ICLR 2026 论文列表

The recent scaling of test-time compute for LLMs has restricted the practical deployment of models to those with strong capabilities that can generate high-quality outputs in an inference-efficient manner. While current Transformer-based models are the standard, their quadratic compute and linear memory bottlenecks have spurred the development of sub-quadratic models with linear-scaling compute with constant memory requirements. However, many recent linear-style models lack certain capabilities or lag behind in quality, and even their linear-time inference is not hardware-efficient. Guided by an inference-first perspective, we introduce three core methodological improvements inspired by the state-space model viewpoint of linear models. We combine a: 1) more expressive recurrence, 2) complex state update rule that enables richer state tracking, and 3) multi-input, multi-output formulation together, resulting in a stronger model that better exploits hardware parallelism during decoding. Together with architectural refinements, our **Mamba-3** model achieves significant gains across retrieval, state-tracking, and downstream language modeling tasks. Our new architecture sets the Pareto-frontier for performance under a fixed inference budget and outperforms strong baselines in a head-to-head comparison.

Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which cannot guarantee that the retrieved pattern has the strongest association with the query, failing correctness. We reframe this problem by proposing that a query is a generative variant of a stored memory pattern, and define a variant distribution to model this subtle context-dependent generative process. Consequently, correct retrieval should return the memory pattern with the maximum a posteriori probability of being the query's origin. This perspective reveals that an ideal similarity measure should approximate the likelihood of each stored pattern generating the query in accordance with variant distribution, which is impossible for fixed and pre-defined similarities used by existing associative memories. To this end, we develop adaptive similarity, a novel mechanism that learns to approximate this insightful but unknown likelihood from samples drawn from context, aiming for correct retrieval. We theoretically prove that our proposed adaptive similarity achieves optimal correct retrieval under three canonical and widely applicable types of variants: noisy, masked, and biased. We integrate this mechanism into a novel adaptive Hopfield network (`A-Hop`), and empirical results show that it achieves state-of-the-art performance across diverse tasks, including memory retrieval, tabular classification, image classification, and multiple instance learning. Our code is publicly available at https://anonymous.4open.science/r/Adaptive-Hopfield-Network-C137/.

In the world of Harry Potter, when Dumbledore's mind is overburdened, he extracts memories into a Pensieve to be revisited later. In the world of AI, while we possess the Pensieve—mature databases and retrieval systems, our models inexplicably lack the "wand" to operate it. They remain like a Dumbledore without agency, passively accepting a manually engineered context as their entire memory. This work finally places the wand in the model's hand. We introduce StateLM, a new class of foundation models endowed with an internal reasoning loop to manipulate their own state. We equip our model with a suite of tools, such as dynamic indexing, context pruning, and note-taking, and train it to actively manage this loop. By learning to dynamically construct its own context, our model breaks free from the architectural prison of a fixed window. The results are prominent: our state-management approach decouples performance from context window size, delivering strong accuracy and sustainability under extremely long contexts with linear inference cost. We demonstrate this by showing StateLM reliably retrieves a "needle" from a 1-million-token haystack, a task far beyond the reach of conventional models. On practical document QA tasks from NovelQA and $\infty$Bench, StateLM outperforms strong instruct baselines while using only 1/4 of their active context. An ablation further shows that our curated training pipeline is more effective for learning memory management than agent-like prompting. Together, these results mark a shift from passive predictors to state-aware systems where reasoning becomes a stateful and manageable process.

Recurrent large language models (Recurrent LLMs) offer linear computational complexity as efficient alternatives to quadratic self-attention-based LLMs (Self-Attention LLMs). However, Recurrent LLMs underperform on long-context tasks due to limited fixed-size memory. Previous research focused on architectural innovations to enhance memory capacity, but failed to match Self-Attention LLM performance. We argue this limitation stems from processing entire contexts at once being ill-suited for Recurrent LLMs. We propose Smooth Reading, a co-design of recurrent architecture and inference method. It introduces a end-to-end multi-round inference method that processes context incrementally and iteratively summarizes information, reducing memory demands. Methodologically, we reveal architecture-inference interactions play an important role for performance, efficiency and scalability, shedding light on future Recurrent LLM design. Besides, our method substantially bridges the performance gap between Recurrent and Self-Attention LLMs on long-context tasks while preserving efficiency advantages. Smooth Reading boosts SWA-3B-4k from 5.68% lower to 3.61% higher performance than Self-Attention LLMs on LongBench, while maintaining 2.5× faster training and 2× faster inference at 64k context.

Recurrent Neural Networks (RNNs) have found widespread applications in machine learning for time series prediction and dynamical systems reconstruction, and experienced a recent renaissance with improved training algorithms and architectural designs. Understanding why and how trained RNNs produce their behavior is important for scientific and medical applications, and explainable AI more generally. An RNN's dynamical repertoire depends on the topological and geometrical properties of its state space. Stable and unstable manifolds of periodic points play a particularly important role: They dissect a dynamical system's state space into different basins of attraction, and their intersections lead to chaotic dynamics with fractal geometry. Here we introduce a novel algorithm for detecting these manifolds, with a focus on piecewise-linear RNNs (PLRNNs) employing rectified linear units (ReLUs) as their activation function. We demonstrate how the algorithm can be used to trace the boundaries between different basins of attraction, and hence to characterize multistability, a computationally important property. We further show its utility in finding so-called homoclinic points, the intersections between stable and unstable manifolds, and thus establish the existence of chaos in PLRNNs. Finally we show for an empirical example, electrophysiological recordings from a cortical neuron, how insights into the underlying dynamics could be gained through our method.

In this paper we propose a memory-efficient hierarchical algorithm for solving large-scale optimal transport (OT) problems with squared Euclidean cost. The core of our proposed approach is the combination of multiscale hierarchical representation of the OT problem and a GPU-implemented Primal-Dual Hybrid Gradient (PDHG) method. Moreover, an active pruning technique is applied to further reduce computational complexity. Theoretically, we establish a scale-independent iteration-complexity upper bound for the refinement phase, which is consistent with our numerical observations. Numerically, experiments on image dataset DOTmark and point cloud dataset ModelNet10 demonstrate that the proposed algorithm effectively addresses the memory and scalability bottlenecks. Compared to state-of-the-art baselines, our method demonstrates significant advantages: for images with $n=1024^2$ pixels, it achieves an $8.9\times$ speedup and $70.5$\% reduction in memory usage under comparable accuracy; for 3D point clouds at scale $n=2^{18}$, it achieves a $1.84\times$ speedup and an $83.2$\% reduction in memory usage with $24.9$\% lower transport cost.

Large Language Models have demonstrated superior reasoning capabilities by generating step-by-step reasoning in natural language before deriving the final answer. Recently, Geiping et al. introduced 3.5B-Huginn as an alternative to this paradigm, a depth-recurrent Transformer that increases computational depth per token by reusing a recurrent block in latent space. Despite its performance gains with increasing recurrences, this approach is inadequate for tasks demanding exploration and adaptivity, a limitation arising from its single, chain-like propagation mechanism. To address this, we propose a novel dynamic multi-branches routing approach for Huginn, termed as Mixture-of-Depth-Recurrent (MoDr) Transformer, which enables effective exploration of the solution space by shifting linear latent reasoning into a LoRA-based multi-branch dynamic relay mode with a learnable hard-gate routing. Meanwhile, we introduce an auxiliary-loss-free load balancing strategy to mitigate the potential routing collapse. Our empirical results reveal that MoDr achieves average accuracy improvements of +7.2% and +2.48% over the original Huginn model and its fine-tuned variant, respectively, across various mathematical reasoning benchmarks and improvements of +21.21% and +1.52% on commonsense reasoning benchmarks.

Training recurrent neural networks (RNNs) to perform neuroscience-style tasks has become a popular way to generate hypotheses for how neural circuits in the brain might perform computations. Recent work has demonstrated that task-trained RNNs possess a strong simplicity bias. In particular, this inductive bias often causes RNNs trained on the same task to collapse on effectively the same solution, typically comprised of fixed-point attractors or other low-dimensional dynamical motifs. While such solutions are readily interpretable, this collapse proves counterproductive for the sake of generating a set of genuinely unique hypotheses for how neural computations might be performed. Here we propose Iterative Neural Similarity Deflation (INSD), a simple method to break this inductive bias. By penalizing linear predictivity of neural activity produced by standard task-trained RNNs, we find an alternative class of solutions to classic neuroscience-style RNN tasks. These solutions appear distinct across a battery of analysis techniques, including representational similarity metrics, dynamical systems analysis, and the linear decodability of task-relevant variables. Moreover, these alternative solutions can sometimes achieve superior performance in difficult or out-of-distribution task regimes. Our findings underscore the importance of moving beyond the simplicity bias to uncover richer and more varied models of neural computation.

The hippocampus contains neurons whose firing correlates with an animal's location and orientation in space. Collectively, these neurons are held to support a cognitive map of the environment, enabling the recall of and navigation to specific locations. Although recent studies have characterised the timelines of spatial neuron development, no unifying mechanistic model has yet been proposed. Moreover, the processes driving the emergence of spatial representations in the hippocampus remain unclear (Tan et al., 2017). Here, we combine computational analysis of postnatal locomotor development with a recurrent neural network (RNN) model of hippocampal function to demonstrate how changes in movement statistics -- and the resulting sensory experiences -- shape the formation of spatial tuning. First, we identify distinct developmental stages in rat locomotion during open-field exploration using published experimental data. Then, we train shallow RNNs to predict upcoming visual stimuli from concurrent visual and vestibular inputs, exposing them to trajectories that reflect progressively maturing locomotor patterns. Our findings reveal that these changing movement statistics drive the sequential emergence of spatially tuned units, mirroring the developmental timeline observed in rats. The models generate testable predictions about how spatial tuning properties mature -- predictions we confirm through analysis of hippocampal recordings. Critically, we demonstrate that replicating the specific statistics of developmental locomotion -- rather than merely accelerating sensory change -- is essential for the emergence of an allocentric spatial representation. These results establish a mechanistic link between embodied sensorimotor experience and the ontogeny of hippocampal spatial neurons, with significant implications for neurodevelopmental research and predictive models of navigational brain circuits.

Understanding how populations of neurons represent information is a central challenge across machine learning and neuroscience. Recent work in both fields has begun to characterize the representational geometry and functionality underlying complex distributed activity. For example, artificial neural networks trained on data with more features than neurons compress data by representing features non-orthogonally in so-called *superposition*. However, the effect of time (or memory), an additional capacity-constraining pressure, on underlying representational geometry in recurrent models is not well understood. Here, we study how memory demands affect representational geometry in recurrent neural networks (RNNs), introducing the concept of temporal superposition. We develop a theoretical framework in RNNs with linear recurrence trained on a delayed serial recall task to better understand how properties of the data, task demands, and network dimensionality lead to different representational strategies, and show that these insights generalize to nonlinear RNNs. Through this, we identify an effectively linear, dense regime and a sparse regime where RNNs utilize an interference-free space, characterized by a phase transition in the angular distribution of features and decrease in spectral radius. Finally, we analyze the interaction of spatial and temporal superposition to observe how RNNs mediate different representational tradeoffs. Overall, our work offers a mechanistic, geometric explanation of representational strategies RNNs learn, how they depend on capacity and task demands, and why.

State-Space Models (SSMs) have recently been shown to achieve strong empirical performance on a variety of long-range sequence modeling tasks while remaining efficient and highly-parallelizable. However, the theoretical understanding of their expressive power remains limited. In this work, we study the expressivity of input-Dependent Complex-valued Diagonal (DCD) State-Space Models (SSMs) on sequential state-tracking tasks for abstract groups. It is easy to show that a single DCD SSM layer with a universal decoder can track any Abelian group at finite precision by decomposing it into a product of cyclic groups. We show that this is tight by proving that such a model cannot track any non-Abelian group at finite precision. We further establish the expressivity of multi-layer DCD SSMs. We show that a $k$-layer DCD SSM tracks a group if and only if that group has a subnormal series of length at most $k$, with Abelian factor groups. Empirically, while multi-layer models are theoretically expressive enough for solvable non-Abelian groups, we find they often fail to learn such solutions in practice, highlighting a gap between expressivity and learnability.

Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for machine learning with noisy intermediate-scale quantum devices. Recent developments have introduced feedback-based quantum reservoir systems, which process temporal information with comparatively fewer components and enable real-time computation while preserving the input history. Motivated by their promising empirical performance, in this work, we study the approximation capabilities of feedback-based quantum reservoir computing. More specifically, we are concerned with recurrent quantum neural networks, which are quantum analogues of classical recurrent neural networks. Our results show that regular state-space systems can be approximated using quantum recurrent neural networks without the curse of dimensionality and with the number of qubits only growing logarithmically in the reciprocal of the prescribed approximation accuracy. Notably, our analysis demonstrates that quantum recurrent neural networks are universal with linear readouts, making them both powerful and experimentally accessible. These results pave the way for practical and theoretically grounded quantum reservoir computing with real-time processing capabilities.

Due to tractable analysis and control, linear state-space models (LSSMs) provide a fundamental mathematical tool for time-series data modeling in various disciplines. In particular, many LSSMs have sparse system matrices because interactions among variables are limited or only a few significant relationships exist. However, current learning algorithms for LSSMs lack the ability to learn system matrices with the sparsity constraint due to the similarity transformation. To address this issue, we impose sparsity-promoting priors on system matrices to balance modeling error and model complexity. By taking hidden states of LSSMs as latent variables, we then explore the expectation-maximization (EM) algorithm to derive a maximum a posteriori (MAP) estimate of both hidden states and system matrices from noisy observations. Based on the Global Convergence Theorem, we further demonstrate that the proposed learning algorithm yields a sequence converging to a local maximum or saddle point of the joint posterior distribution. Finally, experimental results on simulation and real-world problems illustrate that the proposed algorithm can preserve the inherent topological structure among variables and significantly improve prediction accuracy over classical learning algorithms.

We study the problem of designing *sublinear spectral clustering oracles* for well-clusterable graphs. Such an oracle is an algorithm that, given query access to the adjacency list of a graph $G$, first constructs a compact data structure $\mathcal{D}$ that captures the clustering structure of $G$. Once built, $\mathcal{D}$ enables sublinear time responses to \textsc{WhichCluster}$(G,x)$ queries for any vertex $x$. A major limitation of existing oracles is that constructing $\mathcal{D}$ requires $\Omega(\sqrt{n})$ memory, which becomes a bottleneck for massive graphs and memory-limited settings. In this paper, we break this barrier and establish a memory-time trade-off for sublinear spectral clustering oracles. Specifically, for well-clusterable graphs, we present oracles that construct $\mathcal{D}$ using much smaller than $O(\sqrt{n})$ memory (e.g., $O(n^{0.01})$) while still answering membership queries in sublinear time. We also characterize the trade-off frontier between memory usage $S$ and query time $T$, showing, for example, that $S\cdot T=\widetilde{O}(n)$ for clusterable graphs with a logarithmic conductance gap, and we show that this trade-off is nearly optimal (up to logarithmic factors) for a natural class of approaches. Finally, to complement our theory, we validate the performance of our oracles through experiments on synthetic networks.