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L5 pyramidal neurons are the only neocortical cell type with dendrites reaching all six layers of cortex, casting them as one of the main integrators in the cortical column. What is the nature and mode of computation performed in mouse primary visual cortex (V1) given the physiology of L5 pyramidal neurons? First, we experimentally establish active properties of the dendrites of L5 pyramidal neurons of mouse V1 using patch-clamp recordings. Using a detailed multi-compartmental model, we show this physiological setup to be well suited for coincidence detection between basal and apical tuft inputs by controlling the frequency of spike output. We further show how direct inhibition of calcium channels in the dendrites modulates such coincidence detection. To establish the singe-cell computation that this biophysics supports, we show that the combination of frequency-modulation of somatic output by tuft input and (simulated) calcium-channel blockage functionally acts as a composite sigmoidal function. Finally, we explore how this computation provides a mechanism whereby dendritic spiking contributes to orientation tuning in pyramidal neurons.

In vitro evidence suggests that the tuft dendrites of pyramidal neurons can evoke local NMDA spikes. The authors find that these local NMDA spikes occur spontaneously and following sensory input, and influence the number of output action potentials. Recent evidence in vitro suggests that the tuft dendrites of pyramidal neurons are capable of evoking local NMDA receptor–dependent electrogenesis, so-called NMDA spikes. However, it has so far proved difficult to demonstrate their existence in vivo . Moreover, it is not clear whether NMDA spikes are relevant to the output of pyramidal neurons. We found that local NMDA spikes occurred in tuft dendrites of layer 2/3 pyramidal neurons both spontaneously and following sensory input, and had a large influence on the number of output action potentials. Using two-photon activation of an intracellular caged NMDA receptor antagonist (tc-MK801), we found that isolated NMDA spikes typically occurred in multiple branches simultaneously and that sensory stimulation substantially increased their probability. Our results demonstrate that NMDA receptors have a vital role in coupling the tuft region of the layer 2/3 pyramidal neuron to the cell body, enhancing the effectiveness of layer 1 input.

Two-photon microscopy is a mainstay technique for imaging in scattering media and normally provides frame-acquisition rates of ~10–30 Hz. To track high-speed phenomena, we created a two-photon microscope with 400 illumination beams that collectively sample 95,000–211,000 µm2 areas at rates up to 1 kHz. Using this microscope, we visualized microcirculatory flow, fast venous constrictions and neuronal Ca2+ spiking with millisecond-scale timing resolution in the brains of awake mice.

What can artificial intelligence learn from neuroscience, and vice versa?

Apical and tuft dendrites of pyramidal neurons support regenerative electrical potentials, giving rise to long-lasting (approximately hundreds of milliseconds) and strong (~50 mV from rest) depolarizations. Such plateau events rely on clustered glutamatergic input, can be mediated by calcium or by NMDA currents, and often generate somatic depolarizations that last for the time course of the dendritic plateau event. We address the computational significance of such single-neuron processing via reduced but biophysically realistic modeling. We introduce a model based on two discrete integration zones, a somatic and a dendritic one, that communicate from the dendritic to the somatic compartment via a long plateau-conductance. We show principled differences in the way dendritic vs. somatic inhibition controls spike timing, and demonstrate how this could implement spike time control in the face of barrages of synaptic inputs.

L5 pyramidal neurons are the only neocortical cell type with dendrites reaching all six layers of cortex, casting them as one of the main integrators in the cortical column. What is the nature and mode of computation performed in mouse primary visual cortex (V1) given the physiology of L5 pyramidal neurons? First, we experimentally establish active properties of the dendrites of L5 pyramidal neurons of mouse V1 using patch-clamp recordings. Using a detailed multi-compartmental model, we show this physiological setup to be well suited for coincidence detection between basal and apical tuft inputs by controlling the frequency of spike output. We further show how direct inhibition of calcium channels in the dendrites modulates such coincidence detection. To establish the singe-cell computation that this biophysics supports, we show that the combination of frequency-modulation of somatic output by tuft input and (simulated) calcium-channel blockage functionally acts as a composite sigmoidal function. Finally, we explore how this computation provides a mechanism whereby dendritic spiking contributes to orientation tuning in pyramidal neurons.

Reasoning models leverage inference-time compute to significantly enhance the performance of language models on difficult logical tasks, and have become a dominating paradigm in frontier LLMs. Despite their wide adoption, the mechanisms underpinning the enhanced performance of these reasoning models are not well understood. In this work, we show that the majority of new capabilities in reasoning models can be elicited by small, single-rank changes to base model parameters, with many of these changes being interpretable. Specifically, we use a rank-1 LoRA to create a minimal parameter adapter for Qwen-2.5-32B-Instruct which recovers 73-90% of reasoning-benchmark performance compared to a full parameter finetune. We find that the activations of this LoRA are as interpretable as MLP neurons, and fire for reasoning-specific behaviors. Finally, we train a sparse autoencoder on the entire activation state of this LoRA and identify fine-grained and monosemantic features. Our findings highlight that reasoning performance can arise largely from minimal changes to base model parameters, and explore what these changes affect. More broadly, our work shows that parameter-efficient training methods can be used as a targeted lens for uncovering fundamental insights about language model behavior and dynamics.

What computational structures emerge in transformers trained on next-token prediction? In this work, we provide evidence that transformers implement constrained Bayesian belief updating -- a parallelized version of partial Bayesian inference shaped by architectural constraints. We integrate the model-agnostic theory of optimal prediction with mechanistic interpretability to analyze transformers trained on a tractable family of hidden Markov models that generate rich geometric patterns in neural activations. Our primary analysis focuses on single-layer transformers, revealing how the first attention layer implements these constrained updates, with extensions to multi-layer architectures demonstrating how subsequent layers refine these representations. We find that attention carries out an algorithm with a natural interpretation in the probability simplex, and create representations with distinctive geometric structure. We show how both the algorithmic behavior and the underlying geometry of these representations can be theoretically predicted in detail -- including the attention pattern, OV-vectors, and embedding vectors -- by modifying the equations for optimal future token predictions to account for the architectural constraints of attention. Our approach provides a principled lens on how architectural constraints shape the implementation of optimal prediction, revealing why transformers develop specific intermediate geometric structures.

We show that deep neural networks, including transformers and RNNs, pretrained as usual on next-token prediction, intrinsically discover and represent beliefs over 'quantum' and 'post-quantum' low-dimensional generative models of their training data -- as if performing iterative Bayesian updates over the latent state of this world model during inference as they observe more context. Notably, neural nets easily find these representation whereas there is no finite classical circuit that would do the job. The corresponding geometric relationships among neural activations induced by different input sequences are found to be largely independent of neural-network architecture. Each point in this geometry corresponds to a history-induced probability density over all possible futures, and the relative displacement of these points reflects the difference in mechanism and magnitude for how these distinct pasts affect the future.

Advances in optical and electrophysiological recording technologies have made it possible to record the dynamics of thousands of neurons, opening up new possibilities for interpreting and controlling large neural populations in behaving animals. A promising way to extract computational principles from these large datasets is to train data-constrained recurrent neural networks (dRNNs). Performing this training in real-time could open doors for research techniques and medical applications to model and control interventions at single-cell resolution and drive desired forms of animal behavior. However, existing training algorithms for dRNNs are inefficient and have limited scalability, making it a challenge to analyze large neural recordings even in offline scenarios. To address these issues, we introduce a training method termed Convex Optimization of Recurrent Neural Networks (CORNN). In studies of simulated recordings, CORNN attained training speeds ~100-fold faster than traditional optimization approaches while maintaining or enhancing modeling accuracy. We further validated CORNN on simulations with thousands of cells that performed simple computations such as those of a 3-bit flip-flop or the execution of a timed response. Finally, we showed that CORNN can robustly reproduce network dynamics and underlying attractor structures despite mismatches between generator and inference models, severe subsampling of observed neurons, or mismatches in neural time-scales. Overall, by training dRNNs with millions of parameters in subminute processing times on a standard computer, CORNN constitutes a first step towards real-time network reproduction constrained on large-scale neural recordings and a powerful computational tool for advancing the understanding of neural computation.