Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many free parameters that must be estimated for each cell, and existing fitting methods rely on intracellular voltage measurements that are highly challenging to obtain in vivo. Recent advances in neural recording technology with high-density probes and arrays enable dense sampling of extracellular voltage from many sites surrounding a neuron, allowing indirect measurement of many compartments of a cell simultaneously. Here, we propose a method for inferring the underlying membrane voltage, biophysical parameters, and the neuron's position relative to the probe, using extracellular measurements alone. We use an Extended Kalman Filter to infer membrane voltage and channel states using efficient, differentiable simulators. Then, we learn the model parameters by maximizing the marginal likelihood using gradient-based methods. We demonstrate the performance of this approach using simulated data and real neuron morphologies.

Large Language Models exhibit logical inconsistency across multi-turn inference processes, undermining correctness in complex inferential tasks. Challenges arise from ensuring that outputs align with both factual correctness and human intent.

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence length. Previous work on adapting MCMC to modern hardware has therefore focused on running many independent chains in parallel. Here, we take an alternative approach: we propose algorithms to evaluate MCMC samplers in parallel across the chain length. To do this, we build on recent methods for parallel evaluation of nonlinear recursions that formulate the state sequence as a solution to a fixed-point problem and solve for the fixed-point using a parallel form of Newton's method. We show how this approach can be used to parallelize Gibbs, Metropolis-adjusted Langevin, and Hamiltonian Monte Carlo sampling across the sequence length. In several examples, we demonstrate the simulation of up to hundreds of thousands of MCMC samples with only tens of parallel Newton iterations. Additionally, we develop two new parallel quasi-Newton methods to evaluate nonlinear recursions with lower memory costs and reduced runtime. We find that the proposed parallel algorithms accelerate MCMC sampling across multiple examples, in some cases by more than an order of magnitude compared to sequential evaluation.

The emergence of large language models (LLMs) enables the development of intelligent agents capable of engaging in complex and multi-turn dialogues. However, multi-agent collaboration faces critical safety challenges, such as hallucination amplification and error injection and propagation. This paper presents GUARDIAN, a unified method for detecting and mitigating multiple safety concerns in GUARDing Intelligent Agent collaboratioNs. By modeling the multi-agent collaboration process as a discrete-time temporal attributed graph, GUARDIAN explicitly captures the propagation dynamics of hallucinations and errors. The unsupervised encoder-decoder architecture incorporating an incremental training paradigm learns to reconstruct node attributes and graph structures from latent embeddings, enabling the identification of anomalous nodes and edges with unparalleled precision. Moreover, we introduce a graph abstraction mechanism based on the Information Bottleneck Theory, which compresses temporal interaction graphs while preserving essential patterns. Extensive experiments demonstrate GUARDIAN's effectiveness in safeguarding LLM multi-agent collaborations against diverse safety vulnerabilities, achieving state-of-the-art accuracy with efficient resource utilization.

The scaling exponent $α$ in neural scaling laws $L(N) \propto N^{-α}$ is commonly treated as a fixed constant set by architecture and data. We present evidence that $α$ depends systematically on the optimizer. In controlled random-feature regression experiments -- the canonical theoretical framework for neural scaling -- we measure $α$ across five optimizer variants and six spectral conditions. Preconditioned optimizers consistently yield steeper scaling (larger $α$), with the $α$-shift increasing across most of the tested spectral range, peaking near $s = 1.5$, and remaining large at $s = 2.0$. At $s \approx 1.0$ (characteristic of natural language), the full natural gradient achieves $α\approx 0.31$ versus $α\approx 0.12$ for gradient descent -- a $2.6\times$ larger fitted exponent that, within the random-feature model, compounds with each model-size doubling. Whether and how this exponent shift transfers to large-scale LLM training -- where recent evidence suggests the advantage may attenuate with scale -- remains an important open question. Our results imply that scaling-law forecasts should account for optimizer choice, and we provide a spectral diagnostic predicting when advanced optimizers will pay off.

We note that these results are about two of the most commonly used architecture modifications for RNNs. First, the gating mechanism is ubiquitous in RNNs, and usually thought of as a heuristic for smoothing optimization [28]. Second, many of the effective large-scale RNNs use linear (gated) recurrences and deeper models, which is usually thought of as a heuristic for computational efficiency [5]. Our results suggest that neither of these are heuristics after all, and arise from standard ways to approximate ODEs. To be more specific, we show that: 19 Table 6: A summary of the characteristics of popular RNN methods and their approximation mechanisms for capturing the dynamics x(t) = x(t) + f(t,x(t)) (equation (14)). The LSSL entries are for the very specific case with order N = 1 and A= 1,B = 1,C = 1,D= 0; LSSLs are more general.

We propose a novel inference technique based on a pretrained diffusion model for text-conditional video generation. Our approach, called FIFO-Diffusion, is conceptually capable of generating infinitely long videos without additional training. This is achieved by iteratively performing diagonal denoising, which simultaneously processes a series of consecutive frames with increasing noise levels in a queue; our method dequeues a fully denoised frame at the head while enqueuing a new random noise frame at the tail. However, diagonal denoising is a double-edged sword as the frames near the tail can take advantage of cleaner frames by forward reference but such a strategy induces the discrepancy between training and inference. Hence, we introduce latent partitioning to reduce the training-inference gap and lookahead denoising to leverage the benefit of forward referencing. Practically, FIFO-Diffusion consumes a constant amount of memory regardless of the target video length given a baseline model, while well-suited for parallel inference on multiple GPUs. We have demonstrated the promising results and effectiveness of the proposed methods on existing text-to-video generation baselines. Generated video examples and source codes are available at our project page.