Natural gradient descent, and the preconditioned optimizers which have followed from it, correct gradient descent by estimating curvature and applying its inverse to the gradient. For any single layer of a deep neural network, this correction can be shown to approximately separate into two factors: one which accounts for correlations in the gradient signal, and one which accounts for correlations in the data arriving at that layer. Herein we show that this second factor can be expressed as a change of basis rather than of curvature and, considered thus, it can be removed from the optimizer entirely and placed within the network itself. Specifically, we show that, once forward weights are corrected, right-sided natural gradient descent can be implemented in a form which has three exactly equivalent forms: a gradient preconditioner, a decorrelating linear transform in the forward pass, or a set of recurrent dynamics in which all updates are Hebbian and rely only upon locally available signals. The (recurrent) decorrelation method we discover aligns closely with proposed methods for inhibitory learning and homeostatic plasticity in the brain. Notably, our transform requires no matrix inverse, no matrix decomposition, and no information beyond that which is available at an individual synapse. It can therefore be applied in distributed and physically constrained systems, including neuromorphic hardware and nervous systems, where existing preconditioners cannot. We demonstrate its effectiveness empirically in convolutional and residual network models while significantly improving a range of approximate biologically plausible methods for credit assignment.
Reinforcement learning with verifiable rewards (RLVR) typically improves pass@1 but can fall behind its base model at large sampling budgets $k$, commonly interpreted as sharpening existing solutions. Because adjacent pass@$k$ estimates reuse generations, pointwise error bars cannot establish a crossover. We formulate paired inference on the RL-minus-base difference curve: a prompt-level multiplier bootstrap yields a one-sided dominance test and simultaneous confidence bands requiring both an early gain and a later loss. Among nine public RLVR checkpoints at 3k-16k token limits, only one narrowly meets this criterion before multiplicity adjustment; asymmetric truncation can create, mask, or reverse crossovers. On 1,060 deduplicated competition problems at 32k tokens, two 1.5B models exhibit certified crossovers around $k\approx10$-$60$, while two 7B models show no supported loss. A paired variance decomposition shows why adding prompts improves power more than deeper sampling. Prompts with identical base success probability diverge after RLVR, with dispersion replicating across independent generation halves and violating Lipschitz slope bounds for reasonable deterministic maps. Modeling RLVR as a Markov kernel, Jensen's inequality shows that conditional dispersion depresses pass@$k$ for $k\ge2$. Once dispersion is modeled, the conditional-mean log-odds slope is below one in every pair: RLVR improves hard prompts on average, while late-$k$ loss comes from a 2%-3% minority of base-solved prompts collapsing onto a repeated modal wrong answer and resisting prefix rescue up to 4,096 tokens. In controlled runs from one base model on 3,000 new problems, all four GRPO arms fall behind near $k\approx200$ and remain behind through $k=4096$, while SFT stays significantly ahead throughout.
Under temporal nonstationarity, model performance rankings reverse across training horizons due to heterogeneous sensitivities to memory. While existing literature addresses adaptive lookbacks, effective model complexity, and empirical forecast evaluation in isolation, no unified framework explains the structural mechanics driving these rank reversals. We bridge this gap by deriving a model-agnostic decomposition of out-of-sample $R^2$ into target alignment, miscalibrated aggressiveness, and predictive instability. Within this framework, we mathematically characterize complexity phase boundaries, establish closed-form optimal-memory equations for ridge regression under local drift, and extend these guarantees to complex model architectures via surrogate bounds. We validate these theoretical dynamics by benchmarking 14 linear, tree-based, and neural architectures across large-scale financial panels. In doing so, our framework demonstrates that empirical model rank reversals are driven by predictable surges in miscalibrated aggressiveness, providing a rigorous mechanistic diagnosis of generalization under temporal shift.
Transolver has recently gained widespread adoption for solving diverse physical problems on unstructured geometric meshes by leveraging its Physics-Attention mechanism, which seamlessly extends standard softmax attention to handle physical domains at scale. For time-dependent problems, existing literature relies on time-conditioned or autoregressive rollouts to preserve temporal causality while retaining Physics-Attention as the spatial backbone. However, a fundamental limitation of this formulation is its sequential execution model, wherein computational costs scale linearly with the temporal horizon, rendering standard Transolver inefficient for transient problems despite its exceptional spatial efficacy. This bottleneck has historically hindered its broader application in time-dependent physical modeling. To address this limitation, we introduce TB-Transolver (also referred to as Temporally Bundled Transolver), an efficient framework built on temporal bundling that scales Transolver for time-dependent PDEs. Furthermore, we propose \emph{spatiotemporal coherence} (${\rm C(K)}$) as a general metric to systematically quantify snapshot correlation within a temporal bundle, enabling the \emph{a priori} selection of optimal bundle widths using training data alone, thereby avoiding expensive grid searches. We demonstrate the computational efficacy of TB-Transolver across four physically distinct domains, namely, plasticity, fluid dynamics, reaction-diffusion, and global weather forecasting; achieving training speedups of up to $29\times$ over conventional autoregressive and time-conditioned baselines. Finally, these computational gains are further amplified through distributed multi-node and multi-GPU parallelism, yielding aggregated speedups of up to $45.6\times$ at optimal bundle widths for systems exhibiting high spatiotemporal coherence compared to single-GPU implementations.
Speech Emotion Recognition (SER) in low-resource languages remains a challenging problem due to limited labeled data. In this work, we study the use of Whisper for Persian SER with a particular focus on representation dimensionality reduction and language-specific model adaptation. We propose a SER framework in which frame-level embeddings extracted from the Whisper encoder are reduced in dimensionality using PCA, eliminating the need for learned projection layers and substantially reducing the number of trainable parameters. The reduced representations are aggregated using an attention-based pooling mechanism and classified with a lightweight prediction head. In addition, we investigate whether fine-tuning Whisper on a Persian automatic speech recognition (ASR) task improves downstream SER performance. Experiments conducted on the ShEMO dataset under a speaker-independent evaluation protocol show that PCA-based dimensionality reduction consistently improves emotion recognition performance while reducing training latency and memory usage. ASR fine-tuning yields only modest gains for SER, suggesting limited transfer from language adaptation to emotion-related representations under the evaluated conditions. These findings provide practical insights into the efficient use of large pretrained speech models for emotion recognition in low-resource languages.
Alan Nadelsticher Ruvalcaba, Chris Alvin, Supratik Mukhopadhyay, Adam Bess
Identifying ligands for a protein target requires searching a vast chemical space for a comparatively small set of compatible molecules. Existing machine learning approaches primarily address this problem by generating candidate ligands or scoring individual protein-ligand pairs, but provide limited information about the broader chemical space compatible with a binding pocket. We introduce RangeFinder, an SE(3)-equivariant transformer pocket-level model, trained and evaluated on BioLiP2 data, that predicts ranges over nine physicochemical ligand properties directly from pocket structure, chemistry, and evolutionary context. Using an intersection-over-union objective and evaluation metric (range-IoU), RangeFinder achieves a range-IoU of $0.464 \pm 0.002$, outperforming all deployable baselines while requiring only $12.2$ ms per pocket. We also quantify our method's ability to reduce the ligand search space while retaining compatible binders; in this regard, RangeFinder achieves a Reduction-Recall F-Score of $0.543 \pm 0.011$ --- once again outperforming all deployable baselines. Ablation experiments indicate that RangeFinder's performance depends more strongly on the density and quality of ligand supervision than on any individual input modality or specialized training strategy. Together, these results position RangeFinder as an inexpensive and effective molecular filtering prior, with demonstrated potential in narrowing the ligand search space of target pockets before docking, generation, or synthesis. The code for this project can be found at: https://github.com/alannadels/RangeFinder.
Olivier Sprangers, Cristian Challu, Jan Rathfelder, Han Wang, Max Mergenthaler Canseco
Synthetic time series constitute a substantial share of the training corpora of several recent forecasting foundation models. Existing studies report benefits at small data budgets and modest synthetic proportions, but each evaluates individual combinations of model and generator. Studying these benefits systematically requires generators that support controlled configuration, perturbation, reproducibility and mechanism-level ablation, and the 11 existing generators we review show gaps in this combined support. We present SynForecast, an open-source Python library with 32 generators, 19 of which implement named mechanisms with a published source in econometrics, quantitative finance, statistical physics and point-process theory. Perturbations and mechanism families can be varied while everything else is held fixed, output comes in the long format that forecasting libraries accept, and output does not depend on the number of parallel workers. We evaluate SynForecast on M4 at five frequencies with a neural network and a gradient-boosted ensemble. A classical baseline attains the lowest error in nine of ten frequency-history combinations. A synthetic prior outperforms the same network trained from scratch at a fixed budget by up to 34% with a few dozen observations, but loses to it at full history at every frequency, and none of three pre-specified rescalings of history predicts where the sign changes. At the hourly frequency, where the prior fails at every history, the corpus lacks daily cycles; adding them reduces zero-shot error by 43 to 63% for both models. Fine-tuning outperforms training from scratch by up to about 15%, but at short histories a fixed 300-step fine-tune is worse than the pretrained model used as is. Removing the classical mechanism family costs about 2% for both models; every other family has a smaller effect outside the hourly frequency.
Asynchronous reinforcement learning (RL) is becoming a mainstream paradigm for post-training large language models (LLMs), as it improves training efficiency by updating the model as rollouts arrive. Recent work argues that group-wise sampling in GRPO does not naturally fit asynchronous RL training because rollout lengths follow a long-tailed distribution, and proposes Single-rollout Asynchronous Optimization (SAO) to improve stability and off-policy behavior, especially on agentic tasks. However, SAO relies on a closed-source value model obtained from scaling value pretraining. In this paper, we analyze GRPO and LiSAO, our lightweight reproduction of SAO without the pretrained value model, on single-turn reasoning and multi-turn agentic tasks. We find that GRPO outperforms LiSAO on reasoning tasks, while the reverse holds on agentic tasks. Since the value model of LiSAO is not yet well trained , LiSAO lags behind GRPO substantially in early training steps. To address this issue, we propose Li$^{2}$SAO, which Lifts Light Single-rollout Asynchronous Optimization with group-relative actor-critic bootstrapping: while the critic is cold, a group-relative advantage trains the actor and a group-centered return trains the critic, after which training switches to single-rollout GAE. Experiments show that Li$^{2}$SAO catches up with or surpasses GRPO in early training and further raises the later performance ceiling. Code is available at https://github.com/jd-cc-coder/Li2SAO.
Live financial forecasting must synchronize asynchronous bar completions across timeframes without using stale or unavailable information. We introduce HARN (Hierarchical Associative Resonance Network), an event-driven architecture that anchors each event to the finest configured timeframe and maintains persistent states and matrix-valued associative memories across temporal levels. Its timestamp-masked transition updates a level only when its completed-bar timestamp matches the current anchor, preserving inactive representations. HARN integrates causal multi-scale encoding, residual-driven gated associative writes, all-to-all cross-level resonance, and ordered bottom-up evidence aggregation to produce forecasts at each temporal level. Predictions are expressed as basis-point changes and reconstructed on the price scale for evaluation. We evaluate HARN on four assets spanning equities, foreign exchange, and gold (AAPL, EURUSD, USDCHF, and XAUUSD), using chronological 70/15/15 splits, 32-bar lookbacks, one-step horizons, and three random seeds. HARN obtains lower anchor-timeframe test mean absolute errors (MAEs) than the evaluated single-timeframe PatchTST and TimeXer baselines on all four assets. HARN's MAEs are 0.508, 0.000306, 0.000263, and 2.552, respectively; PatchTST records 2.074, 0.000759, 0.000638, and 9.563, while TimeXer records 2.882, 0.010838, 0.014144, and 15.297. These descriptive comparisons do not isolate architectural effects from differences in inputs, target formulations, or training procedures. Single-run component ablations on AAPL and EURUSD show small, non-monotonic differences. The results demonstrate HARN's feasibility for asynchronous multi-timeframe forecasting, while motivating controlled comparisons and broader ablations to establish its relative advantages and component contributions.
Muhammad Rajabinasab, Michael E. Houle, Oussama Chelly, Arthur Zimek
Many novel unsupervised feature selection methods are proposed each year, yet their empirical evaluation is limited to supervised and unsupervised evaluation metrics computed on selected datasets, along with comparisons to existing methods. However, in the absence of an established evaluation baseline, it is difficult to determine the value added to the existing literature by each of these methods, and how effective their underlying approaches are. In this evaluation study, we are using random feature selection as a baseline for evaluating unsupervised feature selection methods. While a random selection of features might seem to be a rather weak baseline, we show in this evaluation study that many of the state-of-the-art methods in unsupervised feature selection are outperformed by random feature selection in both performance and efficiency. Accordingly, we emphasize the strict requirement of considering random feature selection as a baseline in the development process of novel unsupervised feature selection methods, and we encourage the community to develop better evaluation measures for feature selection. Both would help to ensure consistent improvement and realistic assessment.
Softmax routing in mixture-of-experts models can concentrate probability on a subset of experts, suppressing access to the others. We study how this concentration forms, why it persists, and how suppressed probabilities recover. For fixed experts, a stationary-loss barrier identifies the face supporting the optimal routed output. In a common-target square-loss model with freely trainable expert outputs, slow adaptation tracks fixed-expert dynamics on finite horizons, while every fixed positive adaptation rate yields an interior routing limit. An exact normal-velocity decomposition separates complementary-expert covariance from relative gradient advantage. Under positive two-sided power bounds along recovery paths, uniform over initial masses, the resulting coefficient's order of vanishing gives logarithmic or power-law recovery times. Integrations of constructed fields reproduce these orders. An exact discrete log-odds identity relates neural updates to threshold crossing. In paired Transformer-MoE training, removing a class-conditional router-gradient contrast delays confirmed recovery and reduces accumulated log-odds on fixed tokens, both with and without capacity constraints.
Allowing for small fraction of errors in retrieved stored binary patterns, Hopfield-Hebbian neural network (NN) associative memory dynamics [14] achieves linearly scaled capacity. The famous proportionality constant $α_c\approx 0.14$ is obtained in a large dimensional scenario as the ratio of the number of reliably stored patterns $m$ and the patterns' length $n$ under the assumption that uniformly randomly chosen binary patterns are \emph{independent} among themselves. While such an idealized scenario is now well understood, more practical scenarios with correlated/noisy datasets remaining challenging even for classical statistical mechanics replica approaches. We consider precisely such practical settings where each \emph{archetype} pattern is replaced with $M$ correlated \emph{examples} with parameter $r$ governing the quality of correlation. We develop a powerful Random Duality Theory (RDT) based framework to analyze correlated data and already on the first level of RDT lifting obtain capacity characterizations that remarkably well match behavior exhibited through simulated dynamics. Moreover, characterizations explicitly feature correlation parameters $M$ and $r$, which allows to precisely determine their effects on phase-transitioning behavior of the underlying dynamics. Our results are also a well-fitting complement to the existing literature. Namely, to circumvent challenging statistical mechanics analyses, an alternative combination of spectral and replica methods is considered in [4]. We confirm that [4]'s elegant spectral characterizations are excellent approximations in the low correlated regime. At the same time, we also close the gap in the regimes with higher correlation levels where spectral methods deviate from the practical dynamics performance.
Zhenyu Wang, Molei Liu, Jing Lei, Francis Bach, Zijian Guo
When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery of transferable structures and help mitigate systematic biases such as batch effects. We introduce Stable Principal Component Analysis (StablePCA), a distributionally robust framework for constructing stable latent representations by maximizing the worst-case explained variance over multiple sources. A primary challenge in extending classical PCA to the multi-source setting lies in the nonconvex rank constraint, which renders the StablePCA formulation a nonconvex optimization problem. To overcome this challenge, we conduct a convex relaxation of StablePCA and develop an efficient Mirror-Prox algorithm to solve the relaxed problem, with global convergence guarantees. Since the relaxed problem generally differs from the original formulation, we further introduce a data-dependent certificate to assess how well the algorithm solves the original nonconvex problem and establish the condition under which the relaxation is tight. Finally, we explore alternative distributionally robust formulations of multi-source PCA based on different loss functions.
Anton Zamyatin, Patrick Indri, Sagar Malhotra, Thomas Gärtner
In resource-constrained and low-latency settings, uncertainty estimates must be efficiently obtained. Deep Ensembles provide robust epistemic uncertainty (EU) but require training multiple full-size models. BatchEnsemble aims to deliver ensemble-like EU at far lower parameter and memory cost by applying learned rank-1 perturbations to a shared base network. We show that BatchEnsemble not only underperforms Deep Ensembles but closely tracks a single model baseline in terms of accuracy, calibration and out-of-distribution (OOD) detection on CIFAR10/10C/SVHN. A controlled study on MNIST finds members are near-identical in function and parameter space, indicating limited capacity to realize distinct predictive modes. Thus, BatchEnsemble behaves more like a single model than a true ensemble.
Yannan Chen, Beichen Huang, Licheng Zhao, Chris Ding, Kaiming Shen
The normalized cut (NCut) problem is a fundamental one in the area of data clustering. Despite its fractional structure, the NCut problem is seldom considered from a fractional programming (FP) perspective in the existing literature. The main reason is that the conventional FP method is inadequate for this problem case: the classical Dinkelbach's transform can only handle a single ratio and hence is limited to the two-class clustering, whereas the multi-class clustering involves multiple ratio terms. This work proposes a novel so-called multidimensional quadratic transform that is capable of dealing with the multi-ratio case; it recasts the NCut problem into a bipartite matching problem---which can be immediately solved by linear search. Furthermore, we explore the connection between the proposed FP method and the minorization-maximization (MM) theory, and in turn characterize the convergence behavior of our algorithm. Finally, we conduct experiments to numerically demonstrate the advantages of the proposed FP-based algorithm in a variety of data clustering and image segmentation tasks.
Zehui Xiao, Yi Zheng, Guixing Fu, Wenkai Lu, Lingfei He, Tao Tan, Yue Liu, Silun Wang 等 10 位作者
Cross-subject generalization remains a major challenge for EEG-based emotion recognition due to pronounced inter-subject variability in neural activity and emotion-related spatiotemporal patterns. Existing methods mainly alleviate inter subject differences through distribution alignment or contrastive learning, while paying limited attention to representation bias associated with fixed spatiotemporal modeling orders. We hypothesize that high-level emotion representations of the same EEG signal should remain consistent across different spatiotemporal modeling paths. Based on this hypothesis, we propose a Dual-Path Spatiotemporal Contrastive Learning (DP-STCL) framework for cross-subject EEG emotion recognition. DP-STCL employs two complementary encoders with independent parameters, namely a Temporal-to-Spatial (TS) path and a Spatial to-Temporal (ST) path, to model EEG spatiotemporal information under different integration orders. During representation learning, the same emotional stimulus is used to establish cross subject associations, while three complementary relations jointly constrain representation variations across subjects and modeling paths. This promotes stable and discriminative stimulus-related emotion representations. To further handle limited labeled target subject data, we introduce a LoRA-based few-shot adaptation strategy with low parameter overhead. Extensive cross-subject experiments on SEED, SEED-IV, SEED-V, and FACED show that DP-STCL consistently outperforms the compared methods, demonstrating its effectiveness in improving cross-subject EEG emotion recognition.
Many real-world decision problems require allocating limited resources across individuals to maximize total benefit often through interventions that vary in intensity rather than binary treat-or-not decisions. In these settings, higher levels treatments require first applying lower levels of treatment, inducing a precedence constraint that complicates allocation under a fixed budget. While the causal inference literature has largely emphasized accurate estimation of conditional average treatment effects (CATE), recent work has shown that estimation accuracy alone does not guarantee effective resource allocation, motivating ranking-based evaluation frameworks. The Area Under the Targeting Operating Characteristic (AUTOC) provides an effective way to evaluate prioritization rules across budget levels, but existing formulations are limited to binary treatments. We introduce Multi-Level AUTOC (ML-AUTOC), which is a generalization for AUTOC designed for multi-level treatment settings with precedence. We also propose precedence-aware policies for mapping true marginal treatment effects to feasible treatment assignments under fixed budget constraints. Our results show that in the setting of multi-level treatments, maximizing realized treatment effects may require re-allocation of treatments across individuals.
Anas Barakat, John Lazarsfeld, Georgios Piliouras, Antonios Varvitsiotis
We study online learning in linear dynamical games where multiple strategic agents act on a shared state evolving according to a linear dynamical system subject to adversarial disturbances. This setting lies beyond both single-agent nonstochastic online control and classical linear-quadratic games, which typically focus on quadratic objectives and noiseless or stochastic dynamics. Each agent seeks to minimize its own sequence of convex losses under full-state observability. Following the stabilizing-baseline paradigm in nonstochastic online control, we assume access to linear controllers that stabilize the noiseless system and focus on online adaptation by learning disturbance-action corrections. This extends adversarial online control to strategic multi-agent shared-state systems, where each agent's actions shape the state trajectory and hence the realized losses of all learners. Under state-only and aggregate-input feedback models, we analyze agents running online gradient descent with memory to update their own disturbance-action policies. We prove per-agent regret bounds that are sublinear and near-optimal in the time horizon, with population dependence that varies under the specified feedback, opponent policy, and stability assumptions. In the common-interest case, where all agents have identical cost functions, we show that the induced online problem forms a time-varying potential game and derive equilibrium tracking guarantees. Together, our results provide a theoretical framework for adversarial online learning in stabilized linear dynamical games, connecting online control with learning in games.
Han Guo, Songlin Yang, Tarushii Goel, Eric P. Xing, Tri Dao, Yoon Kim
AI 速览：提出对数线性注意力，用对数增长的多隐藏状态替代固定大小隐藏状态，在保持矩阵乘法并行性的同时兼顾线性注意力效率与softmax注意力表达力。
The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space models enable linear-time, constant-memory sequence modeling and can moreover be trained efficiently through matmul-rich parallelization across sequence length. However, at their core these models are still RNNs, and thus their use of a fixed-size hidden state to model the context is a fundamental limitation. This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention. Log-linear attention replaces the fixed-size hidden state with a logarithmically growing set of hidden states. We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length. Log-linear attention is a general framework and can be applied on top of existing linear attention variants. As case studies, we instantiate log-linear variants of two recent architectures -- Mamba-2 and Gated DeltaNet -- and find they perform well compared to their linear-time variants.
Ali Behrouz, Meisam Razaviyayn, Peilin Zhong, Vahab Mirrokni
Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias-the natural tendency to prioritize certain events or stimuli-we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules that learn a mapping of keys and values using an internal objective, referred to as attentional bias. Surprisingly, we observed that most existing sequence models leverage either (1) dot-product similarity, or (2) L2 regression objectives as their attentional bias. Going beyond these objectives, we present a set of alternative attentional bias configurations along with their effective approximations to stabilize their training procedure. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization, providing a novel set of forget gates for sequence models. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on four choices of: (i) associative memory architecture, (ii) attentional bias objective, (iii) retention gate, and (iv) memory learning algorithm. We present three novel sequence models-Moneta, Yaad, and Memora-that go beyond the power of existing linear RNNs while maintaining a fast parallelizable training process. Our experiments show different design choices in Miras yield models with varying strengths. For example, certain instances of Miras achieve exceptional performance in special tasks such as language modeling, commonsense reasoning, and recall intensive tasks, even outperforming Transformers and other modern linear recurrent models.