic Top-K routing. SMIDT features: (1) an adaptive, module-level uneven partitioning strategy to balance computation across PP stages, (2) a memory-aware expert replication scheme (DPMoE) that reduces communication overhead, and (3) a lightweight search algorithm combining binary search and dynamic programming to generate efficient parallelism plans. We implement SMIDT on SGLang, a state-of-the-art LLM inference framework, evaluate it on 32 A40 GPUs and 16 A100 GPUs, and compare with manually tuned parallelism strategies. Experimental results show that, when co-locating prefill and decoding phases, SMIDT achieves 1.20–3.13x throughput improvements for prefill-only tasks and 1.05–1.89x for prefill-decoding tasks. When disaggregating prefill and decoding tasks, SMIDT improves average and P99 time-to-first-token (TTFT) by 1.10–1.17x and 1.21–1.26x, respectively.

Technical
Partial Action Replacement: Tackling Distribution Shift in Offline MARL

Yue Jin, Giovanni Montana

Expand abstract

Offline multi-agent reinforcement learning (MARL) is severely hampered by the challenge of evaluating out-of-distribution (OOD) joint actions. Our core finding is that when the behavior policy is factorized—a common scenario where agents act fully or partially independently during data collection—a strategy of partial action replacement (PAR) can significantly mitigate this challenge. PAR updates a single or part of agents' actions while the others remain fixed to the behavioral data, reducing distribution shift compared to full joint-action updates. Based on this insight, we develop Soft-Partial Conservative Q-Learning (SPaCQL), using PAR to mitigate OOD issue and dynamically weighting different PAR strategies based on the uncertainty of value estimation. We provide a rigorous theoretical foundation for this approach, proving that under factorized behavior policies, the induced distribution shift scales linearly with the number of deviating agents rather than exponentially with the joint-action space. This yields a provably tighter value error bound for this important class of offline MARL problems. Our theoretical results also indicate that SPaCQL adaptively addresses distribution shift using uncertainty-informed weights. Our empirical results demonstrate SPaCQL enables more effective policy learning, and manifest its remarkable superiority over baseline algorithms when the offline dataset exhibits the independence structure.

Technical
GeoNum: Bridging Numerical Continuity and Language Semantics via Geometric Embedding

Shengkai Jin, Tianyu Chen, Chonghan Gao, Jun Han

Expand abstract

Large language models excel at semantic reasoning yet struggle with numerical tasks because tokenization disrupts geometric continuity. Traditional methods fragment numerically close values into inconsistent token sequences, severing the correspondence between numerical proximity and representational similarity, which is essential for numerical cognition. We introduce GeoNum, a geometrically coherent numerical embedding based on polar coordinate decomposition. By encoding integer magnitudes through classification and fractional components via trigonometric regression, GeoNum constructs a continuous manifold where numerical distance is preserved geometrically. A three-stage framework progressively integrates GeoNum into pretrained language models via self-supervised pretraining, projection alignment, and efficient adaptation. Experimental results across diverse arithmetic benchmarks demonstrate consistent gains in high-precision accuracy and improved interpolation and extrapolation, underscoring the promising benefits of geometric continuity for numerical modeling in large language models.

Technical
Beyond Adapter Retrieval: Latent Geometry-Preserving Composition via Sparse Task Projection

Pengfei Jin, Peng Shu, Sifan Song, Sekeun Kim, Qing Xiao, Cheng Chen, Tianming Liu, Xiang Li, Quanzheng Li

Expand abstract

Recent advances in parameter-efficient transfer learning have demonstrated the utility of composing LoRA adapters from libraries of pretrained modules. However, most existing approaches rely on simple retrieval heuristics or uniform averaging, which overlook the latent structure of task relationships in representation space. We propose a new framework for adapter reuse that moves beyond retrieval, formulating adapter composition as a geometry-aware sparse reconstruction problem. Specifically, we represent each task by a latent prototype vector derived from the base model’s encoder and aim to approximate the target task prototype as a sparse linear combination of retrieved reference prototypes, under an L1-regularized optimization objective. The resulting combination weights are then used to blend the corresponding LoRA adapters, yielding a composite adapter tailored to the target task. This formulation not only preserves the local geometric structure of the task representation manifold, but also promotes interpretability and efficient reuse by selecting a minimal set of relevant adapters. We demonstrate the effectiveness of our approach across multiple domains—including medical image segmentation, medical report generation and image synthesis. Our results highlight the benefit of coupling retrieval with latent geometry-aware optimization for improved zero-shot generalization.

Technical
Addressing Polarization and Unfairness in Performative Prediction

Kun Jin, Tian Xie, Yang Liu, Xueru Zhang

Expand abstract

In many real-world applications of machine learning—such as recommendations, hiring, and lending—deployed models influence the data they are trained on, leading to feedback loops between predictions and data distribution. The performative prediction (PP) framework captures this phenomenon by modeling the data distribution as a function of the deployed model. While prior work has focused on finding performative stable (PS) solutions for robustness, their societal impacts, particularly regarding fairness, remain underexplored. We show that PS solutions can lead to severe polarization and prediction performance disparities, and that conventional fairness interventions in previous works often fail under model-dependent distribution shifts due to failing the PS criteria. To address these challenges in PP, we introduce novel fairness mechanisms that provably ensure both stability and fairness, validated by theoretical analysis and empirical results.

Technical
Revisiting Differentiable Structure Learning: Inconsistency of L1 Penalty and Beyond

Kaifeng Jin, Ignavier Ng, Kun Zhang, Biwei Huang

Expand abstract

Recent advances in differentiable structure learning have framed the combinatorial problem of learning directed acyclic graphs as a continuous optimization problem. Various aspects, including data standardization, have been studied to identify factors that influence the empirical performance of these methods. In this work, we investigate critical limitations in differentiable structure learning methods, focusing on settings where the true structure can be identified up to Markov equivalence classes, particularly in the linear Gaussian case. While recent work highlighted potential non-convexity issues in this setting, we demonstrate and explain why the use of L1-penalized likelihood in such cases is fundamentally inconsistent, even if the global optimum of the optimization problem can be found. To resolve this limitation, we develop a hybrid differentiable structure learning method based on L0-penalized likelihood with hard acyclicity constraint, where the L0 penalty can be approximated by different techniques including Gumbel-Softmax. Specifically, we first estimate the underlying moral graph, and use it to restrict the search space of the optimization problem, which helps alleviate the non-convexity issue. Experimental results show that the proposed method enhances empirical performance both before and after data standardization, providing a more reliable path for future advancements in differentiable structure learning, especially for learning Markov equivalence classes.

Technical