ICML 2026 论文列表

Neural population geometry shapes downstream computation. Recent empirical findings in neurobiology suggest that a hyperbolic structure underlies population activity in the hippocampus. Here we provide a theoretical framework for this phenomenon. First, we propose a plausible construction of hippocampal tuning curves that statistically induces hyperbolic geometry. Next, we establish a connection between neural decoding and associative memory by demonstrating that the Modern Hopfield Network update rule computes the minimum mean-squared-error (MMSE) estimator. Finally, we introduce a novel associative memory model defined in hyperbolic space that yields significantly larger capacity than leading models. Our results suggest that animals encode spatial information as a latent hyperbolic cognitive map, improving both memory capacity and decoding accuracy.

Small language models (SLMs) are attractive for low-cost agent deployment, and their growing capabilities make them promising for procedure-centric workloads that repeatedly execute specialized task families with similar workflows. However, SLM agents still struggle in long-horizon interaction because limited context budgets make it difficult to reliably retain and reuse decision-relevant state across many steps. Existing working-memory methods attempt to mitigate context growth, but their reliance on unstructured natural-language summarization can discard critical facts, introduce state drift, and compound errors in SLM execution. We present LightWM, a training-free hierarchical working-memory framework that decomposes procedure-centric tasks into subgoals and organizes memory into task-level global memory and subtask-level local memory, where local memory directly conditions SLM action selection and is updated from new observations through structured updates. To instantiate such memories without training, a one-time offline LLM-based induction pipeline builds reusable schemas per task family from a few successful traces, requiring no SLM parameter updates or online LLM calls. On ALFWorld valid_unseen, Qwen3-4B reaches 0.910 success, whereas representative prompting and prior working-memory baselines under the same setting remain below 0.320.

Streaming video understanding (SVU) must answer queries that arrive asynchronously while visual tokens stream continuously under strict GPU-memory and query-time latency budgets. A key challenge is delayed query: decisive cues may appear briefly, yet many subsequent updates occur before the query arrives, increasing the risk that those cues are evicted or diluted under bounded memory. We propose ProtoKV, a constant-footprint SVU memory that represents far history as a fixed-capacity summary state rather than retaining token instances. ProtoKV keeps an exact near-window KV cache and aggregates older content into a semantic–spatial prototype bank with residual statistics. At query time, each prototype is exposed through a bounded pseudo-token interface that is drop-in compatible with standard attention. Under matched budgets and comparable query-time cost, ProtoKV improves accuracy by up to 12.5 points over token-retention baselines on SVU benchmarks in the long-delay regime, with gains that grow as query delay increases.

The state space duality (SSD) framework, central to modern state-space models (SSMs) such as Mamba, has established an efficient attention-like mechanism by leveraging the commutative property of linear recurrences. However, existing formulations are limited to single-input single-output (SISO) systems that enforce commutativity with a restrictive scalar-identity constraint, which prevents cross-dimensional interactions within the state dynamics. In this work, we generalize SSD to the multi-input multi-output (MIMO) setting by introducing a matrix polynomial parameterization. This approach not only provides a principled way to ensure commutativity for generalized duality but also induces a shared algebraic structure across state transitions, thereby significantly reducing parameter redundancy. Building on this foundation, we present \textbf{MIMOMamba}, a multi-head SSM architecture that captures rich cross-dimensional dynamics while retaining linear-time training. Empirical evaluations on a sequence modeling benchmark demonstrate that MIMOMamba achieves performance comparable to or surpassing that of standard Transformers while utilizing substantially fewer parameters.

Equivariant neural networks exploit underlying task symmetries to improve generalization, but strict equivariance constraints can induce more complex optimization dynamics that can hinder learning. Prior work addresses these limitations by relaxing strict equivariance during training, but typically relies on prespecified, explicit, or implicit target levels of relaxation for each network layer, which are task-dependent and costly to tune. We propose Recurrent Equivariant Constraint Modulation (RECM), a layer-wise constraint modulation mechanism that learns appropriate relaxation levels solely from the training signal and the symmetry properties of each layer's input-target distribution, without requiring any prior knowledge about the task-dependent target relaxation level. We demonstrate that under the proposed RECM update, the relaxation level of each layer provably converges to a value upper-bounded by its symmetry gap, namely the degree to which its input-target distribution deviates from exact symmetry. Consequently, layers processing symmetric distributions recover full equivariance, while those with approximate symmetries retain sufficient flexibility to learn non-symmetric solutions when warranted by the data. Empirically, RECM outperforms prior methods across diverse exact and approximate equivariant tasks, including the challenging molecular conformer generation on the GEOM-Drugs dataset.

Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data. Long-range information propagation is a key challenge while learning representations, wherein it is important to retain and update information over long temporal horizons. Existing approaches restrict models to capture one-hop or local temporal neighborhoods and fail to capture multi-hop or global structural patterns. To mitigate this, we derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs $\texttt{(CTDG-SSM)}$ from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator ($\texttt{CTT-HiPPO}$), a novel memory-based reformulation of $\texttt{HiPPO}$ to jointly encode temporal dynamics and graph structure. The solution from $\texttt{CTT-HiPPO}$ is obtained by projecting the classical HiPPO solution through a polynomial of the Laplacian matrix, yielding topology-aware memory updates that admit an equivalent state-space formulation for CTDGs ($\texttt{CTDG-SSM}$). Then a computationally efficient discrete formulation is obtained using the zero-order hold approach for model implementation. Across benchmarks on dynamic link prediction, dynamic node classification, and sequence classification, $\texttt{CTDG-SSM}$ achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.

WiFi-based human pose estimation offers privacy-preserving and occlusion-robust sensing, but current Transformer-based approaches suffer from quadratic complexity and lack explicit inductive biases for the structure of Channel State Information (CSI). We propose WiFi-Mamba, the first State Space Model (SSM) architecture for WiFi-based 3D multi-person pose estimation. Our approach introduces three key contributions: (1) a Dual-Stream Selective SSM that processes amplitude and phase through parallel pathways with cross-stream state coupling to respect their distinct physical properties, (2) Selective State Attention for pose query decoding with SSM-derived sequential context, and (3) Persistent SSM Memory for temporal consistency across frames without recurrent memory explosion. Extensive experiments on the Person-in-WiFi 3D dataset, covering both single-person and multi-person, demonstrate a 16-27% MPJPE reduction across varying numbers of persons while using only 4.4\% of the baseline parameters (2.14M vs. 48.2M), achieving superior efficiency-accuracy trade-offs particularly beneficial for edge deployment in privacy-sensitive continuous monitoring scenarios.

Visual Mamba models have recently emerged as alternatives to Vision Transformers (ViTs), which suffer from quadratic complexity. While the recurrent scanning mechanism of Mamba offers computational efficiency, it inherently limits non-causal interactions between image patches. Prior works have attempted to address this limitation through various multi-scan strategies; however, these approaches suffer from inefficiencies due to suboptimal scan designs and frequent data rearrangement. Moreover, Mamba exhibits relatively slow computational speed under short token lengths, commonly used in visual tasks. In pursuit of a truly efficient vision encoder, we rethink the scan operation for vision and the computational efficiency of Mamba. To this end, we propose SF-Mamba, a novel visual Mamba with two key proposals: auxiliary patch **swapping** for encoding bidirectional information flow under an unidirectional scan and batch **folding** with periodic state reset for advanced GPU parallelism. Extensive experiments on image classification, object detection, and instance and semantic segmentation consistently demonstrate that our proposed SF-Mamba significantly outperforms state-of-the-art baselines while improving throughput across different model sizes. The source code is available at: https://github.com/sony/SF-Mamba.

History-dependent sampling can reduce long-run Monte Carlo variance by discouraging redundant revisits, but existing schemes typically encode history through empirical measure on finite state spaces, which is infeasible in high-dimensional discrete configuration spaces or ill-posed in continuous domains. We propose *Score-Repellent Monte Carlo* (SRMC) framework that summarizes trajectory history by a running average of score evaluations in $\mathbb{R}^d$, where $d$ is the dimension of the score and state representation. This history is converted into a surrogate target through an exponential *score tilt*, indexed with $\alpha$ that represents the *strength of repellence* in controlling the magnitude of the history-based repulsion. The surrogate family is normalization-free in the standard MCMC sense, yielding a generic wrapper: at each iteration, any base kernel targeting $\pi$ can instead be run on the current surrogate $\pi_{\theta_n}$ while the history is updated online. We analyze the coupled evolution of the history recursion and Monte Carlo estimators using stochastic approximation with controlled Markovian noise, establishing almost sure convergence and a joint central limit theorem. We further identify regimes in which the asymptotic covariance decreases as $\alpha$ increases, with scaling $O(1/\alpha)$, extending the near-zero-variance effect of finite-state history-dependent samplers to general state spaces with constant memory. Experiments on continuous targets and discrete energy-based models demonstrate improved estimator variance and mode coverage, while retaining $O(d)$ memory usage and modest per-iteration overhead.

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

Linear attention reformulates sequence modeling as recurrent state evolution, enabling efficient linear-time inference. Under the key–value associative paradigm, existing approaches restrict the role of the query to the readout operation, decoupling it from state evolution. We show that query-conditioned state readout induces a structured value prediction over accumulated memory that complements key-based retrieval. Based on this insight, we propose Q-Delta, a query-aware delta rule that integrates mixed key--query prediction errors into state evolution, enabling jointly corrective dynamics while preserving delta-rule efficiency. We establish stability guarantees for the resulting dynamics and derive a hardware-efficient chunkwise-parallel formulation with a custom Triton implementation. Empirical results demonstrate stable optimization, competitive throughput, and consistent improvements over strong baselines on language modeling and long-context retrieval tasks. Code is available at \url{https://github.com/psmiz/Q-Delta}.

Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by the need to process temporal data sequentially and the prohibitive memory footprint of high-dimensional reservoirs. To address these limitations, we revisit RC through the lens of structured operators and state space modeling, introducing Parallel Echo State Network (ParalESN). Leveraging diagonal linear recurrence in the complex domain, ParalESN enables parallel processing of temporal data and the construction of efficient, high-dimensional reservoirs. A thorough theoretical analysis demonstrates that the Echo State Property and the universality guarantees of traditional Echo State Networks are preserved, while also admitting an equivalent representation of arbitrary linear reservoirs in the complex diagonal form. Empirically, ParalESN achieves competitive predictive accuracy with traditional RC and with fully trainable sequence models, while delivering computational savings by orders of magnitude. Overall, ParalESN offers a scalable and principled pathway for integrating RC within the deep learning landscape.

State-space language models such as Mamba match Transformer quality while permitting linear complexity inference, yet still comprise billions of parameters that hinder deployment. While existing one-shot pruning methods are effective for generic linear and attention blocks, they are not designed with the overall Mamba architecture in mind and fail to account for the time-shared and discretized state-transition matrix at the heart of the selective state-space module (SSM). In this paper, we introduce SparseSSM, the first training-free pruning framework that extends the classic optimal brain surgeon (OBS) framework to state space architectures. Our layer-wise algorithm (i) derives an approximate second-order saliency score that aggregates Hessian-trace information across time steps, (ii) incorporates a component sensitivity analysis to guide feed-forward network (FFN) pruning, which also sheds light on where redundancy resides in mamba architecture, (iii) can be easily extended to semi-structured and structured sparsity, and generalized to other SSM-based architectures. Empirically, we prune 50% of SSM weights without fine-tuning and observe only limited performance degradation, achieving the current state-of-the-art one-shot pruning algorithm for Mamba-based LLMs.

We study the computational cost of differential privacy in terms of memory efficiency. Specifically, we establish for the first time an unconditional space lower bound for user-level differential privacy by introducing a novel proof technique based on a multi-player communication game. We apply our framework, as an example, to the fundamental problem of estimating the number of distinct elements in a stream: we prove that any private algorithm requires almost $\widetilde{\Omega}(T^{1/3})$ space (where $T$ denotes the length of the stream) to achieve certain error rates in a promise variant of the problem, resolving an open problem in the literature (by Jain et al. 2023 and Cummings et al. 2025) and establishes the first exponential separation between the space complexity of private algorithms and their non-private $\widetilde{O}(1)$ counterparts for a natural statistical estimation task. Furthermore, we show that this communication-theoretic technique generalizes to broad classes of problems, yielding lower bounds for private medians, quantiles, and max-select.

State space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling. However, existing SSMs often suffer from instability and memory degradation over extended horizons due to poorly conditioned first-order updates and unbalanced update geometry. We introduce MuonSSM, a general framework that stabilizes SSM training by explicitly conditioning the geometry of memory updates rather than the recurrent transition matrix. MuonSSM augments SSMs with a momentum-based pathway and a lightweight Newton-Schulz transformation on low-rank input injections, yielding bounded and spectrally conditioned updates while preserving parallel scan complexity. Theory shows that MuonSSM improves gradient propagation, mitigates spectral amplification, and enriches memory representations over long horizons. Extensive experiments across language, vision, and time-series benchmarks show consistent gains in accuracy, robustness, and long-context performance when integrated into diverse SSM backbones. These results establish geometric conditioning of updates as a principled pathway to stable, scalable sequence modeling.

Predictive memory has recently emerged as a powerful mechanism for online video models, enabling temporal reasoning beyond static memory banks. However, we observe a paradoxical phenomenon in which predictive memory often exacerbates drift under occlusion or rapid motion, as inaccurate predictions contaminate the internal state and lead to irreversible identity loss. We identify this failure as a reliability mismatch: predictive dynamics are applied uniformly despite high uncertainty and weak observations. To address this issue, we reinterpret video memory as a dynamic latent process rather than a static buffer. Building on this insight, we introduce Reliability-Guided Predictive Memory (RPM), a framework that explicitly regulates when and how predictive dynamics should influence online video perception. RPM integrates a latent world model based on state-space dynamics to generate predictive priors, while employing a reliability-aware fusion policy that suppresses unreliable predictions during occlusion. We instantiate RPM on a SAM2-based model and evaluate it on visual object tracking benchmarks. Experiments demonstrate that our method reduces drift after occlusion, consistently outperforming strong baselines that rely on either static memory or unconditional predictive modeling. We further show that this reliability-guided mechanism transfers to video object segmentation across multiple standard benchmarks. These findings establish that predictive memory is beneficial only when its reliability is explicitly modeled, and define a general principle for robust online video perception. The code is available at https://github.com/minwookim01/memory-as-dynamics.

Structured State-Space Duality (SSD) [Dao \& Gu, ICML 2024] is an equivalence between a simple Structured State-Space Model (SSM) and a masked attention mechanism. In particular, a state-space model with a scalar-times-identity state matrix is equivalent to a masked self-attention with a $1$-semiseparable causal mask. Consequently, the same sequence transformation (model) has two algorithmic realizations: as a linear-time $O(T)$ recurrence or as a quadratic-time $O(T^2)$ attention. In this note, we formalize and generalize this duality: (i) we extend SSD from the scalar‑identity case to general diagonal SSMs (diagonal state matrices); (ii) we show that these diagonal SSMs match the scalar case's training complexity lower bounds while supporting richer dynamics; (iii) we establish a necessary and sufficient condition under which an SSM is equivalent to $1$-semiseparable masked attention; and (iv) we show that such duality fails to extend to standard softmax attention due to rank explosion. Together, these results tighten the bridge between recurrent SSMs and Transformers, and widen the design space for expressive yet efficient sequence models. Code is available at https://github.com/MAGICS-LAB/state_space_daulity.

Transformers have been established as the de-facto backbones for most recent advances in sequence modeling, mainly due to their growing memory capacity that scales with the context length. While plausible for retrieval tasks, it causes quadratic complexity and so has motivated recent studies to explore viable subquadratic recurrent alternatives. Despite showing promising preliminary results in diverse tasks, such recurrent architectures underperform Transformers in recall-intensive tasks, {often attributed to their fixed-size memory. In this paper, we introduce Memory Caching (MC), a simple yet effective technique that enhances recurrent models by caching checkpoints of their memory states (a.k.a. hidden states). Memory Caching allows the effective memory capacity of RNNs to grow with sequence length, offering a flexible trade-off that interpolates between the fixed memory ( $O(L)$ complexity) of RNNs and the growing memory ( $O(L^2)$ complexity) of Transformers. We propose four variants of MC, including gated aggregation and sparse selective mechanisms, and discuss their implications on both linear and deep memory modules.} Our experimental results on language modeling, and long-context understanding tasks show that MC enhances the performance of recurrent models, supporting its effectiveness. In in-context recall tasks, our results indicate that while Transformers still achieve the best performance, our MC variants show competitive performance, close the gap with Transformers, and performs better than state-of-the-art recurrent models.

State-space models (SSMs) offer efficient sequence modeling but lag behind Transformers on benchmarks that require in-context retrieval. Prior work links this gap to a small set of attention heads, termed Gather-and-Aggregate (G&A), which SSMs struggle to reproduce. We propose *retrieval-aware distillation*, which converts a pretrained Transformer into a hybrid student by preserving only these retrieval-critical heads and distilling the rest into recurrent heads. We identify the essential heads via ablation on a synthetic retrieval task, producing a hybrid with sparse, non-uniform attention placement. We show that preserving **just 2% of attention heads recovers over 95% of teacher performance on retrieval-heavy tasks** (10 heads in a 1B model), requiring far fewer heads than hybrids that retain at least 25%. We further find that large recurrent states often compensate for missing retrieval: once retrieval is handled by these heads, the SSM backbone can be simplified with limited loss, even with an 8× reduction in state dimension. By reducing both the attention cache and the SSM state, the resulting hybrid is 5–6× more memory-efficient than comparable hybrids, closing the Transformer–SSM gap at a fraction of the memory cost.