Discontinuous Gating

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5 papers in the last four weeks, up 67% on the four weeks before. 0.1% of all new papers.

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Latest papers 36

Sep 28, 2026cs.CL

MS-GLA: Multi-Scale Gated Linear Attention for Addressing Representational Bottlenecks via Multi-Temporal Resolution

Gated Linear Attention (GLA) Transformers advance linear recurrent models through data-dependent gating, but face a core limitation: the fixed-capacity memory matrices across all heads operate at a single temporal resolution, where each token is processed individually, forcing them to simultaneously encode local syntactic patterns and long-range semantic structure, creating a representational bottleneck that gating alone is insufficient to resolve. We introduce Multi-Scale Gated Linear Attention (MS-GLA), which addresses this by distributing attention heads across multiple temporal resolutions. Coarser resolutions pool longer token spans naturally specializing toward long-range dependencies, while finer head groups retain sensitivity to local syntactic structure. A learnable, input-dependent fusion layer dynamically recombines head group outputs at each timestep, expanding effective memory capacity without increasing per-head state size. This multi-resolution decomposition draws on principles from Multi-Scale State-Space Models (MS-SSM), adapting them to the gated linear attention setting. We evaluate MS-GLA on language modeling, recall-intensive tasks, and long-context generalization. Across all settings, MS-GLA consistently achieves higher accuracy and lower perplexity than GLA at matched parameter counts, with up to 18.9% improvement on recall-intensive tasks and 9.5% lower average perplexity on language modeling benchmarks, validating multi-temporal resolution decomposition as a principled and effective extension of Gated Linear Attention.

Prasoon Dev, Anirudh Sankar, Vasudeva Varma

Language Technologies Research Center International Institute of Information Technology Hyderabad Hyderabad, Telangana, India

Linear Attention Multi-Scale Attention Discontinuous Gating Recurrent Model Bottlenecks

Sep 27, 2026cs.LG

Task-Aware Discretization of Differentiable Logic Gate Networks

Differentiable logic gate networks (DLGNs) enable gradient-based training of highly efficient Boolean networks by relaxing discrete logic gates during training and discretizing them for inference. Standard approaches make this discretization decision locally, typically through argmax selection and confidence- or entropy-based convergence criteria. We show that local discretization can be task-suboptimal even for globally optimal relaxed solutions, with high gate confidence providing no general guarantee, and derive bounds relating task-aware gate selection to tractable interventions in the relaxed network. Motivated by these results, we study first-order downstream task information for progressive discretization and characterize when this local approximation is reliable. Experiments on convolutional DLGNs reveal a strong locality dependence: first-order scores become unreliable when directly optimized over nonlocal interventions, but accurately assess local argmax decisions for progressive freezing.

Thore Gerlach

Independent Researcher

Differentiable Logic Gate Networks Differentiable Optimization Discontinuous Gating Discretization

Sep 24, 2026cs.SD

On a Separate Note: Robust Score-Informed Note Separation with a Two-Stream TFC-TDF U-Net and Adaptive Set Ownership

Score-informed note separation seeks to extract the performed waveform of all individual notes, often from a polyphonic recording. Existing deep learning systems generally only target instrument-level stems. We present, to our knowledge, the first deep learning approach to score-informed note separation, NoteSep. NoteSep extracts the queried notes by applying an extraction stage model, NoteGrab, once per note. Conditioned on pitch, onset, and offset, NoteGrab separates harmonic and percussive components in two U-Nets linked by bidirectional cross-attention; selective harmonic gating suppresses lower-octave interference while preserving percussive attacks. Finally, a joint separation stage applies Adaptive Set Ownership (ASO) to compare concurrent NoteGrab estimates and reallocate mixture energy. We curate SCNS-Train (25,729 mixtures and 743,920 targets) for training and SCNS-Eval (16 instruments, disjoint scores and libraries) for evaluation. On SCNS-Eval, NoteSep reaches a median SI-SDR of 7.39~~dB, compared with 2.49~~dB for our strongest baseline. See the demo page at https://benschou.com/notesep.

Benjamin Shiue-Hal Chou, Purvish Jajal, Nicholas John Eliopoulos +5

Purdue University · Loyola University Chicago · University of Michigan

Speech Separation Separation Notes U-Net Discontinuous Gating

Sep 15, 2026cs.LG

On the Importance of Gating: Memorization vs. In-Context Learning in State Space Models

State Space Models (SSMs) have emerged as a compelling alternative to Transformers, enabling sequence modeling with constant memory and linear compute. Although SSMs exhibit reasonable performance and favorable computational characteristics, they continue to lag behind Transformers on tasks that require in-context learning and precise retrieval, slowing their adoption for large-scale language modeling. In this work, we demonstrate that both the success and failure of SSMs in these domains can be explained by studying the role of the gating mechanism, a prevalent component in modern recurrent networks. Specifically, we show through theory and experiments that this gating mechanism causes SSMs to first learn an in-weights "memorization" solution, while delaying, or even preventing, convergence to a correct in-context learning solution. Importantly, this happens even in cases where there are no fundamental limitations due to the architecture or its memory capacity. On the other hand, we find that gating is often beneficial for improving generalization to long sequence lengths. Our results illuminate the crucial role of the gating mechanism in shaping both the training dynamics and generalization of SSMs, and provide a basis for understanding and improving linear-time models.

William L. Tong, Aryo Lotfi, Emmanuel Abbe +6

Harvard University · Apple

State Space Models Sequence Modeling Discontinuous Gating In-Context Learning Recurrent Neural Networks Gating+1

Aug 31, 2026cs.LG

Liquid Gated Attention

Real-world time series often exhibit irregular sampling and extended temporal horizons, requiring models to capture continuous-time dynamics across arbitrary intervals without prohibitive scaling costs. Discrete-time methods collapse variable time intervals into static positional steps; solver-dependent continuous-time models preserve temporal structure but rely on sequential integration, precluding parallelization; and solver-free approximations avoid this cost yet none couples observed time intervals with input-driven state modulation. We propose Liquid Gated Attention (LGA), a solver-free parallel temporal operator. By parameterizing an input-driven gating mechanism with observed time intervals, LGA introduces a continuous-time inductive bias and formulates hidden state evolution as a fast-weight associative memory, enabling parallel computation across the temporal dimension. Using matrix associativity in non-causal encoding and a prefix scan in causal encoding, LGA attains linear temporal complexity in sequence length in both modes. A sequence-level normalization bounds cumulative temporal decay for stable long-horizon optimization. Building on LGA, we instantiate LFormer, a modular backbone for continuous-time representation learning. Across six tasks and sixteen datasets spanning up to 17,984 steps, LFormer demonstrates long-range dependency modeling, fine-grained state tracking, and trajectory reconstruction from sparse and noisy observations, while delivering competitive performance against state-of-the-art discrete-time and continuous-time baselines with linear scaling efficiency.

Yiheng Jiang, Yuanbo Xu, Yongjian Yang

Mobile Intelligent Computing Laboratory, College of Computer Science and Technology, Jilin University, China

Temporal Attention Discontinuous Gating

Aug 31, 2026q-bio.NC

"More Is Different'' in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs of Biological Neuronal Networks

Canonical neural circuit motifs are usually described functionally: divisive normalization rescales population activity by a pooled signal, and winner-take-all competition selects one pattern through recurrent excitation and shared inhibition. We represent them, and their compositions, algebraically as finite transformation systems and analyze the transition monoids generated by their input-conditioned updates, distinguishing structure already present in a generator from structure that appears only through composition, and, on a joint state space, structure inherited from one factor from structure that lives on a joint configuration. Individually aperiodic updates can generate non-aperiodic monoids. In the WTA, every frozen-drive generator collapses to fixed points, yet short input sequences create local cycles of winner-dependent inhibitory gating: globally dissipative dynamics with a reversible action. The strongest result arises in WTA-to-DN composition. The composed monoid then contains a genuinely composite local cycle in which normalization state and the winner's gating state change together, although every primitive generator is aperiodic. Holonomy analysis certifies this as a group component of the Krohn-Rhodes cascade rather than an incidental cycle, and finds most group-carrying image sets on joint configurations, whereas the uncoupled product has none. An exhaustive interface sweep shows that the composite cycle is a property of the coupling rather than of a chosen map. If motifs are building blocks of neural computation, composing them is a form of programming: one chooses primitives and interfaces so that the generated algebra has the intended repertoire. The transition monoid is that repertoire - what a primitive presents to any later construction. Recurrent circuits are compositional transformation systems; their algebra constrains what they can be programmed to compute.

Nima Dehghani

McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA · The NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI), Cambridge, Massachusetts, USAa)

Neural Circuits Neurons Finite Groups Recurrence Discontinuous Gating Emergence

Aug 12, 2026cs.CL

Hybrid Gated Attention

Gated attention is an effective approach to mitigate attention sinks and enhance the representational capacity of attention. To further extend its effectiveness-efficiency Pareto frontier, we propose a Hybrid Gated Attention (HyGA) framework that contains three types of gating strategies. Specifically, these gates leverage diverse information from multiple stages of attention, and collaboratively build element-wise/head-wise gating from multiple perspectives, capturing intra-head and cross-head information interactions. Through our hybrid gating components, HyGA could provide multi-source modulation signals, enabling more comprehensive control over information flow and improving the representational capacity of attention. We also introduce low-rank matrix decomposition and learnable attention sink to further enhance training efficiency and stability. In experiments, we evaluate HyGA on widely-used benchmarks based on different backbones. The experimental results show that our HyGA comprehensively improves both training loss and various downstream performances compared with Gated attention. HyGA has also been verified to achieve the best performance at different computation costs, with comprehensive model analyses for better understanding. The proposed HyGA sheds light on a more effective, efficient, and stable attention mechanism.

Zekun Zhou, Ruobing Xie, Lanrui Wang +1

Tencent Hunyuan · Peking University

Discontinuous Gating Representational Capacity

Aug 8, 2026cs.CV

Advantage-Guided Gate: Reshaping Open-Ended Reasoning for Vision-Based Spatial Intelligence

Multimodal large language models (MLLMs) have demonstrated significant potential in complex spatial scene understanding and reasoning tasks. However, their open-ended reasoning process is prone to decision errors and error accumulation, leading to instability in answer quality. To address this, we propose an advantage-guided gating framework that dynamically intervenes in and corrects deviations during the reasoning process. Specifically, we model step-by-step reasoning as a finite-horizon decision process and introduce Monte Carlo value evaluation on the reasoning tree to provide intermediate supervision signals. The framework includes Step-Advantage Gate and Trajectory-Advantage Gate, which dynamically select high-value reasoning steps and high-quality complete reasoning trajectories, respectively. During training, we perform supervised learning for the gates using reasoning trees generated via multi-branch sampling, and combine shared-parameter initialization with task-specific heads to achieve cross-task robustness and diversity. During inference, the model greedily selects high-value prefix reasoning steps while choosing the optimal reasoning head based on the problem type, thereby significantly improving the accuracy of the final answer. Furthermore, we constructed the Reasoning-Tree-160k dataset and performed two-stage learning on it. Extensive experiments demonstrate that this advantage-guided gating framework effectively enhances the performance of benchmark MLLMs in visual-based spatial understanding and reasoning tasks. The code is open to the public for research: https://github.com/LingLin-ll/Advantage-Guided-Gate.

Ling Lin, Yang Bai, Congcong Zhu +6

School of Artificial Intelligence and Data Science, University of Science and Technology of China, Hefei 230000, China · Suzhou Institute for Advanced Research, USTC, Suzhou 215123, China · Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR), Singapore +4

Spatial Reasoning Multimodal Large Language Models Recent Vision-Language Models Discontinuous Gating Intelligence

Aug 7, 2026cs.LG

Hidden Gauge Controls Feature Specialization in ReLU Networks

Training changes a network's predictions while allocating task-relevant structure across its internal units. In an overparameterized ReLU network, several neurons can begin with exactly the same functional role, yet one may acquire a teacher feature while the others become redundant. We call the identity of that neuron feature ownership and ask whether it can be controlled by a parameter choice invisible to the initial predictor. In a tractable Gaussian teacher--student model, we fix the complete initial function and vary only a positive-homogeneous scaling gauge. Opposite gauges produce distinct feature trajectories and a sharp

Θ(D^2)

separation in specialization time that no global change of clock can explain. Among any fixed number of initially duplicate students, assigning the favorable gauge to one neuron deterministically selects it as the owner and drives the remaining functional contribution to zero. An exact reaction--transport decomposition attributes the effect to different mobilities for changing a feature's coefficient and direction. We prove global selection and functional pruning, extend finite-time selection to visible perturbations and small-step full-batch gradient descent, and verify the predicted loss, alignment, pruning, and dissipation trajectories in population and finite-sample training. The initial predictor therefore determines neither when the feature is learned nor which neuron learns it.

Tongxi Wang

School of Future Technology Southeast University Nanjing, China

Feature Learning Rectified Linear Unit Networks Sparse Structural Specialization Discontinuous Gating Latent Transport

Jul 31, 2026cs.LG

Gated Q-learning: Add Off-Policy Bias to Taste

Multistep credit assignment is critical for sample-efficient reinforcement learning, yet managing off-policy bias in Q-learning remains a fundamental challenge. For 30 years, practitioners have been limited to a binary choice: eliminate the bias at the cost of severely truncated eligibility traces (Watkins' Q(

λ

)), or ignore the bias to learn faster while injecting detrimental errors into the value estimates (Peng's Q(

λ

)). Modern off-policy estimators fail to resolve this tension, as importance-sampling ratios collapse under Q-learning's greedy target policy. We introduce Gated Q-learning, a novel algorithmic framework that ends this dilemma by smoothly interpolating between the two historical extremes. Rather than relying on importance sampling, our approach employs a continuous, state-action-dependent gating mechanism to selectively attenuate eligibility traces in an exploration-aware manner. We provide a rigorous theoretical foundation for this mechanism, proving that the expected operator remains a contraction mapping and deriving its exact fixed point. Empirical evaluations verify that intermediate gating safely enables longer credit-assignment horizons, yielding faster initial learning than either extreme. Gated Q-learning offers a simple alternative to importance sampling while enabling customization of the effective multistep horizon and the amount of off-policy bias in Q-learning agents.

Brett Daley

Meta

Q-Learning Off-Policy Learning Credit Assignment Discontinuous Gating

Jul 29, 2026cs.CV

TPCD: Tone-Pressure Contrastive Decoding and the Label-Free Gating Bottleneck in Vision-Language Models

High-pressure prompts can push vision-language models (VLMs) into unsupported commitments, such as reading illegible text, reporting indeterminate times, or affirming absent objects. This paper asks whether the pressure-induced distribution itself can serve as a contrastive-decoding negative branch. Tone-pressure contrastive decoding (TPCD) subtracts logits produced under a high-pressure instruction from logits produced under a safe neutral instruction. On the 800-example tone-matters benchmark, LLaVA-1.5-7B under pressure reaches 66.75% attack success rate (ASR); safe neutralization reduces ASR to 9.88%; full TPCD reaches 0.50% but collapses positives to 15.56%. A benchmark-specific task-prior/disagreement gate preserves measured positive accuracy (54.44%) while lowering ASR to 1.63% on LLaVA. Treating this LLaVA analysis as the design split, full

n=800

negative and

n=780

matched-positive held-out runs on GLM-4.6V and Llama-3.2-Vision show that simple gates can improve over safe neutralization, with sensitivity analyses bounding the weak time-positive subtask. A category-prior-free answer-disagreement router reduces held-out aggregate ASR to 6.93%, improving over both safe neutralization (10.98%) and branch disagreement (9.67%) while matching branch disagreement's 79.94% positive accuracy, although it remains post-hoc and surface-form based. We conclude that pressure is a useful probe of commitment bias and a viable mitigation signal, but the current gates are not yet independently validated grounding-aware detectors.

Jinkun Zhao, Kui Zhang, Wenjun Wu

Beihang University

Contrastive Decoding Discontinuous Gating

Jul 22, 2026cs.IR

Zero-Observation User Reactivation with Gap-Driven Dimensional Gating

Sequential recommendation (SR) models capture continuously observed behavior, but a returning user may have no interactions for months or years. We define this setting as Zero-Observation Reactivation: the user has a pre-gap history, while the platform observes no behavioral signals during a macro-gap Delta t. Under a chronologically aligned Gap-Synthesize Protocol on three Amazon datasets (Video Games, CDs & Vinyl, and Movies & TV), Hit@10 decreases monotonically across the evaluated gap buckets and reaches its lowest level beyond one year. The pattern appears across recurrent, unidirectional, and bidirectional SR backbones. We propose DeltaGate, a lightweight output-layer plugin that keeps the backbone frozen and routes each representation dimension between the personalized history and a learned, zero-initialized global prior. The gate is conditioned jointly on Delta t and the personalized representation. In a controlled diagnostic, we hold the personalized representation fixed and vary Delta t to isolate the trained gate's response to the gap input. In the >365d Video Games bucket, DG-SASRec reaches 0.047 Hit@10 versus 0.031 for SASRec, while DG-BERT4Rec reaches 0.046 versus 0.025 for BERT4Rec, with 66K trainable parameters (2--4% overhead). End-to-end retraining attains higher absolute accuracy but changes the backbone embeddings; the frozen plugin preserves zero backbone drift, uses about 40x fewer trainable parameters, and retains observable dimension-wise routing. The source code is available at https://github.com/jdding/DeltaGate.

Jiandong Ding, Tianying Liu, Fuyuan Liu +2

Fudan University Shanghai, China · Huawei Technologies Shanghai, China

Sequential Recommendation Discontinuous Gating Gated Deltanet

Jul 18, 2026cs.AI

Exact Network Surgery: Functional Invariance and Gradient Plasticity in Reactive Computational Graphs

Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program. We formalize Exact Network Surgery: the in-place insertion of a residual block into a live computational graph such that (i) the network function is preserved -- bit-exactly under explicit floating-point hypotheses -- and (ii) inserted parameters remain trainable immediately after insertion. We prove an identity-morphism theorem for gated residual blocks, a structural-locality theorem showing that a reactive invalidation engine recomputes exactly the downstream cone of the insertion point, leaving every other node's value and optimizer state untouched, and an escape-from-initialization proposition showing that the Gradient Shadowing gate alpha, initialized at zero over a randomly initialized branch, receives a generically non-zero gradient at insertion time. We identify a degenerate configuration -- zero-initialized output projections combined with a zero gate -- that is an exact saddle point gradient descent cannot escape. Every claim is validated on the reference implementation in NeuroDSL, a reactive graph engine in Julia: grafting is bit-exact on every logit tested (0 mismatches out of 1600); the gate escapes zero at the first optimizer step and unlocks branch gradients at the second, exactly as predicted; the degenerate configuration exhibits gradients identically zero for the entire 600-step run; surgery cost tracks downstream cone size with r = 0.9992 while graft-plus-invalidation bookkeeping is constant (about 0.75 ms) across insertion depths; and training resumes bit-identically across a real process restart. A flagged preliminary appendix reports first single-seed observations on post-insertion gate dynamics.

Abdallah Khemais

ISITCOM, University of Sousse

Discontinuous Gating Gradient Descent Graph Representations

Jul 16, 2026cs.LG

What Does Model Growth Really Add? Functional Capacity Beyond Parameter Count

Model growth adds parameters to a trained checkpoint and continues training, aiming to increase capacity while reusing the existing model instead of training from scratch. But does growing a trained model actually create new functional capacity that survives subsequent training? Parameter count alone cannot answer this question, and ``capacity'' is itself ambiguous; it can refer to parameter count, effective dimensionality, or the ability to represent new functions. We measure it directly, as the number of new, functionally independent directions a growth step adds, formalized as the rank increment of the model's functional Jacobian and estimated matrix-free at scale. For zero-gated function-preserving growth, this increment is exactly

K

under a transversality condition, i.e.

\operatorname{rank}(J_{\mathrm{grown}})=\operatorname{rank}(J_{\mathrm{old}})+K

. Continually training a Transformer grown from

253\mathrm{M}

to

857\mathrm{M}

parameters across three domains, we find these added directions persist, with all

K=36

remaining independent after continual learning, even when the model catastrophically forgets (perplexity

28\to481

) or we deliberately destroy the old function (

25.9\to127

). Geometric capacity and retained function are therefore decoupled. The functional capacity introduced by growth persists, while the previously learned function is not retained. A second, geometrically distinct mechanism, Net2Net, reaches the same

K

-dimensional capacity from directions that are dormant at initialization (

0 \to K

) and then retains it, so the decoupling is not specific to the zero-gate parameterization. The implication is precise. Catastrophic forgetting need not reflect a loss of functional capacity, and preserving dimensionality alone is insufficient to preserve the learned function.

Dante Lok

Votee AI · Beever AI

Catastrophic Forgetting Continual Learning Discontinuous Gating Jacobian Growth

Jul 10, 2026cs.LG

Fully Trainable Deep Differentiable Logic Gate Networks and Lookup Table Networks

We introduce a novel method for both partial and full optimization of the connections in deep differentiable logic gate networks (LGNs) and lookup table networks (LUTNs). Our training method utilizes a probability distribution over a set of connections per gate/lookup table (LUT) input pin, selecting the connection with highest merit, all whilst the optimal gate types or LUT-entries are learned in parallel. We show that the connection-optimized LGNs outperform standard fixed-connection LGNs on the Yin-Yang, MNIST Handwritten Digits and Fashion-MNIST benchmarks, while requiring only a fraction of the number of logic gates. We achieve 98.92% on the MNIST dataset with two layers of 8000 gates. With only one layer of 8000 gates, we obtain 98.45%, showing that our method requires almost 50 times fewer gates compared to fixed-connection LGNs. Training stability up to ten layers has been ensured by employing a high learning rate, straight-through estimators and trimming constant-output gate types. Additionally, we present a LUT neuron description that enables stable training with backpropagation, tested up to 6-layer deep networks. The model requires four times fewer trainable parameters and still achieves a higher accuracy compared to the fixed-connection LGN training algorithm. Our connection-training algorithm also works well for the LUTNs, achieving an accuracy of 98.88% for two layers of 2000 6-input LUTs.

Wout Mommen, Lars Keuninckx, Matthias Hartmann +2

imec, Kapeldreef 75, Leuven, 3001, , Belgium · Vrije Universiteit Brussel, Peinlaan 2, Elsene, 1050, , Belgium

Differentiable Logic Gate Networks Mnist Discontinuous Gating

Jul 4, 2026cs.LG

A Structural Interpretation of GELU and Threshold-Transmission Activations via the First-Order Loss Function

The Gaussian Error Linear Unit is usually motivated as the expected output of an input-dependent Bernoulli gate. This work gives an alternative interpretation: GELU is the expected output of a hard linear gate with a Gaussian random threshold. This view provides a generative interpretation for the Bernoulli gate: the gate opens once the input clears a latent Gaussian threshold. This interpretation stems from a decomposition based on well-known results in stochastic inventory theory and leads to a threshold-transmission family that includes ReLU, GELU, SiLU/Swish, and hard swish as special cases. By considering a latent uniform threshold, we recover a hard-swish-like piecewise-polynomial gate whose nonlinear transition is confined to a finite interval, yielding fixed- and learned-width variants. Controlled experiments on compact vision and language models show that calibrated or learned uniform-threshold gates are consistently competitive with GELU, ReLU, and SiLU/Swish, improve over them in most tested settings, and use the finite transition region nontrivially.

Roberto Rossi

Business School, University of Edinburgh, Edinburgh, UK

Discontinuous Gating Loss Function Gaussian Primitives Transmission Structured Context

Jul 3, 2026cs.LG

Rethinking Neural Nonlinearity as Gating

Activation functions are considered an essential primitive for neural nonlinearity, i.e., they enable neural networks to serve as universal approximators. In this paper, we show that this nonlinearity can also be achieved by input-conditioned threshold gating through branches as a universal primitive. We demonstrate that standard activations -- whether piecewise-linear (ReLU, PReLU, Hardtanh) or smooth (SiLU, Sigmoid, Tanh, GELU) -- are in fact instances of a single Threshold Gating (TG) primitive. For softmax, we show that it admits an exact TG conversion via its equivalent per-element Sigmoid form. We then validate these equivalences by converting pretrained networks across CNNs, transformer-based models, and recurrent architectures, preserving model performance without requiring retraining. Threshold Gating also enables training from scratch that goes beyond replacing existing activations, enabling gains in model compression, performance, and shorter training. We also propose a 'Minimal Branch Theorem' which relates the minimum number of required branches in our primitive to the trainability of general deep neural networks. In terms of hardware implementation, TG maps to a unified implementation in the case of analog in-memory systems, addressing the bottleneck of analog-to-digital and digital-to-analog converters (ADC/DAC) that is known to significantly impact power consumption and on-chip area.

Muhammad Sabih, Frank Hannig, Jürgen Teich

Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany

Activation Functions Discontinuous Gating Nonlinearity Decision Thresholds Analog

Jun 20, 2026cs.LG

Gated MLPs as Symmetry-Broken Rank-1 Bilinear Attention

We show that the conventional gated MLP can be viewed as a rank-1 approximation to a bilinear attention mechanism with two distinct factors corresponding to the query and the key. We further show that moving the nonlinearity onto one factor breaks the exchange symmetry between the two factors and, for non-homogeneous activations, the inverse-scaling symmetry as well. This perspective may help explain why gated MLPs are effective in practice and inform the design of future architectures.

Nathan Breslow

Discontinuous Gating Multilayer Perceptrons Activation Functions

Jun 15, 2026q-bio.NC

Learning Hybrid Biophysical Neuron Models with Neural ODEs

Biophysical neuron models link measurements of neural activity to underlying cellular mechanisms. Yet, a central challenge is that the kinetics of many ion channels are poorly characterized, and practical simplifications -- omitting channels or reducing morphological detail -- introduce systematic gaps between model and biology. Bridging these gaps requires approaches that can flexibly discover unmodeled dynamics while preserving mechanistic interpretability. Here, we introduce a hybrid modeling framework that embeds neural ordinary differential equations into conductance-based biophysical models to capture unknown currents or mis-specified channel kinetics. By parameterizing the neural ODE in terms of voltage-dependent steady-state and time-constant functions, we recover interpretable gating dynamics directly from voltage recordings without assuming a functional form. We show that the hybrid model fits the gating kinetics of 2400 ion channel models and recovers unknown gating dynamics from single current-clamp recordings, generalizing to out-of-distribution stimulus regimes under realistic inputs and parameter misspecification. We also use our method to reduce a multicompartment model of a cortical neuron into a single-compartment hybrid model with a learned axial current, yielding up to an order of magnitude lower computational cost. Together, our results establish a plug-and-play framework for selectively replacing unknown components of conductance-based models with neural ODEs while preserving their mechanistic structure.

Jonas Beck, Michael Deistler, Dóra Viktória Molnár +2

Hertie Institute for AI in Brain Health, Tübingen, Germany · Tübingen AI Center, University of Tübingen, Tübingen, Germany · Machine Learning in Science, Excellence Cluster Machine Learning, University of Tübingen, Tübingen, Germany +2

Neural Ordinary Differential Equations Neurons Discontinuous Gating Kinetics Voltage Channel Modeling

Jun 9, 2026cs.CL

Provenance-Grounded Gating and Adaptive Recovery in Synthetic Post-Training Data Curation

Synthetic post-training pipelines commonly filter generated samples with reward models or holistic LLM judges, yet two practices remain rarely examined together: whether the filtering signal is grounded in the source evidence that induced each generation, and whether rejected samples can be systematically recovered rather than permanently discarded. We present a controlled study of both questions across gate configurations, recovery strategies, and generator scales, using adversarially injected corpora to provide ground-truth failure labels. We find that exact source provenance improves faithfulness gating for stronger judges, that hallucination and reward gates reject largely disjoint sample populations making both necessary, and that an adaptive recovery pipeline combining failure diagnosis with targeted regeneration achieves higher yield, recovery rate, and injection recall than naive resampling. Downstream fine-tuning quality is driven primarily by generator scale, with filtration and recovery conditions contributing meaningfully but secondarily.

Soham Bhattacharjee, Karun Sharma, Vinay Kumar Sankarapu +1

Lexsi Labs

Post-Training Data-Curation Resampling Discontinuous Gating

Jun 5, 2026cs.RO

Lane Change Trajectory Planning for Personalized Driving Comfort and Mobility Efficiency

Lane changing entails simultaneous longitudinal and lateral motions that affect driving comfort and mobility efficiency. Because these motions are tightly coupled and subject to substantial inter-vehicle variability, trajectory planning for lane-change maneuvers is characterized by a highly personalized nature. This study proposes a neural network-driven planner that integrates a third-order polynomial trajectory generator with a learning module that infers optimal trajectory parameters across diverse driving conditions. Using a shared backbone with dual heads, one head ensures all-condition operational guarantees, while the other captures driver-specific preferences for comfort or mobility efficiency. A head-gated switching mechanism, realized through a statistical gate based on error-winner logistic regression, adaptively selects the appropriate head under varying driving conditions, which enables context-aware lane-change trajectory planning. Representative cases and Monte Carlo simulations show that the proposed planner achieves personalized comfort and mobility during lane changes, while the baseline ensures feasible trajectories under driving conditions where personalized data are insufficient or inaccessible.

Haoxuan Dong, Dongjun Li, Ziyou Song

Department of Mechanical Engineering National University of Singapore Singapore 117575, Singapore · Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, MI 48109, USA

Mobility Single Trajectory Dynamic Driving Scenes Discontinuous Gating Change

Jun 2, 2026q-bio.MN

BRIDGE: Biological Evidence Refinement and Heterogeneous Dynamic Gating for Gene Regulatory Networks

Motivation: Gene regulatory network inference from single-cell RNA sequencing (scRNA-seq) data is important for uncovering cell-state-specific transcriptional programs. However, scRNA-seq measurements are sparse and noisy, and experimentally validated TF-target interactions remain limited, making reliable inference challenging. Although graph neural networks have advanced GRN prediction, existing methods often rely on biologically unconstrained graph augmentation, such as random edge perturbation, and insufficiently control information transfer between genes and cells. These limitations may distort regulatory structures and weaken robustness under noisy and weakly supervised settings. Results: To address these issues, we propose an innovative framework named Biological Evidence Refinement and Heterogeneous Dynamic Gating for Gene Regulatory Networks (BRIDGE). BRIDGE extracts gene and cell representations from the expression matrix and its matrix dual, and performs contrastive learning in the gene space and cell space between self and neighbors across the co-expression-refined regulatory view and the original graph. It then applies heterogeneous gated encoding to adaptively regulate information transfer between genes and cells, enabling robust transcription factor-to-target gene prediction. Experiments on benchmark datasets spanning three network types and seven cell types show that BRIDGE achieves state-of-the-art AUROC and AUPRC in most settings. In particular, on Specific networks, BRIDGE improves average AUPRC by 5% over the second-best baseline, GCLink. In cross-cell-type few-shot transfer, BRIDGE consistently outperforms GCLink and GENELink across all six target cell types. A case study on hESC further supports the biological relevance of the predictions, with 9 of the top 10 and 46 of the top 100 novel TF-target interactions validated by ChIPBase.

Ziyang Dong, Shanwen Tan, Hengchuang Yin +5

College of Computer Science, Sichuan University, Chengdu, 610065, China · Xinjiang Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Urumqi, 830011, China · School of Mathematics, Sichuan University, Chengdu, 610065, China +2

Regulatory Networks Single-Cell Rna Discontinuous Gating Few-Shot Learning

May 28, 2026cs.LG

Composing Non-Conjugate Factor Graphs with Closed-Form Variational Inference

Stacking probabilistic building blocks into deeper architectures typically breaks closed-form inference. We show that closed-form inference can be preserved. We identify five factor-graph primitives: a bilinear factor, an exponential link, a Gamma prior, a Gaussian likelihood, and an equality node, and prove that any model composed from them admits closed-form variational message passing. The construction works because each primitive preserves a small set of message families: under mean-field factorization, messages on Gaussian variables remain Gaussian and messages on precision variables remain Gamma, while the only non-conjugate interface, the exponential link, remains tractable through the Gaussian moment-generating function and the sufficient statistics of the Gamma family. We demonstrate composition at increasing depth, from static ensembles through input-dependent gating to split-branch routing, and show that stacking routing layers encodes arbitrary decision trees, establishing universal function approximation with closed-form inference. Applied to ensemble time-series forecasting, the framework yields a Bayesian mixture of experts in which gating functions are inferred rather than learned, providing calibrated uncertainty over expert selection across five benchmark datasets.

Mykola Lukashchuk, Kyrylo Yemets, Wouter M. Kouw +4

Eindhoven University of Technology, the Netherlands · Lviv Polytechnic National University, Lviv, Ukraine · Lazy Dynamics, Utrecht, the Netherlands +1

Variational Inference Factor Graphs Probabilistic Model Discontinuous Gating Mean-Field Limit

May 25, 2026cs.LG

RotMoLE: Enhancing Mixture of Low-Rank Experts through Rotational Gating Mechanism

While Large Language Models (LLMs) are commonly fine-tuned to handle domain-specific tasks before being applied to vertical applications, adapting them to complex scenarios with diverse specialized knowledge remains challenging. Meanwhile, Mixture-of-Experts (MoE) architecture has risen as a crucial paradigm for training LLMs, and some recent works have also incorporated MoE into Parameter-Efficient Fine-Tuning (PEFT) to propose the Mixture of Low-rank Experts (MoE-LoRA), to enhance the power of low-rank adapters for learning complicated knowledge. However, conventional gating mechanisms in MoE typically apply only a scalar reweighing to selected experts, thereby limiting their underlying capacity of representation and generalization. Motivated and enabled by the low-rank structures in MoE-LoRA, we propose RotMoLE, a specialized MoE framework for low-rank experts featuring an additional rotation gate. Beyond simple scaling, RotMoLE implements a rotation mechanism for each selected expert, enabling superior expert exploitation and specialization for learning diverse data, especially when expert candidates are limited. Empirical results on complex multi-task and multilingual training scenarios validate our effectiveness.

Mengyang Sun, Maochuan Dou, Tao Feng +5

Tsinghua University · Beijing Information Science and Technology University · National University of Singapore +2

Mixture-Of-Experts Large Language Models Mixture-Of-Experts Experts Low-Rank Structure Mixtures Discontinuous Gating

May 13, 2026cs.LG

OSDN: Improving Delta Rule with Provable Online Preconditioning in Linear Attention

Linear attention and state-space models offer constant-memory alternatives to softmax attention, but often struggle with in-context associative recall. The Delta Rule mitigates this by writing each token via one step of online gradient descent. However, its step size relies on a single scalar gate that ignores the feature-wise curvature of the inner objective. We propose Online Scaled DeltaNet (OSDN), which augments the scalar gate with a diagonal preconditioner updated online via hypergradient feedback. Crucially, this right-preconditioning is algebraically equivalent to a per-feature scaling of the write-side key. This equivalence allows OSDN to strictly preserve the hardware-friendly chunkwise parallel pipeline of DeltaNet without incurring high-dimensional state overhead. Theoretically, by exploiting the exact-quadratic structure of the inner regression loss, we establish super-geometric convergence against a right-Newton comparator and prove an algorithm-aligned token-local residual contraction bound. To handle non-stationary contexts, we further introduce Adaptive Preconditioner Forgetting (APF) to dynamically refresh stale calibration. Empirically, OSDN demonstrates strong performance across scales. At the 340M-parameter scale, OSDN improves JRT-style in-context recall by 32% over DeltaNet. Scaling to 1.3B parameters, it achieves a 39% reduction in the recall residual ratio while maintaining parity on general downstream tasks (e.g., perplexity and LongBench) -- demonstrating that our online-preconditioning mechanism effectively transfers and amplifies at the billion-parameter scale.

Chenyu Zhou, Hongpei Li, Yuerou Liu +3

Shanghai Jiao Tong University · Northwestern University · Huazhong University of Science and Technology +1

Kimi Delta Attention Linear Attention Gated Deltanet Spectral Preconditioning Discontinuous Gating

May 11, 2026cs.LG

A Random-Matrix Criterion for Initializing Gated Recurrent Neural Networks

Proper weight initialization prior to training has historically been one of the key factors that helped kick off the deep learning revolution. Initialization is even more crucial in "reservoir computing", where the weights of a readout layer are learned linearly while the reservoir weights are fixed and largely determine the richness, stability and memory of the resulting dynamics. In the infinite-width limit it has been shown that meaningful initializations are those sitting at an effective critical point of the randomly initialized model. The phase transition is controlled by the weight variance

g^2

and separates an ordered phase from a chaotic one where information progressively degrades. Here we derive a simple criterion to estimate the critical

g_c

for a broad class of recurrent architectures and we show that it closely tracks the gain at which a gated-RNN reservoir achieves peak performance on a chaotic forecasting task. Finally, we argue that our criterion can serve as a design principle for future initialization schemes.

Tommaso Fioratti, Riccardo Marcaccioli, Francesco Casola

Capital Fund Management, 75007 Paris, France · Institute of Mathematics, EPFL, 1015 Lausanne, Switzerland

Recurrent Neural Networks Discontinuous Gating Infinities Neural Network Phase Transitions

May 9, 2026cs.LG

Fitting Multilinear Polynomials for Logic Gate Networks

We study learnable logic gate networks that stack layers of 2-input Boolean gates to build combinational circuits. Every 2-input gate has a unique multilinear polynomial with 4 coefficients, so the 16 Boolean gates form a codebook of prototypes in a 4-dimensional space, reducing training to a vector-quantization problem. The baseline method, Soft-Mix, learns a 16-dimensional softmax over gate identities, but the codebook has rank~4: 11 of 15 simplex directions carry nullspace gradient, and at uniform initialization the backward signal vanishes exactly. We prove that no affine product reparameterization fixes the resulting interaction-coefficient starvation under STE, and show that the covariance Jacobian of soft-VQ selection bypasses it by coupling the starved coefficient to the always-active constant channel. Working in the 4-dimensional polynomial space reduces each neuron from 16 to 4 parameters. On seven datasets, at least one 4-parameter method matches or exceeds Soft-Mix on every dataset; the CovJac advantage over STE grows monotonically with interaction demand across all seven datasets. At depth, Soft-Mix collapses (

-37.3

pp on CIFAR-10 at 12 layers) while CovJac holds (

-0.5

pp on CIFAR-10, stable on MNIST).

Youngsung Kim

Department of AI; and Department of ECE, Inha University

Differentiable Logic Gate Networks Polynomials Discontinuous Gating Gumbel-Softmax Relaxation

May 7, 2026cs.LG

Inductive Power Grid Cascading Failure Analysis with GRU-Gated Graph Attention

Identifying vulnerable transmission lines in power grids before a cascading failure occurs is challenging: existing methods can learn inter-line failure correlations from cascade data, but they are trained and evaluated on a single grid, and transferring the learned knowledge to an unseen grid remains an open problem. We address this by training a single Gated Recurrent Unit (GRU)-gated Graph Attention Network on combined cascading failure data from limited training grids and applying it directly to any unseen grid without retraining. A GRU gate controls what information each node retains or discards at each cascade iteration. Empirical evaluation shows that the model transfers zero-shot to multiple new grids spanning inter-time and inter-domain settings. Using information extracted from the trained model, we consistently identify more vulnerable lines than established structural and electrical baselines.

Tianxin Zhou, Xiang Li, Haibing Lu

Department of Computer Science & Engineering, Santa Clara University, Santa Clara, USA · Dept. of Information Systems & Analytics, Santa Clara University, Santa Clara, USA

Power Systems Interleaved Graph Attention Discontinuous Gating

May 5, 2026cs.CV

MILE: Mixture of Incremental LoRA Experts for Continual Semantic Segmentation across Domains and Modalities

Continual semantic segmentation requires models to adapt to new domains or modalities without sacrificing performance on previously learned tasks. Expert-based learning, in which task-specific modules specialize in different domains, has proven effective in mitigating forgetting. These methods include dynamic expansion, which suffers from scalability issues, or parameter isolation, which constrains the ability to learn new tasks. We introduce Mixture of Incremental LoRA Experts (MILE), a modular and parameter-efficient framework for continual segmentation across both domains and modalities. MILE leverages Low-Rank Adaptation (LoRA) to instantiate lightweight experts for each new task while keeping the pretrained base network frozen. Each expert is trained exclusively on its task data, thus avoids overwriting previously learned information. A prototype-guided gating mechanism dynamically selects the most appropriate expert at inference. MILE achieves the benefits of expert-based learning while overcoming its scalability limitations. It requires only a marginal parameter increase per task and tens of LoRA adapters are needed before matching the size of a single full model, making it highly efficient in both training and storage. Across domain- and modality-incremental benchmarks, MILE achieves strong performance while ensuring better stability, plasticity, and scalability.

Shishir Muralidhara, Didier Stricker, René Schuster

German Research Center for Artificial Intelligence (DFKI), Trippstadter Str. 122, 67663 Kaiserslautern, Germany · University of Kaiserslautern-Landau (RPTU), Gottlieb-Daimler-Str. 47, 67663 Kaiserslautern, Germany

Efficient Semantic Segmentation Semantic Segmentation Multimodal Benchmarks Mixtures Discontinuous Gating

Apr 19, 2026cs.CV

Where to Focus: Query-Modulated Multimodal Keyframe Selection for Long Video Understanding

Long video understanding remains a formidable challenge for Multimodal Large Language Models (MLLMs) due to the prohibitive computational cost of processing dense frame sequences. Prevailing solutions, which select a keyframe subset, typically rely on either a single visual-centric metric (e.g., CLIP similarity) or a static fusion of heuristic scores. This

one-size-fits-all'' paradigm frequently fails: visual-only metrics are ineffective for plot-driven narrative queries, while indiscriminately incorporating textual scores introduces severe

modal noise'' for purely visual tasks. To break this bottleneck, we propose Q-Gate, a plug-and-play and training-free framework that treats keyframe selection as a dynamic modality routing problem. We decouple the retrieval process into three lightweight expert streams: Visual Grounding for local details, Global Matching for scene semantics, and Contextual Alignment for subtitle-driven narratives. Crucially, Q-Gate introduces a Query-Modulated Gating Mechanism that leverages the in-context reasoning of an LLM to assess the query's intent and dynamically allocate attention weights across the experts. This mechanism intelligently activates necessary modalities while ``muting'' irrelevant ones, thereby maximizing the signal-to-noise ratio. Extensive experiments on LongVideoBench and Video-MME across multiple MLLM backbones demonstrate that Q-Gate substantially outperforms state-of-the-art baselines. By effectively suppressing modality-specific noise, it provides a robust, highly interpretable solution for scalable video reasoning.

Shaoguang Wang, Weiyu Guo, Ziyang Chen +2

Thrust of Artificial Intelligence, HKUST (Guangzhou) Guangzhou, China · Department of CSE, HKUST Hong Kong SAR, China

Video Understanding Keyframe Selection Multimodal Large Language Models Modalities Discontinuous Gating Narratives

Apr 19, 2026cs.LG

Revisiting Auxiliary Losses for Conditional Depth Routing: An Empirical Study

Conditional depth execution routes a subset of tokens through a lightweight cheap FFN while the remainder execute the standard full FFN at each controlled layer. The central difficulty is gate training: the gate decision must propagate through many layers before it influences the language modeling (LM) loss, so the resulting gradients are weak and noisy. Auxiliary losses are commonly stacked to stabilise training, yet the interactions among them -- particularly between a predictive auxiliary and explicit score supervision -- have not been systematically compared under controlled conditions. We evaluate two gate designs under a 157.5M-parameter decoder-only model with controller-only training, 50% full-path budget, and 3-seed runs on a fineweb-edu subset. The MLP gate (G1) maps the current hidden state to a utility score; the JEPA-guided gate (G3) adds an action-conditional predictor that forecasts, in a low-dimensional latent space, the outcome of executing full vs. cheap per token, aligned against a fixed target head. Under the standard recipe with oracle-style utility regression and pairwise rank supervision (util/rank), G3 improves early-to-mid optimisation over G1 in 3/3 seeds (lower avg LM, faster threshold hits, ~10.3x lower grad norms), with 20k-step endpoint LM within a 0.005 heuristic reference. A key finding (ablation A3): jointly removing util/rank improves best/avg LM and threshold-hit speed in 3/3 seeds for both gates, and the early-to-mid advantage of G3 over G1 disappears. We trace this to an off-policy oracle label that assumes all subsequent layers execute full, whereas gated execution routes only a fraction through full -- making util/rank net-negative under the current recipe. Removing util/rank also cuts the training FLOPs proxy from ~1.53x to ~1.07x full-only (2.87h to 1.75h on a V100-32GB, ~39%). Conclusions are scoped to the studied regime.

Qingwei Lin

Independent Researcher

Discontinuous Gating Empirical Study

Apr 16, 2026cs.LG

Gating Enables Curvature: A Geometric Expressivity Gap in Attention

Multiplicative gating is widely used in neural architectures and has recently been applied to attention layers to improve performance and training stability in large language models. Despite the success of gated attention, the mathematical implications of gated attention mechanisms remain poorly understood. We study attention through the geometry of its representations by modeling outputs as mean parameters of Gaussian distributions and analyzing the induced Fisher--Rao geometry. We show that ungated attention operator is restricted to intrinsically flat statistical manifolds due to its affine structure, while multiplicative gating enables non-flat geometries, including positively curved manifolds that are unattainable in the ungated setting. These results establish a geometric expressivity gap between ungated and gated attention. Empirically, we show that gated models exhibit higher representation curvature and improved performance on tasks requiring nonlinear decision boundaries whereas they provide no consistent advantage on tasks with linear decision boundaries. Furthermore, we identify a structured regime in which curvature accumulates under composition, yielding a systematic depth amplification effect.

Satwik Bathula, Anand A. Joshi

Department of Electrical and Computer Engineering University of Southern California

Discontinuous Gating Local Curvature Expressivity

Mar 13, 2026cs.RO

TacVLA: Contact-Aware Tactile Fusion for Robust Vision-Language-Action Manipulation

Vision-Language-Action (VLA) models have demonstrated significant advantages in robotic manipulation. However, their reliance on vision and language often leads to suboptimal performance in tasks involving visual occlusion, fine-grained manipulation, and physical contact. To address these challenges, we propose TacVLA, a fine-tuned VLA model by incorporating tactile modalities into the transformer-based policy to enhance fine-grained manipulation capabilities. Specifically, we introduce a contact-aware gating mechanism that selectively activates tactile tokens only when contact is detected, enabling adaptive multimodal fusion while avoiding irrelevant tactile interference. The fused visual, language, and tactile tokens are jointly processed within the transformer architecture to strengthen cross-modal grounding during contact-rich interaction. Extensive experiments on constraint-locked disassembly, in-box picking and robustness evaluations demonstrate that TacVLA outperforms baselines, %including existing VLA models and diffusion policies, improving the performance by averaging 20% success rate in disassembly and 60% in in-box picking, achieving a 2.1

\times

improvement under visual occlusion, and showing recovery behavior under human disturbance. Videos are available at https://sites.google.com/view/tacvla.

Kaidi Zhang, Heng Zhang, Zhengtong Xu +7

Edwardson School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA · Human-Robot Interfaces and Interaction Lab, Istituto Italiano di Tecnologia, Genova, Italy · Ph.D. program of national interest in Robotics and Intelligent Machines (DRIM) and Universit`a di Genova, Genoa, Italy

Diffusion-Based Vision-Language-Actions Tactile Diverse Occlusion-And-Revelation Scenarios Discontinuous Gating

Feb 5, 2026cs.CV

Geometric Observability Index: An Operator-Theoretic Framework for Per-Feature Sensitivity, Weak Observability, and Dynamic Effects in SE(3) Pose Estimation

We introduce the Geometric Observability Index (GOI), a per-feature sensitivity measure for pose estimation on SE(3). For a Gauss-Newton curvature matrix

H=E[J^\top WJ]

and a Riemannian metric

G

on the Lie algebra, the index is the

G

-norm of the influence a single measurement exerts on the estimated pose:

\mathrm{GOI}(z)=\|\mathcal{A}_{OO}^{-1}P_O\,\varphi(z)\|_G

, where

ψ(z)=J^\top Wr(z)

is the score,

\varphi=G^{-1}ψ

its gradient representative,

\mathcal{A}=G^{-1}H

the curvature operator (self-adjoint in the

G

-inner product),

O=\mathrm{range}(\mathcal{A})

the observable subspace, and

\mathcal{A}_{OO}

its restriction. This single object (i) equals the norm of the M-estimator influence function, (ii) is governed by the Fisher information, which coincides with the curvature, (iii) exposes weak observability through the smallest eigenvalue

λ_{\min}

, which (iv) also governs finite-sample stability. Operationally the theory cuts both ways. The index is the exact per-measurement attribution: it predicts the true leave-one-out pose shift with log-correlation

r=1.00

. But we also prove that the influence standardized by its inlier null covariance collapses exactly to the classical chi-square residual statistic: residual gating is the leverage-corrected influence test, explaining its robustness from first principles, while raw-influence gating conflates a measurement's information with its harm and over-rejects high-leverage inliers in weakly observable geometry. Experiments on synthetic problems, five TUM RGB-D dynamic sequences, and two KITTI odometry sequences confirm the picture: the two criteria coincide under well-conditioned geometry, and raw-influence gating degrades significantly at

\mathrm{cond}(H)\approx 10^4

, as the leverage analysis predicts for noise-dominated weak directions. All quantitative claims are validated; code is released.

Joe-Mei Feng, Sheng-Wei Yu, Hsin-Hsiung Kao

Department of Mathematics, Tamkang University, New Taipei, Taiwan · Department of Information Management, Central Police University, Taoyuan, Taiwan

Robust Geometric Model Estimation Partial Observability Discontinuous Gating

Jul 8, 2025cs.CL

A Systematic Analysis of Hybrid Linear Attention

Transformers face quadratic complexity and memory issues with long sequences, prompting the adoption of linear attention mechanisms using fixed-size hidden states. However, linear models often suffer from limited recall performance, leading to hybrid architectures that combine linear and full attention layers. Despite extensive hybrid architecture research, the choice of linear attention component has not been deeply explored. We systematically evaluate various linear attention models across generations - vector recurrences to advanced gating mechanisms - both standalone and hybridized. To enable this comprehensive analysis, we trained and open-sourced 72 models: 36 at 340M parameters (20B tokens) and 36 at 1.3B parameters (100B tokens), covering six linear attention variants across five hybridization ratios. Benchmarking on standard language modeling and recall tasks reveals that superior standalone linear models do not necessarily excel in hybrids. While language modeling remains stable across linear-to-full attention ratios, recall significantly improves with increased full attention layers, particularly below a 3:1 ratio. Our study highlights selective gating, hierarchical recurrence, and controlled forgetting as critical for effective hybrid models. We recommend architectures such as HGRN-2 or GatedDeltaNet with a linear-to-full ratio between 3:1 and 6:1 to achieve Transformer-level recall efficiently. Our models are open-sourced at https://huggingface.co/collections/m-a-p/hybrid-linear-attention-research-686c488a63d609d2f20e2b1e.

Dustin Wang, Rui-Jie Zhu, Steven Abreu +9

1UC Santa Cruz · 2ByteDance Seed · University of Groningen +3

Kimi Delta Attention Transformer Architectures Discontinuous Gating

May 16, 2025cs.LG

Regularity and Stability Properties of Selective SSMs with Discontinuous Gating

Selective State-Space Models (SSMs) such as Mamba have become central to long-sequence modeling. Still, their stability is poorly understood: their state-space coefficients are modulated online by a token-dependent gating signal, making the recurrence neither linear time-invariant nor classically nonlinear. We study continuous-time selective SSMs through passivity, dissipativity, and Input-to-State Stability (ISS), explicitly separating the selection signal

x(\cdot)

from the driving input

u(\cdot)

. We obtain four results: exponential forgetting under strict dissipativity; a canonical

\mathrm{AUC}_{\mathrm{loc}}

quadratic storage for the frozen-selection subsystem that accommodates discontinuous gating; a parametric LMI together with universal kernel constraints and "irreversible forgetting" under universal quadratic storage; and sufficient conditions for global ISS uniformly over admissible selection schedules. We then bridge to practice by deriving a sampled block LMI for the Mamba selective-scan core, which is used as a differentiable training-time regularizer. Across seven standard time-series datasets and four prediction horizons, the regularizer reduces sampled Mamba-core LMI violations by roughly

92\%

in

28/28

pairs at a clean-MSE cost of less than

0.018\%

. It improves internal Mamba passivity and state-norm diagnostics under injected perturbations. Our results turn classical control-theoretic tools into verifiable structural and training criteria for selective SSMs, while honestly scoping which guarantees transfer to a deep selective-scan architecture.

Nikola Zubić, Davide Scaramuzza

Robotics and Perception Group University of Zurich

State Space Models Discontinuous Gating Regularity Passive Unsupervised Detection