Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

State Space Models (SSMs), particularly the Mamba architecture, have recently emerged as powerful alternatives to Transformers for sequence modeling, offering linear computational complexity while achieving competitive performance. Yet, despite their effectiveness, understanding how these Vision SSMs process spatial information remains challenging due to the lack of transparent, attention-like mechanisms. To address this gap, we introduce a controllability-based interpretability framework that quantifies how different parts of the input sequence (tokens or patches) influence the internal state dynamics of SSMs. We propose two complementary formulations: a Jacobian-based method applicable to any SSM architecture that measures influence through the full chain of state propagation, and a Gramian-based approach for diagonal SSMs that achieves superior speed through closed-form analytical solutions. Both methods operate in a single forward pass with linear complexity, requiring no architectural modifications or hyperparameter tuning. We validate our framework through experiments on three diverse medical imaging modalities, demonstrating that SSMs naturally implement hierarchical feature refinement from diffuse low-level textures in early layers to focused, clinically meaningful patterns in deeper layers. Our analysis reveals domain-specific controllability signatures aligned with diagnostic criteria, progressive spatial selectivity across the network hierarchy, and the substantial influence of scanning strategies on attention patterns. Beyond medical imaging, we articulate applications spanning computer vision, natural language processing, and cross-domain tasks. Our framework establishes controllability analysis as a unified, foundational interpretability paradigm for SSMs across all domains. Code and analysis tools will be made available upon publication

When a language model generates text, the selection of individual tokens might lead it down very different reasoning paths, making uncertainty difficult to quantify. In this work, we consider whether reasoning language models represent the alternate paths that they could take during generation. To test this hypothesis, we use hidden activations to control and predict a language model's uncertainty during chain-of-thought reasoning. In our experiments, we find a clear correlation between how uncertain a model is at different tokens, and how easily the model can be steered by controlling its activations. This suggests that activation interventions are most effective when there are alternate paths available to the model -- in other words, when it has not yet committed to a particular final answer. We also find that hidden activations can predict a model's future outcome distribution, demonstrating that models implicitly represent the space of possible paths.

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Reinforcement Learning (RL) has proven effective in solving complex decision-making tasks across various domains, but challenges remain in continuous-time settings, particularly when state dynamics are governed by stochastic differential equations (SDEs) with jump components. In this paper, we address this challenge by introducing the Mean-Square Bipower Variation Error (MSBVE) algorithm, which enhances robustness and convergence in scenarios involving significant stochastic noise and jumps. We first revisit the Mean-Square TD Error (MSTDE) algorithm, commonly used in continuous-time RL, and highlight its limitations in handling jumps in state dynamics. The proposed MSBVE algorithm minimizes the mean-square quadratic variation error, offering improved performance over MSTDE in environments characterized by SDEs with jumps. Simulations and formal proofs demonstrate that the MSBVE algorithm reliably estimates the value function in complex settings, surpassing MSTDE's performance when faced with jump processes. These findings underscore the importance of alternative error metrics to improve the resilience and effectiveness of RL algorithms in continuous-time frameworks.

This study investigates the learnability of Recurrent Neural Networks (RNNs) in classifying structured formal languages, focusing on counter and Dyck languages. Traditionally, both first-order (LSTM) and second-order (O2RNN) RNNs have been considered effective for such tasks, primarily based on their theoretical expressiveness within the Chomsky hierarchy. However, our research challenges this notion by demonstrating that RNNs primarily operate as state machines, where their linguistic capabilities are heavily influenced by the precision of their embeddings and the strategies used for sampling negative examples. Our experiments revealed that performance declines significantly as the structural similarity between positive and negative examples increases. Remarkably, even a basic single-layer classifier using RNN embeddings performed better than chance. To evaluate generalization, we trained models on strings up to a length of 40 and tested them on strings from lengths 41 to 500, using 10 unique seeds to ensure statistical robustness. Stability comparisons between LSTM and O2RNN models showed that O2RNNs generally offer greater stability across various scenarios. We further explore the impact of different initialization strategies revealing that our hypothesis is consistent with various RNNs. Overall, this research questions established beliefs about RNNs' computational capabilities, highlighting the importance of data structure and sampling techniques in assessing neural networks' potential for language classification tasks. It emphasizes that stronger constraints on expressivity are crucial for understanding true learnability, as mere expressivity does not capture the essence of learning.

By thinking of each state in a hidden Markov model as corresponding to some spatial region of a fictitious topology space it is possible to naturally define neigh(cid:173) bouring states as those which are connected in that space. The transition matrix can then be constrained to allow transitions only between neighbours; this means that all valid state sequences correspond to connected paths in the topology space. I show how such constrained HMMs can learn to discover underlying structure in complex sequences of high dimensional data, and apply them to the problem of recovering mouth movements from acoustics in continuous speech. Probabilistic unsupervised learning for such sequences requires models with two essential features: latent (hidden) variables and topology in those variables. Hidden Markov models (HMMs) can be thought of as dynamic generalizations of discrete state static data models such as Gaussian mixtures, or as discrete state versions of linear dynam(cid:173) ical systems (LDSs) (which are themselves dynamic generalizations of continuous latent variable models such as factor analysis).

We devise and experiment with a dynamical kernel-based system for tracking hand movements from neural activity. The state of the system corresponds to the hand location, velocity, and acceleration, while the system's input are the instantaneous spike rates. The system's state dy- namics is defined as a combination of a linear mapping from the previous estimated state and a kernel-based mapping tailored for modeling neural activities. In contrast to generative models, the activity-to-state mapping is learned using discriminative methods by minimizing a noise-robust loss function. We use this approach to predict hand trajectories on the basis of neural activity in motor cortex of behaving monkeys and find that the proposed approach is more accurate than both a static approach based on support vector regression and the Kalman filter. The paper focuses on the problem of tracking hand movements, which constitute smooth spatial trajectories, from spike trains of a neural population. We do so by devising a dynam- ical system which employs a tailored kernel for spike trains along with a linear mapping corresponding to the states' dynamics.