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General Machine Learning · Hardware and Software

Seungheon Lee, Jeongmin Sun, Jaeyong Chung

Differentiable logic gate networks map learned models directly to gate-level circuits, enabling ultra-low-latency inference, yet their logic footprint often exceeds FPGA capacity budgets. Tightly fitting a trained model to a target FPGA requires a post-training mechanism to trade off network complexity and accuracy—analogous to pruning in standard neural networks. To this end, we introduce *unit tying*: a simplification that forces selected gates to constants (0 or 1), enabling constant propagation and downstream logic elimination. However, we observe that naively extending pruning criteria to logic networks is unreliable under such near-discrete modifications. We therefore propose a two-stage algorithm for unit tying: (i) a fast Gauss–Newton screening step under a teacher-referenced logit-distortion objective that constructs a high-recall overshoot set and (ii) a refinement step that corrects approximation and interaction-driven errors using a small number of finite-difference evaluations. On CIFAR-10 and MNIST, our method consistently improves the accuracy–area trade-off over common saliency baselines, yielding substantial post-synthesis LUT reductions of up to 48% on CIFAR-10 and 43% on MNIST, with modest accuracy degradation.

General Machine Learning · Evaluation

Sang Truong, Yuheng Tu, Rylan Schaeffer, Sanmi Koyejo

Scaling laws provide a fundamental framework for understanding the performance of Large Language Models (LLMs), yet deriving them requires prohibitively expensive evaluations across thousands of checkpoints or millions of inference samples. To address this, we introduce Item Response Scaling Laws (IRSL), a unified framework that integrates Item Response Theory (IRT) within scaling law formulation. Unlike traditional approaches that treat each model-benchmark pair in isolation, IRSL disentangles latent model ability from question characteristics, factorizing the scaling law estimation for $M$ models and $N$ questions to significantly reduce parameter complexity from $O(M \times N)$ to $O(M + N)$. We propose Beta-IRT, a novel extension that leverages the empirical probability responses of LLMs, such as token probabilities in pre-training and pass rates in test-time sampling, to capture richer signals than binary responses. We validate our approach across two prevalent scaling paradigms: (1) pre-training downstream scaling, using 6,612 LLM checkpoints and 37,682 questions from 10 benchmarks; and (2) test-time scaling, using 12 LLMs and 120 questions from 4 benchmarks with up to 2,500 samples per question. In both cases, we demonstrate that IRSL yields more reliable scaling estimates under limited query budgets. Furthermore, we show that the estimated latent model abilities are generalizable, enabling accurate performance forecasting across benchmarks that share the same measurement objective.

General Machine Learning · Causality

Qianglin Wen, Xiangkun Wu, Chengchun Shi, Ting Li, Niansheng Tang, Yingying Zhang, Hongtu Zhu

Experimental design has emerged as a powerful approach for improving the sample efficiency of A/B testing, yet existing designs rely critically on correctly specified models. We study robust sequential experimental design under model misspecification and develop a unified framework that covers both contextual bandit and dynamic settings. Theoretically, we prove that our design bounds the worst-case mean squared error of the estimated treatment effect. Empirically, we demonstrate the effectiveness of the proposed approach using synthetic and real-world datasets from a leading technology company.

Deep Learning · Everything Else

Rim Assouel, Amir Bar, Michal Drozdzal, Adriana Romero-Soriano

Despite remarkable progress in Multimodal Large Language Models (MLLMs), these models still struggle with fine-grained understanding tasks. In this work, we propose **Procedurally Generated Tasks (PGT)** a simple data-driven framework that serves a dual purpose: inducing fine-grained visual understanding and acting as a low-cost diagnostic tool to identify the source of perception failures. By overlaying unambiguous geometric primitives on images, PGT generate additional dense supervision that disentangles visual grounding capability from semantic priors. Extensive experiments on relational, quantitative, and 3D/depth understanding benchmarks show that PGT yields remarkable gains across diverse architectures. Instruction tuning MLLMs on LLaVA-v1.5-Instruct augmented with PGT data results in improvements of up to +20\% on the What’sUp benchmark and +13.3\% on CV-Bench-2D, while maintaining general perception capabilities. Moreover, finetuning state-of-the-art MLLMs on PGT data leads to boosts of up to +5.5\% on What’sUp and +8.3\% on CV-Bench-2D. These findings demonstrate that PGT effectively address the bottleneck of fine-grained perception, revealing that many spatial reasoning deficits stem from inadequate supervision signals rather than inherent architectural or resolution limitations.

General Machine Learning · Scalable Algorithms

Shuo Ji, Jie Hu, Zhouqiao He, Zijie Zhao, Tianrui Li, Jie Xu

Computation overhead has emerged as a critical bottleneck in Federated Learning (FL). Coreset selection tackles this challenge by constructing an informative subset to represent the full dataset. However, existing approaches optimize coreset construction solely at the data level and enforce a uniform retention ratio across all clients, ignoring client heterogeneity and introducing detrimental fragmented clients. In this paper, we first introduce a *gradient projection Shapley value* (GPSV) to evaluate client contributions. GPSV captures both the directional and magnitude information of client updates and enables exact Shapley value calculation with $\mathcal{O}(1)$ per-coalition evaluation. Building on GPSV, we then propose ShapCCS, the first client-level coreset selection strategy for FL. ShapCCS prioritizes clients with high GPSV scores while excluding fragmented clients with negligible or even negative GPSV. As a client-level coreset selection strategy, ShapCCS can be integrated with a data-level selection approach, and additionally reduces communication costs, an advantage unattainable by data-level methods alone. Extensive experiments demonstrate the superiority of ShapCCS on model performance and robustness to noise. The code is available at https://anonymous.4open.science/r/ShapCCS-5CBB.

Deep Learning · Large Language Models

Jian Yao, Xiongcai Luo, Ran Cheng, KC Tan

Recent advances in Large Reasoning Models have significantly improved chain-of-thought (CoT) capabilities via reinforcement learning (RL). However, generated reasoning chains frequently suffer from structural redundancy (i.e., \emph{overthinking}), incurring high computational overhead without improving answer correctness. Existing mitigation strategies typically rely on token-uniform length penalties, which provide coarse, segment-agnostic pressure toward shorter outputs and can inadvertently suppress useful reasoning alongside redundancy. To address this, we demonstrate that inefficiency concentrates in high-probability segments with low marginal utility. We derive a theoretical characterization of segment suboptimality under the correctness-length trade-off objective and propose \textsc{SLAT} (Segment-Level Adaptive Trimming), an RL framework that selectively suppresses redundant segments based on this criterion. Empirical results on standard benchmarks indicate that \textsc{SLAT} establishes a superior accuracy-efficiency Pareto frontier, reducing reasoning length by 50\% relative to uncompressed baselines while maintaining competitive accuracy. Overall, our results suggest that theoretically grounded, segment-aware trimming is a promising direction for efficient CoT reasoning in large language models.

Optimization · Convex

Miria Feng, Mert Pilanci

Fine-tuning large language models (LLMs) to align with human preferences has driven the success of systems such as Gemini and ChatGPT. However, approaches like Reinforcement Learning from Human Feedback (RLHF) remain computationally expensive and complex. Direct Preference Optimization (DPO) offers a simpler alternative but has limitations such as inconsistent ranking accuracy, high dependence on expensive GPU resources, and sensitive hyperparameter tuning. We propose the Convex Optimization for Alignment and Preference Learning Algorithm (COALA): a novel lightweight strategy with strong theoretical guarantees. By leveraging the convex optimization reformulation of neural networks, COALA eliminates the need for a reference model and obtains significant reduction in both training time and VRAM consumption, thus enabling efficient training on a single GPU. Experiments across three datasets—including a 23,228-sample synthetic Educational Feedback dataset—and five models (including LLaMA-8B) demonstrate COALA's competitive performance and efficiency in utilizing as little as ${\approx}17.6$% of DPO's total TFLOPS. COALA exhibits stable, monotonically increasing rewards and reaches peak margins in significantly less time than traditional methods such as DPO and ORPO. To the best of our knowledge, this is the first time convex optimization has been effectively applied to preference fine-tuning of LLMs.

General Machine Learning · Causality

YiXin Ren, Chenghou Jin, Yewei Xia, Zichuan Lin, Deheng Ye, Hao Zhang, Jihong Guan, Shuigeng Zhou

Real-time estimation of average treatment effects (ATE) in streaming observational data poses two key challenges: strict memory constraints that preclude storing the full data history, and distributional shifts in both treatment assignment and outcome-generating process. Existing methods either require offline access to the entire dataset for covariate balancing or rely on parametric online models that are vulnerable to model misspecification under such shifts. This paper proposes a novel model-agnostic method for ATE estimation in streaming data, which effectively addresses the above challenges. Based on discrepancy theory, we first compress streaming data into feature coresets that preserve covariate balancing objectives over a rich nonparametric function class, enabling linear-time updates with bounded memory. Then, by directly learning balancing weights and bypassing parametric propensity score estimation, we enhance the model's robustness against the shift in treatment assignment, while by balancing over an expressive function space we make the model more adaptive to the shift in the outcome-generating process. Theoretically, we establish convergence guarantees with explicit bounds on memory usage and computational complexity. Empirically, extensive experiments on both synthetic and real-world datasets show the effectiveness and robustness of the proposed method, consistently outperforming existing techniques.

Optimization · Stochastic

Dimitris Oikonomou, Nicolas Loizou

Sharpness-Aware Minimization (SAM) has established itself as a powerful and widely adopted optimizer for training machine learning models. By explicitly minimizing the sharpness of the loss landscape, SAM often improves generalization while delivering strong empirical performance. However, SAM and its variants, like most training algorithms, are sensitive to the choice of learning rate, which is typically tuned by trial and error or via schedulers. In this work, motivated by recent advances on the effectiveness of stochastic Polyak step sizes for Stochastic Gradient Descent (SGD), we derive Polyak schedulers tailored to SAM-style updates, yielding novel adaptive algorithms in both deterministic and stochastic settings. In smooth setting, for the proposed methods, we prove linear convergence for strongly convex objectives and an $O(1/T)$ rate (up to a neighborhood in the stochastic setting) for convex objectives. Numerical experiments demonstrate that the proposed Polyak schedulers match or surpass tuned SAM baselines while substantially reducing the need for learning-rate tuning.

Deep Learning · Theory

Moritz Brösamle, Stephan Eckstein

Existing expressivity results for transformers typically rely on hardmax attention, high precision, and other architectural modifications that disconnect them from the models used in practice. We bridge this gap by analyzing standard transformer decoders with softmax attention and rounding of activations and attention weights, while allowing depth and width to grow logarithmically with the context length. As an intermediate step, we construct hardmax transformers with ternary activations and well-separated attention scores that simulate Turing machines using Chain-of-Thought (CoT). This lets us convert the constructions to equivalent softmax transformers without the unrealistic parameter magnitudes or activation precision that prior approaches would require. Using the same technique, we analyze a recently proposed summarized CoT paradigm (InftyThink) and show that it simulates Turing machines more efficiently, with model size scaling logarithmically in a space bound rather than a time bound. We empirically demonstrate this advantage by training small transformers to solve Sudokus almost perfectly with summarized CoT, even on instances requiring more than a million reasoning tokens.

Deep Learning · Large Language Models

Sanghyun Lee, Seungryong Kim, Jongho Park, Dongmin Park

Masked Diffusion Models (MDMs) as language models generate by iteratively unmasking tokens, yet their performance crucially depends on the inference-time order of unmasking. Conventional methods such as confidence-based sampling are short-sighted, focusing on local optimization which neglects test-time computation and allows early decoding errors to cascade. We propose Lookahead Unmasking (LookUM), which addresses these concerns by guiding sampling path with a verifier over alternative unmasking orders, without requiring an external reward model. Our framework couples (i) a path generator that proposes paths by sampling from pools of unmasking sets with (ii) a verifier that computes the uncertainty of the proposed paths and performs importance sampling to subsequently select the final paths. Erroneous unmasking inflates sequence-level uncertainty, and our method exploits this to avoid error-prone trajectories. We validate our framework across six benchmarks, such as mathematics, planning, and coding, and demonstrate consistent performance improvements. LookUM requires only two to three paths to achieve peak performance. LLaDA with LookUM matches the performance of RL-tuned LLaDA 1.5 and yields additional gains when applied to LLaDA 1.5, suggesting complementarity with reinforcement learning.

General Machine Learning · Methodology

Travis Pence, Daisuke Yamada, Vikas Singh

Tensor Product Representations provide the structural fidelity required for symbolic reasoning in models but suffer from *exponential* dimensionality growth when encoding deep recursive structures. Conversely, Vector Symbolic Architectures maintain *constant* dimensionality but sacrifice capacity and fidelity due to noisy compression via superposition. In this work, we propose **Orthogonal Subspace Carving (OSC)**, a memory architecture that binds *fillers* to *roles* by projecting onto the null space of the role basis before aggregating into a fixed order-$p$ tensor. OSC uses projections to enforce geometric orthogonality between bound structures within a {\em static} memory trace. We show that this mechanism decouples the tensor order from the structural depth, enabling deep recursive binding within a *constant* memory footprint. This construction allows for component vectors that are *orders of magnitude* smaller than the memory tensor, giving excellent memory efficiency in settings involving high superposition. We also show that TPR is a special case of binding in Clifford algebra, and give a Clifford formulation of OSC.

Deep Learning · Theory

Takashi Furuya, Davide Murari, Carola-Bibiane Schönlieb

Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for architectures that explicitly preserve Lipschitz continuity have yet to be established. In this work, we bridge this gap by introducing a class of gradient-descent-type in-context Transformers that are Lipschitz-continuous by construction. We realize both MLP and attention blocks as explicit Euler steps of negative gradient flows, ensuring inherent stability without sacrificing expressivity. We prove a universal approximation theorem for this class within a Lipschitz-constrained function space. Crucially, our analysis adopts a measure-theoretic formalism, interpreting Transformers as operators on probability measures, to yield approximation guarantees independent of token count. These results provide a rigorous theoretical foundation for the design of robust, Lipschitz continuous Transformer architectures.

Deep Learning · Large Language Models

Lanxiang Hu, Siqi Kou, Yichao Fu, Samyam Rajbhandari, Tajana Rosing, Yuxiong He, Zhijie Deng, Hao Zhang

Multi-token generation has emerged as a promising paradigm for accelerating language model inference, with the diffusion Large Language Models (dLLMs) as the most notable approach recently. Popular dLLMs like SDAR and Fast-dLLM v2 are post-trained on pre-trained AR models to minimize training cost while maintaining high performance. However, there exists a fundamental pretrain-to-posttrain mismatch -- the masked data distribution and bidirectional attention in post-training deviates significantly from the real data distribution and causal attention for pretraining. As a result, the post-trained dLLMs usually suffer from limited speedup or substantially degraded performance. To address this, we introduce Jacobi Forcing to bypass the dLLM formulation, directly post-training a causal multi-token predictor from an AR LLM. In particular, we force the model to learn to leap along its own parallel token generation trajectories based on Jacobi Decoding, and introduce an elaborate progressive distillation paradigm. The trained models achieve $3.8\times$ wall-clock speedup on coding and math benchmarks with minimal loss in performance. Based on the trajectory characteristics of the model, we further introduce multi-block decoding with rejection recycling, which enables up to $4.6\times$ higher token acceptance count per iteration and $4.0\times$ wall-clock speedup, effectively trading additional compute for lower inference latency.

Applications · Computer Vision

Haoyu Liu, Sucheng Ren, Tingyu Zhu, Peng Wang, Cihang Xie, Alan Yuille, Zeyu Zheng, Feng Wang

Rotary Position Embedding (RoPE) is the de facto positional encoding in large language models due to its ability to encode relative positions and support length extrapolation. When adapted to vision transformers, the standard axial formulation decomposes two-dimensional spatial positions into horizontal and vertical components, implicitly restricting positional encoding to axis-aligned directions. We identify this directional constraint as a fundamental limitation of the standard axial 2D RoPE, which hinders the modeling of oblique spatial relationships that naturally exist in natural images. To overcome this limitation, we propose Spiral RoPE, a simple yet effective extension that enables multi-directional positional encoding by partitioning embedding channels into multiple groups associated with uniformly distributed directions. Each group is rotated according to the projection of the patch position onto its corresponding direction, allowing spatial relationships to be encoded beyond the horizontal and vertical axes. Across a wide range of vision tasks including classification, segmentation, and generation, Spiral RoPE consistently improves performance. Qualitative analyzes of attention maps further show that Spiral RoPE exhibits more concentrated activations on semantically relevant objects and better respects local object boundaries, highlighting the importance of multi-directional positional encoding in vision transformers.

Deep Learning · Foundation Models

Sicheng Liu, Xunkai Li, Daohan Su, Ru Zhang, Hongchao Qin, Rong-Hua Li, Guoren Wang

Graph Foundation Models (GFMs) have achieved remarkable success in generalizing across diverse domains. However, they mainly focus on Text-Attributed Graphs (TAGs), leaving Multimodal-Attributed Graphs (MAGs) largely untapped. Developing Multimodal Graph Foundation Models (MGFMs) allows for leveraging the rich multimodal information in MAGs, and extends applicability to broader types of downstream tasks. While recent MGFMs integrate diverse modality information, our empirical investigation reveals two fundamental limitations of existing MGFMs: (1)they fail to explicitly model modality interaction, essential for capturing intricate cross-modal semantics beyond simple aggregation, and (2)they exhibit sub-optimal modality alignment, which is critical for bridging the significant semantic disparity between distinct modal spaces. To address these challenges, we propose PLANET (graPh topoLogy-aware modAlity iNteraction and alignmEnT), a novel framework employing a Divide-and-Conquer strategy to decouple modality interaction and alignment across distinct granularities. At the embedding granularity, (1)Embedding-wise Domain Gating (EDG) performs local semantic enrichment by adaptively infusing topology-aware cross-modal context, achieving modality interaction. At the node granularity, (2)Node-wise Discretization Retrieval (NDR) ensures global modality alignment by constructing a Discretized Semantic Representation Space (DSRS) to bridge modality gaps. Extensive experiments demonstrate that PLANET significantly outperforms state-of-the-art baselines across diverse graph-centric and multimodal generative tasks.

General Machine Learning · Causality

Luong Doan, Khanh Quoc, Duc Nguyen, Mai Hung, Phong Ho, Nhung Duong, Tuan Do

Classical sample complexity bounds for causal structure learning are minimax in nature, characterizing worst-case difficulty without distinguishing between easy and hard instances. We study instance-specific complexity for Markov equivalence class (MEC) recovery in linear Gaussian structural equation models. We introduce the Fisher dimension, defined as the inverse squared minimum partial correlation that must be detected to recover the MEC. We prove that the Fisher dimension governs sample complexity: it provides both a lower bound and an upper bound (tight up to logarithmic factors) for MEC recovery. A key theoretical finding is that under spectrally well-conditioned models, with bounded noise variances, bounded covariance eigenvalues, and constant-order edge coefficients, the Fisher dimension is uniformly bounded regardless of graph structure. Thus, significant instance-specific variation arises from parametric rather than structural features. Empirical validation shows strong correlation between our predictor and observed sample complexity for structured graph families.

Optimization · Everything Else

Michael Crawshaw, Chirag Modi, Mingrui Liu, Robert Gower

To define a steepest descent method over a neural network, we need to choose a norm for each layer, a way to aggregate these norms across layers, and whether to use normalization. We systematically explore different alternatives for aggregating norms across layers, both formalizing existing combinations of Adam and the recently proposed Muon as a type of non-Euclidean gradient descent, and deriving new variants of the Muon optimizer. Through a comprehensive experimental evaluation of the optimizers within our framework, we find that Muon is sensitive to the choice of learning rate, whereas a new variant we call MuonMax is significantly more robust. We then show how to combine any non-Euclidean gradient method with model based momentum (known as Momo). The new Momo variants of Muon are significantly more robust to hyperparameter tuning, and often achieve a better validation score. Thus for new tasks, where the optimal hyperparameters are not known, we advocate for using Momo in combination with MuonMax to save on costly hyperparameter tuning.

Applications · Health / Medicine

XinRui Chen, YIZHEN LUO, Siqi Fan, Zaiqing Nie

\textit{De novo} functional protein design aims to generate protein sequences that realize specified biochemical functions without relying on evolutionary templates, enabling broad applications in biotechnology and medicine. Existing approaches adopt either direct function-to-sequence mapping or decoupled structure-sequence generation strategies but often fail to achieve functionality and foldability simultaneously. To address this, we propose \textbf{CodeFP}, a \textbf{Co}-generative protein language model for \textit{\textbf{de} novo} \textbf{F}unctional \textbf{P}rotein design that simultaneously decodes sequence and structure tokens, thereby enabling superior simultaneous realization of functionality and foldability. CodeFP utilizes functional local structures to enrich functional semantic encodings, overcoming the suboptimal translation of flat encodings into structure tokens, while introducing auxiliary functional supervision to alleviate training ambiguity stemming from the one-to-many structure-to-token mapping. Extensive experiments show that CodeFP consistently achieves average improvements of 6.1\% in functional consistency and 3.2\% in foldability over the strongest baseline.

Probabilistic Methods · Gaussian Processes

Aurélien Pion, Emmanuel Vazquez

Bayesian optimization (BO) selects evaluation points for expensive black-box objectives using Gaussian process (GP) predictive distributions. Kernel choice and hyperparameter selection can lead to miscalibrated predictive distributions, which can distort the exploration--exploitation trade-off. In the minimization setting, sampling criteria such as expected improvement (EI) depend on the predictive lower tail and can therefore be sensitive to miscalibration. This article studies goal-oriented calibration of GP predictive distributions below a low threshold $t$ in the noiseless setting, complementing standard GP modeling with hyperparameters selected by maximum likelihood. A framework for predictive reliability below $t$ is introduced, based on two notions of spatial calibration: occurrence calibration over the design space and thresholded $\mu$-calibration on the sublevel set $\lbrace x\in\mathbb{X}, f(x)\le t \rbrace$. Building on this framework, we propose tcGP, a post-hoc method that calibrates GP predictive distributions below $t$, and we establish a convergence result for the resulting EI-based global optimization algorithm. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and global calibration GP models.