We introduce SoundVista, a method to generate the ambient sound of an arbitrary scene at novel viewpoints. Given a pre-acquired recording of the scene from sparsely distributed microphones, SoundVista can synthesize the sound of that scene from an unseen target viewpoint. The method learns the underlying acoustic transfer function that relates the signals acquired at the distributed microphones to the signal at the target viewpoint, using a limited number of known recordings. Unlike existing works, our method does not require constraints or prior knowledge of sound source details. Moreover, our method efficiently adapts to diverse room layouts, reference microphone configurations and unseen environments. To enable this, we introduce a visual-acoustic binding module that learns visual embeddings linked with local acoustic properties from panoramic RGB and depth data. We first leverage these embeddings to optimize the placement of reference microphones in any given scene. During synthesis, we leverage multiple embeddings extracted from reference locations to get adaptive weights for their contribution, conditioned on target viewpoint. We benchmark the task on both publicly available data and real-world settings. We demonstrate significant improvements over existing methods.

In mixed reality applications, a realistic acoustic experience in spatial environments is as crucial as the visual experience for achieving true immersion. Despite recent advances in neural approaches for Room Impulse Response (RIR) estimation, most existing methods are limited to the single environment on which they are trained, lacking the ability to generalize to new rooms with different geometries and surface materials. We aim to develop a unified model capable of reconstructing the spatial acoustic experience of any environment with minimum additional measurements. To this end, we present xRIR, a framework for cross-room RIR prediction. The core of our generalizable approach lies in combining a geometric feature extractor, which captures spatial context from panorama depth images, with a RIR encoder that extracts detailed acoustic features from only a few reference RIR samples. To evaluate our method, we introduce AcousticRooms, a new dataset featuring high-fidelity simulation of over 300,000 RIRs from 260 rooms. Experiments show that our method strongly outperforms a series of baselines. Furthermore, we successfully perform sim-to-real transfer by evaluating our model on four real-world environments, demonstrating the generalizability of our approach and the realism of our dataset.

3D spatial reasoning in dynamic, audio-visual environments is a cornerstone of human cognition yet remains largely unexplored by existing Audio-Visual Large Language Models (AV-LLMs) and benchmarks, which predominantly focus on static or 2D scenes. We introduce SAVVY-Bench, the first benchmark for 3D spatial reasoning in dynamic scenes with synchronized spatial audio. SAVVY-Bench is comprised of thousands of carefully curated question–answer pairs probing both directional and distance relationships involving static and moving objects, and requires fine-grained temporal grounding, consistent 3D localization, and multi-modal annotation. To tackle this challenge, we propose SAVVY, a novel training-free reasoning pipeline that consists of two stages: (i) Egocentric Spatial Tracks Estimation, which leverages AV-LLMs as well as other audio-visual methods to track the trajectories of key objects related to the query using both visual and spatial audio cues, and (ii) Dynamic Global Map Construction, which aggregates multi-modal queried object trajectories and converts them into a unified global dynamic map. Using the constructed map, a final QA answer is obtained through a coordinate transformation that aligns the global map with the queried viewpoint. Empirical evaluation demonstrates that SAVVY substantially enhances performance of state-of-the-art AV-LLMs, setting a new standard and stage for approaching dynamic 3D spatial reasoning in AV-LLMs.

Intracortical Brain-Computer Interfaces (iBCI) decode behavior from neural population activity to restore motor functions and communication abilities in individuals with motor impairments. A central challenge for long-term iBCI deployment is the nonstationarity of neural recordings, where the composition and tuning profiles of the recorded populations are unstable across recording sessions. Existing approaches attempt to address this issue by explicit alignment techniques; however, they rely on fixed neural identities and require test-time labels or parameter updates, limiting their generalization across sessions and imposing additional computational burden during deployment. In this work, we address the problem of cross-session nonstationarity in long-term iBCI systems and introduce SPINT - a Spatial Permutation-Invariant Neural Transformer framework for behavioral decoding that operates directly on unordered sets of neural units. Central to our approach is a novel context-dependent positional embedding scheme that dynamically infers unit-specific identities, enabling flexible generalization across recording sessions. SPINT supports inference on variable-size populations and allows few-shot, gradient-free adaptation using a small amount of unlabeled data from the test session. We evaluate SPINT on three multi-session datasets from the FALCON Benchmark, covering continuous motor decoding tasks in human and non-human primates. SPINT demonstrates robust cross-session generalization, outperforming existing zero-shot and few-shot unsupervised baselines while eliminating the need for test-time alignment and fine-tuning. Our work contributes an initial step toward a robust and scalable neural decoding framework for long-term iBCI applications.

Hybrid Optical Neural Networks (ONNs, typically consisting of an optical frontend and a digital backend) offer an energy-efficient alternative to fully digital deep networks for real-time, power-constrained systems. However, their adoption is limited by two main challenges: the accuracy gap compared to large-scale networks during training, and discrepancies between simulated and fabricated systems that further degrade accuracy. While previous work has proposed end-to-end optimizations for specific datasets (e.g., MNIST) and optical systems, these approaches typically lack generalization across tasks and hardware designs. To address these limitations, we propose a task-agnostic and hardware-agnostic pipeline that supports image classification and segmentation across diverse optical systems. To assist optical system design before training, we design the metasurface layout based on fabrication constraints. For training, we introduce Neural Tangent Knowledge Distillation (NTKD), which aligns optical models with electronic teacher networks, thereby narrowing the accuracy gap. After fabrication, NTKD also guides fine-tuning of the digital backend to compensate for implementation errors. Experiments on multiple datasets (e.g., MNIST, CIFAR, Carvana Masking) and hardware configurations show that our pipeline consistently improves ONN performance and enables practical deployment in both pre-fabrication simulations and physical implementations.

Video encompasses both visual and auditory data, creating a perceptually rich experience where these two modalities complement each other. As such, videos are a valuable type of media for the investigation of the interplay between audio and visual elements. Previous studies of audio-visual modalities primarily focused on either audio-visual representation learning or generative modeling of a modality conditioned on the other, creating a disconnect between these two branches. A unified framework that learns representation and generates modalities has not been developed yet. In this work, we introduce a novel framework called Vision to Audio and Beyond (VAB) to bridge the gap between audio-visual representation learning and vision-to-audio generation. The key approach of VAB is that rather than working with raw video frames and audio data, VAB performs representation learning and generative modeling within latent spaces. In particular, VAB uses a pre-trained audio tokenizer and an image encoder to obtain audio tokens and visual features, respectively. It then performs the pre-training task of visual-conditioned masked audio token prediction. This training strategy enables the model to engage in contextual learning and simultaneous video-to-audio generation. After the pre-training phase, VAB employs the iterative-decoding approach to rapidly generate audio tokens conditioned on visual features. Since VAB is a unified model, its backbone can be fine-tuned for various audio-visual downstream tasks. Our experiments showcase the efficiency of VAB in producing high-quality audio from video, and its capability to acquire semantic audio-visual features, leading to competitive results in audio-visual retrieval and classification.

We propose a novel approach for rendering high-quality spatial audio for 3D scenes that is in synchrony with the visual stream but does not rely or explicitly conditioned on the visual rendering. We demonstrate that such an approach enables the experience of immersive virtual tourism - performing a real-time dynamic navigation within the scene, experiencing both audio and visual content. Current audio-visual rendering approaches typically rely on visual cues, such as images, and thus visual artifacts could cause inconsistency in the audio quality. Furthermore, when such approaches are incorporated with visual rendering, audio generation at each viewpoint occurs after the rendering of the image of the viewpoint and thus could lead to audio lag that affects the integration of audio and visual streams. Our proposed approach, AV-Cloud, overcomes these challenges by learning the representation of the audio-visual scene based on a set of sparse AV anchor points, that constitute the Audio-Visual Cloud, and are derived from the camera calibration. The Audio-Visual Cloud serves as an audio-visual representation from which the generation of spatial audio for arbitrary listener location can be generated. In particular, we propose a novel module Audio-Visual Cloud Splatting which decodes AV anchor points into a spatial audio transfer function for the arbitrary viewpoint of the target listener. This function, applied through the Spatial Audio Render Head module, transforms monaural input into viewpoint-specific spatial audio. As a result, AV-Cloud efficiently renders the spatial audio aligned with any visual viewpoint and eliminates the need for pre-rendered images. We show that AV-Cloud surpasses current state-of-the-art accuracy on audio reconstruction, perceptive quality, and acoustic effects on two real-world datasets. AV-Cloud also outperforms previous methods when tested on scenes "in the wild".

The content of visual and audio scenes is multi-faceted such that a video stream can be paired with various audio streams and vice-versa. Thereby, in video-to-audio generation task, it is imperative to introduce steering approaches for controlling the generated audio. While Video-to-Audio generation is a well-established generative task, existing methods lack such controllability. In this work, we propose VATT, a multi-modal generative framework that takes a video and an optional text prompt as input, and generates audio and optional textual description (caption) of the audio. Such a framework has two unique advantages: i) Video-to-Audio generation process can be refined and controlled via text which complements the context of the visual information, and ii) The model can suggest what audio to generate for the video by generating audio captions. VATT consists of two key modules: VATT Converter, which is an LLM that has been fine-tuned for instructions and includes a projection layer that maps video features to the LLM vector space, and VATT Audio, a bi-directional transformer that generates audio tokens from visual frames and from optional text prompt using iterative parallel decoding. The audio tokens and the text prompt are used by a pretrained neural codec to convert them into a waveform. Our experiments show that when VATT is compared to existing video-to-audio generation methods in objective metrics, such as VGGSound audiovisual dataset, it achieves competitive performance when the audio caption is not provided. When the audio caption is provided as a prompt, VATT achieves even more refined performance (with lowest KLD score of 1.41). Furthermore, subjective studies asking participants to choose the most compatible generated audio for a given silent video, show that VATT Audio has been chosen on average as a preferred generated audio than the audio generated by existing methods. VATT enables controllable video-to-audio generation through text as well as suggesting text prompts for videos through audio captions, unlocking novel applications such as text-guided video-to-audio generation and video-to-audio captioning.

It is often the case that human body movements include rhythmic patterns. A video camera system that captures these patterns and responds to them with rhythmic sounds or music, as these happen, could create a unique interactive experience. Creating such an experience requires a real-time translation of related visual cues into in-rhythm sounds and warrants novel real-time methods. In this work, we propose a novel learning-based system, called ‘InteractiveBeat’, which generates an evolving interactive soundtrack for a camera input that captures person’s movements. InteractiveBeat infers body skeleton keypoints and translates them into drum rhythms using a series of sequence models. It then implements a conditional drum generation network for generating polyphonic drum sounds based on the rhythms. To guarantee real-time function, these models are integrated into a time-evolving pipeline with rules for updates. InteractiveBeat is trained and evaluated on a well-annotated large-scale dance database (AIST), and in addition, we collected a dataset of in-the-wild videos with people performing movements of various activities that correspond to background music. Furthermore, we develop a ‘live’ demo prototype of the system. Our evaluation results show that the system can generate interactive rhythmic drums more accurately than existing methods and achieves a non-cumulative latency of 34ms (approx. 30 fps). This allows InteractiveBeat to be synchronized with the video stream and react to real-time movements.

Abstract Recurrent neural networks (RNN) are ubiquitous computing systems for sequences and multivariate time-series data. While several robust RNN architectures are known, it is unclear how to relate RNN initialization, architecture, and other hyperparameters with accuracy for a given task. In this work, we propose treating RNN as dynamical systems and correlating hyperparameters with accuracy through Lyapunov spectral analysis, a methodology designed explicitly for nonlinear dynamical systems. To address the fact that RNN features go beyond the existing Lyapunov spectral analysis, we propose to infer relevant features from the Lyapunov spectrum with an Autoencoder and an embedding of its Latent representation (AeLLE). Our studies of various RNN architectures show that AeLLE successfully correlates RNN Lyapunov spectrum with accuracy. Furthermore, the Latent representation learned by AeLLE is generalizable to novel inputs from the same task and is formed early in the process of RNN training. The latter property allows for predicting the accuracy to which RNN would converge when training is complete. We conclude that the representation of RNN through the Lyapunov spectrum, along with AeLLE, provides a novel method for the organization and interpretation of variants of RNN architectures.

Action recognition from temporal multivariate sequences of features, such as identifying human actions, is typically approached by supervised training as it requires many ground truth annotations to reach high recognition accuracy. Unsupervised methods for the organization of sequences into clusters have been introduced, however, such methods continue to require annotations to associate clusters with actions. The challenges in annotation necessitate an effective classification methodology that minimizes the required number of labels. Active learning (AL) approaches have been proposed to address these challenges and were able to establish robust results on image classification. Such approaches are not directly applicable to sequences, since for sequences, the variations are in both spatial and temporal domains. In this brief, we introduce a novel method for AL for sequences, called "AL-SAR," which combines unsupervised training with sparsely supervised annotation. In particular, AL-SAR employs a multi-head mechanism for robust uncertainty evaluation of the latent space learned by an encoder-decoder framework. It aims to iteratively select a sparse set of samples, which annotation contributes the most to the disentanglement of the latent space. We evaluate our system on common benchmark datasets with multiple sequences and actions, such as NW-UCLA, NTU RGB+D 60, and UWA3D. Our results indicate that AL-SAR coupled with encoder-decoder network outperforms other AL methods coupled with the same network structure.

Modeling sounds emitted from physical object interactions is critical for immersive perceptual experiences in real and virtual worlds. Traditional methods of impact sound synthesis use physics simulation to obtain a set of physics parameters that could represent and synthesize the sound. However, they require fine details of both the object geometries and impact locations, which are rarely available in the real world and can not be applied to synthesize impact sounds from common videos. On the other hand, existing video-driven deep learning-based approaches could only capture the weak correspondence between visual content and impact sounds since they lack of physics knowledge. In this work, we propose a physics-driven diffusion model that can synthesize high-fidelity impact sound for a silent video clip. In addition to the video content, we propose to use additional physics priors to guide the impact sound synthesis procedure. The physics priors include both physics parameters that are directly estimated from noisy real-world impact sound examples without sophisticated setup and learned residual parameters that interpret the sound environment via neural networks. We further implement a novel diffusion model with specific training and inference strategies to combine physics priors and visual information for impact sound synthesis. Experimental results show that our model outperforms several existing systems in generating realistic impact sounds. Lastly, the physics-based representations are fully interpretable and transparent, thus allowing us to perform sound editing flexibly. We encourage the readers visit our project page11https://sukun1045.github.io/video-physics-sound-diffusion/ to watch demo videos with the audio turned on to experience the result.

Fully immersive and interactive audio-visual scenes are dynamic such that the listeners and the sound emitters move and interact with each other. Reconstruction of an immersive sound experience, as it happens in the scene, requires detailed reconstruction of the audio perceived by the listener at an arbitrary location. The audio at the listener location is a complex outcome of sound propagation through the scene geometry and interacting with surfaces and also the locations of the emitters and the sounds they emit. Due to these aspects, detailed audio reconstruction requires extensive sampling of audio at any potential listener location. This is usually difficult to implement in realistic real-time dynamic scenes. In this work, we propose to circumvent the need for extensive sensors by leveraging audio and visual samples from only a handful of A/V receivers placed in the scene. In particular, we introduce a novel method and end-to-end integrated rendering pipeline which allows the listener to be everywhere and hear everything (BEE) in a dynamic scene in real-time. BEE reconstructs the audio with two main modules, Joint Audio-Visual Representation, and Integrated Rendering Head. The first module extracts the informative audio-visual features of the scene from sparse A/V reference samples, while the second module integrates the audio samples with learned time-frequency transformations to obtain the target sound. Our experiments indicate that BEE outperforms existing methods by a large margin in terms of quality of sound reconstruction, can generalize to scenes not seen in training and runs in real-time speed.

Latent Variable Models (LVMs) propose to model the dynamics of neural populations by capturing low-dimensional structures that represent features involved in neural activity. Recent LVMs are based on deep learning methodology where a deep neural network is trained to reconstruct the same neural activity given as input and as a result to build the latent representation. Without taking past or future activity into account such a task is non-causal. In contrast, the task of forecasting neural activity based on given input extends the reconstruction task. LVMs that are trained on such a task could potentially capture temporal causality constraints within its latent representation. Forecasting has received less attention than reconstruction due to recording challenges such as limited neural measurements and trials. In this work, we address modeling neural population dynamics via the forecasting task and improve forecasting performance by including a prior, which consists of pairwise neural unit interaction as a multivariate dynamic system. Our proposed model---Additive, Multiplicative, and Adaptive Graph Neural Network (AMAG)---leverages additive and multiplicative message-passing operations analogous to the interactions in neuronal systems and adaptively learns the interaction among neural units to forecast their future activity. We demonstrate the advantage of AMAG compared to non-GNN based methods on synthetic data and multiple modalities of neural recordings (field potentials from penetrating electrodes or surface-level micro-electrocorticography) from four rhesus macaques. Our results show the ability of AMAG to recover ground truth spatial interactions and yield estimation for future dynamics of the neural population.

Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal activity is a combination of its time-invariant identity and the inputs the neuron receives from the rest of the circuit. Here, we propose a self-supervised learning based method to assign time-invariant representations to individual neurons based on permutation-, and population size-invariant summary of population recordings. We fit dynamical models to neuronal activity to learn a representation by considering the activity of both the individual and the neighboring population. Our self-supervised approach and use of implicit representations enable robust inference against imperfections such as partial overlap of neurons across sessions, trial-to-trial variability, and limited availability of molecular (transcriptomic) labels for downstream supervised tasks. We demonstrate our method on a public multimodal dataset of mouse cortical neuronal activity and transcriptomic labels. We report >35\% improvement in predicting the transcriptomic subclass identity and >20\% improvement in predicting class identity with respect to the state-of-the-art.

Modeling neural population dynamics underlying noisy single-trial spiking activities is essential for relating neural observation and behavior. A recent non-recurrent method - Neural Data Transformers (NDT) - has shown great success in capturing neural dynamics with low inference latency without an explicit dynamical model. However, NDT focuses on modeling the temporal evolution of the population activity while neglecting the rich covariation between individual neurons. In this paper we introduce SpatioTemporal Neural Data Transformer (STNDT), an NDT-based architecture that explicitly models responses of individual neurons in the population across time and space to uncover their underlying firing rates. In addition, we propose a contrastive learning loss that works in accordance with mask modeling objective to further improve the predictive performance. We show that our model achieves state-of-the-art performance on ensemble level in estimating neural activities across four neural datasets, demonstrating its capability to capture autonomous and non-autonomous dynamics spanning different cortical regions while being completely agnostic to the specific behaviors at hand. Furthermore, STNDT spatial attention mechanism reveals consistently important subsets of neurons that play a vital role in driving the response of the entire population, providing interpretability and key insights into how the population of neurons performs computation.

The spatial acoustic information of a scene, i.e., how sounds emitted from a particular location in the scene are perceived in another location, is key for immersive scene modeling. Robust representation of scene's acoustics can be formulated through a continuous field formulation along with impulse responses varied by emitter-listener locations. The impulse responses are then used to render sounds perceived by the listener. While such representation is advantageous, parameterization of impulse responses for generic scenes presents itself as a challenge. Indeed, traditional pre-computation methods have only implemented parameterization at discrete probe points and require large storage, while other existing methods such as geometry-based sound simulations still suffer from inability to simulate all wave-based sound effects. In this work, we introduce a novel neural network for light-weight Implicit Neural Representation for Audio Scenes (INRAS), which can render a high fidelity time-domain impulse responses at any arbitrary emitter-listener positions by learning a continuous implicit function. INRAS disentangles scene’s geometry features with three modules to generate independent features for the emitter, the geometry of the scene, and the listener respectively. These lead to an efficient reuse of scene-dependent features and support effective multi-condition training for multiple scenes. Our experimental results show that INRAS outperforms existing approaches for representation and rendering of sounds for varying emitter-listener locations in all aspects, including the impulse response quality, inference speed, and storage requirements.

The representation of the flow of information between neurons in the brain based on their activity is termed the causal functional connectome. Such representation incorporates the dynamic nature of neuronal activity and causal interactions between them. In contrast to connectome, the causal functional connectome is not directly observed and needs to be inferred from neural time series. A popular statistical framework for inferring causal connectivity from observations is the directed probabilistic graphical modeling. Its common formulation is not suitable for neural time series since it was developed for variables with independent and identically distributed static samples. In this work, we propose to model and estimate the causal functional connectivity from neural time series using a novel approach that adapts directed probabilistic graphical modeling to the time series scenario. In particular, we develop the Time-Aware PC (TPC) algorithm for estimating the causal functional connectivity, which adapts the PC algorithm-a state-of-the-art method for statistical causal inference. We show that the model outcome of TPC has the properties of reflecting causality of neural interactions such as being non-parametric, exhibits the directed Markov property in a time-series setting, and is predictive of the consequence of counterfactual interventions on the time series. We demonstrate the utility of the methodology to obtain the causal functional connectome for several datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex.

One of the primary purposes of video is to capture people and their unique activities. It is often the case that the experience of watching the video can be enhanced by adding a musical soundtrack that is in-sync with the rhythmic features of these activities. How would this soundtrack sound? Such a problem is challenging since little is known about capturing the rhythmic nature of free body movements. In this work, we explore this problem and propose a novel system, called `RhythmicNet', which takes as an input a video which includes human movements and generates a soundtrack for it. RhythmicNet works directly with human movements by extracting skeleton keypoints and implements a sequence of models which translate the keypoints to rhythmic sounds.RhythmicNet follows the natural process of music improvisation which includes the prescription of streams of the beat, the rhythm and the melody. In particular, RhythmicNet first infers the music beat and the style pattern from body keypoints per each frame to produce rhythm. Next, it implements a transformer-based model to generate the hits of drum instruments and implements a U-net based model to generate the velocity and the offsets of the instruments. Additional types of instruments are added to the soundtrack by further conditioning on the generated drum sounds. We evaluate RhythmicNet on large scale datasets of videos that include body movements with inherit sound association, such as dance, as well as 'in the wild' internet videos of various movements and actions. We show that the method can generate plausible music that aligns well with different types of human movements.

We propose a novel system for unsupervised skeleton-based action recognition. Given inputs of body-keypoints sequences obtained during various movements, our system associates the sequences with actions. Our system is based on an encoder-decoder recurrent neural network, where the encoder learns a separable feature representation within its hidden states formed by training the model to perform the prediction task. We show that according to such unsupervised training, the decoder and the encoder self-organize their hidden states into a feature space which clusters similar movements into the same cluster and distinct movements into distant clusters. Current state-of-the-art methods for action recognition are strongly supervised, i.e., rely on providing labels for training. Unsupervised methods have been proposed, however, they require camera and depth inputs (RGB+D) at each time step. In contrast, our system is fully unsupervised, does not require action labels at any stage and can operate with body-keypoints input only. Furthermore, the method can perform on various dimensions of body-keypoints (2D or 3D) and can include additional cues describing movements. We evaluate our system on three action recognition benchmarks with different numbers of actions and examples. Our results outperform prior unsupervised skeleton-based methods, unsupervised RGB+D based methods on cross-view tests and while being unsupervised have similar performance to supervised skeleton-based action recognition.

We present a novel system that gets as an input, video frames of a musician playing the piano, and generates the music for that video. The generation of music from visual cues is a challenging problem and it is not clear whether it is an attainable goal at all. Our main aim in this work is to explore the plausibility of such a transformation and to identify cues and components able to carry the association of sounds with visual events. To achieve the transformation we built a full pipeline named 'Audeo' containing three components. We first translate the video frames of the keyboard and the musician hand movements into raw mechanical musical symbolic representation Piano-Roll (Roll) for each video frame which represents the keys pressed at each time step. We then adapt the Roll to be amenable for audio synthesis by including temporal correlations. This step turns out to be critical for meaningful audio generation. In the last step, we implement Midi synthesizers to generate realistic music. Audeo converts video to audio smoothly and clearly with only a few setup constraints. We evaluate Audeo on piano performance videos collected from Youtube and obtain that their generated music is of reasonable audio quality and can be successfully recognized with high precision by popular music identification software.

We present a method that gets as input an audio of violin or piano playing, and outputs a video of skeleton predictions which are further used to animate an avatar. The key idea is to create an animation of an avatar that moves their hands similarly to how a pianist or violinist would do, just from audio. Notably, it's not clear if body movement can be predicted from music at all and our aim in this work is to explore this possibility. In this paper, we present the first result that shows that natural body dynamics can be predicted. We built an LSTM network that is trained on violin and piano recital videos uploaded to the Internet. The predicted points are applied onto a rigged avatar to create the animation.

We study the dynamics of a quadratic integrate-and-fire model of a single-compartment neuron with a slow recovery variable, as input current and parameters describing timescales, recovery variable, and postspike reset change. Analysis of a codimension 2 bifurcation reveals that the domain of attraction of a stable hyperpolarized rest state interacts subtly with reset parameters, which reposition the system state after spiking. We obtain explicit approximations of instantaneous firing rates for fixed values of the recovery variable, and use the averaging theorem to obtain asymptotic firing rates as a function of current and reset parameters. Along with the different phase-plane geometries, these computations provide explicit tools for the interpretation of different spiking patterns and guide parameter selection in modeling different cortical cell types.