🧠 neuroscience

Model-based pupil deconvolution reveals latent attentional dynamics

This paper introduces a dual-kernel deconvolution model that separates pupillary constriction and dilation to recover high-temporal-resolution latent attentional dynamics from pupil signals, overcoming the limitations of the sluggish pupillary response in rapid visual paradigms.

Original authors: Maity, S., Mathot, S., Ray, S. B.

Published 2026-10-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Maity, S., Mathot, S., Ray, S. B.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The human brain is a master of filtering, constantly sifting through a flood of visual information to focus on what matters most. When we look at a busy street or a crowded room, our attention acts like a spotlight, illuminating specific details while leaving the rest in the shadows. However, this spotlight does not switch on and off instantly; it takes a moment to engage and a moment to disengage. If two important things appear in our vision very close together in time, the brain often struggles to process the second one. This phenomenon, known as the attentional blink, is a well-documented limit of human perception. To study how this spotlight works, scientists have long turned to the pupil of the eye. The pupil does more than just react to light; it also expands in response to mental effort and attention. By watching the pupil, researchers can get a glimpse into the brain's cognitive state. Yet, there is a significant problem with this method: the pupil is slow. It takes time to widen and time to shrink, meaning that if two events happen quickly one after another, the pupil's reaction to the first event is still unfolding when the second event occurs. The two reactions blur together, making it nearly impossible to tell exactly when the brain paid attention to each specific item.

A team of researchers set out to solve this timing problem by developing a new way to look at the data. They wanted to see if they could untangle the blurred pupil signals to reveal the hidden, rapid-fire moments of attention that occurred deep within the brain. To do this, they designed an experiment where participants watched a rapid stream of faces flashing on a screen. The faces appeared so quickly—each for just 100 milliseconds, followed by a brief pause—that the brain had to work hard to keep up. In most of the trials, two emotional faces, such as a happy or angry expression, were hidden among neutral ones. The researchers asked the participants to identify these emotional faces. As the participants watched, the team recorded their pupil movements with high-speed cameras. The goal was to see if the pupil's behavior changed depending on whether the participant successfully noticed both emotional faces or missed the second one.

The challenge was that the raw pupil data looked like a single, messy wave. Because the faces flashed so fast, the pupil's reaction to the first face had not finished before the second face appeared, causing the signals to overlap completely. To cut through this confusion, the researchers created a new mathematical model. Instead of treating the pupil's reaction as a single, slow event, they modeled it as two distinct parts working together. The first part is the immediate, reflexive shrinking of the pupil when a bright image hits the eye. The second part is the slower, deliberate widening that happens when the brain focuses its attention. By separating these two physical processes, the team could mathematically reverse the process. They took the messy, overlapping wave of the recorded pupil data and worked backward to estimate the hidden pattern of attention that must have caused it. This approach allowed them to reconstruct the timeline of attention with a precision that the raw data alone could never provide.

When they applied this new method to the data, the hidden patterns emerged clearly. The researchers found that when participants successfully identified both emotional faces, the model revealed two distinct peaks of attention. The first peak corresponded to the moment the brain focused on the first face, and the second peak appeared when the brain focused on the second face. However, when participants missed the second face—a classic "attentional blink"—the second peak was significantly weaker or missing entirely. This confirmed that the model could successfully recover the hidden moments of attention, even when the physical pupil response was too slow to show them directly. The study also looked at whether the emotion of the faces, such as happiness or anger, changed the strength of these attentional peaks. While the participants' performance on the screen did vary slightly depending on the emotions, the model showed that the underlying strength of the attentional episodes remained surprisingly consistent across different emotional combinations.

This work demonstrates that the slow, sluggish nature of the pupil does not have to be a barrier to understanding fast brain processes. By using a dual-part model to separate the reflexive shrinking from the attentional widening, the researchers could extract a clear timeline of mental focus from a blurred signal. The findings suggest that attention operates in discrete, short bursts, and that these bursts can be measured non-invasively by looking at the eyes. The team also made their new method available as a software tool for other scientists to use, opening the door for more precise studies of how the human mind navigates a fast-paced visual world. Ultimately, the study proves that even when the body's signals are slow, the right analytical lens can reveal the speed and rhythm of the mind.

Technical Summary: Model-based Pupil Deconvolution Reveals Latent Attentional Dynamics

Problem Statement

Visual attention operates on a timescale significantly faster than the physiological pupillary response. While pupil size is a well-established non-invasive proxy for attentional engagement and cognitive load, its slow temporal dynamics (characterized by a sluggish rise and prolonged decay) make it difficult to resolve attentional responses to stimuli presented in rapid succession, such as in Rapid Serial Visual Presentation (RSVP) paradigms. In these scenarios, the pupil responses to successive events overlap extensively, obscuring the distinct temporal profile of individual attentional episodes.

Furthermore, existing methods for estimating latent attentional episodes from pupil data via deconvolution (e.g., Wierda et al., 2012) primarily model the dilation phase of the pupil response. They fail to account for the biphasic nature of the pupil's reaction to visual stimuli, which includes an early, fast constriction phase (the pupillary light reflex, PLR) followed by a slower dilation phase. This limitation prevents accurate dissociation of attentional events that occur during the early constriction window or when multiple stimuli overlap within the biphasic response.

Methodology

Experimental Paradigm

The study employed an RSVP task adapted from Ray et al. (2020) to elicit the Attentional Blink (AB) effect.

Stimuli: Emotional faces (Happy, Angry) served as targets, while Neutral faces served as distractors. Images were sourced from the Radboud Face Database and luminance-equalized.
Procedure: Trials began with a 1000 ms fixation, followed by a stream of 15 faces presented for 100 ms each, interleaved with 50 ms blanks.
Conditions:
- Two-target trials (80%): Two emotional targets (T1 and T2) were presented. T1 appeared at serial positions 4–6. T2 appeared at varying lags relative to T1 (Lag 1: 150 ms, Lag 2: 300 ms, Lag 3: 450 ms, Lag 5: 750 ms).
- Single-target trials (20%): Only T1 was presented.
Participants: 32 participants (after exclusion criteria) from the University of Groningen. Pupil data were recorded monocularly at 500 Hz using an EyeLink 1000.

The Dual-Kernel Deconvolution Model

The core methodological contribution is a model-based deconvolution approach that treats the pupil response as a Linear Time-Invariant (LTI) system driven by latent attentional events. Unlike previous single-kernel approaches, this model utilizes two distinct impulse response functions (kernels):

Constriction Kernel ( $h_{constriction}$ ): Modeled as an inverted Erlang-Gamma function to capture the fast, reflexive pupil constriction triggered by the onset of the visual stream. It is anchored to the estimated PLR latency (derived from the steepest negative slope within the first 400 ms).
Dilation Kernel ( $h_{dilation}$ ): Modeled using the standard Erlang-Gamma function (Hoeks & Levelt, 1993) to capture the slower, task-evoked dilation associated with attentional engagement. This kernel is convolved at discrete time points corresponding to potential attentional episodes (150 ms bins).

Signal Reconstruction:
The observed pupil signal $y(t)$ is modeled as the sum of:

The convolution of a single constriction event with the constriction kernel.
The convolution of a sequence of latent attentional episodes ( $i_{attn}$ ) with the dilation kernel.
A linear drift component to account for baseline fluctuations.

$\hat{y}(t) = (i_{PLR} * h_{PLR})(t) + (i_{attn} * h_{attn})(t) + \beta t$

Optimization:
The amplitudes of the latent attentional episodes and the drift parameter were estimated by minimizing the mean squared error between the predicted and observed pupil signals using a bounded quasi-Newton method (L-BFGS-B). The optimization was repeated 50 times with randomized initializations to avoid local minima.

Software Implementation:
The authors developed PupilDeconvolve, an open-source Python package implementing this dual-kernel pipeline, utilizing Fast Fourier Transform (FFT) for efficient convolution.

Key Results

Behavioral Performance

Attentional Blink: A robust AB effect was confirmed, with T2 accuracy significantly lower at Lag 1 compared to later lags.
Emotional Modulation: The magnitude of the AB varied as a function of the emotional pairing of T1 and T2 (e.g., Happy-Happy vs. Angry-Angry), replicating previous findings (Ray et al., 2020).

Pupil Response Analysis

Raw Pupil Data: Direct analysis of the raw pupil signal revealed no significant differences between "Blink" (T2 missed) and "No-Blink" (T2 detected) trials, nor between different emotional conditions. The overlapping nature of the responses in the RSVP stream prevented the isolation of condition-specific effects in the raw signal.

Latent Attentional Episodes (Deconvolved Data)

The deconvolution model successfully recovered distinct temporal dynamics that were invisible in the raw data:

Blink vs. No-Blink: The amplitude of the recovered attentional episodes was significantly higher in the "No-Blink" condition compared to the "Blink" condition, particularly in a time window between 900 ms and 1800 ms. This aligns with the hypothesis that successful T2 processing requires greater attentional engagement.
Temporal Structure: In "No-Blink" trials, two distinct groups of attentional episodes were observed: one corresponding to T1 processing (700–900 ms) and a second corresponding to T2 processing (1100–1400 ms).
Single-Target Condition: Even in trials with only one target, a second attentional episode was observed (1100–1300 ms), which the authors interpret as an expectancy effect given the low probability (20%) of single-target trials.
Emotional Valence: Despite behavioral differences based on emotional valence, the amplitude of the recovered attentional episodes did not differ significantly across emotional pair conditions (HH, HA, AA, AH). The authors suggest this may be due to the aggregation of trials across lags or the temporal window of the RSVP being insufficient to resolve valence-specific dynamics in the pupil response.

Significance and Claims

The paper claims that the proposed dual-kernel deconvolution model overcomes the temporal resolution limitations of conventional pupillometry in rapid visual paradigms. By explicitly modeling both the constriction and dilation phases, the method allows for the recovery of latent attentional episodes that are temporally distinct, even when the underlying pupil signals overlap substantially.

The study demonstrates that:

Latent dynamics are recoverable: The temporal profile of attentional allocation (specifically the episodic nature of attention described by the eSTST model) can be inferred from the pupil signal with a resolution previously obscured by the pupil's sluggishness.
Validation against theory: The recovered attentional episodes align with established theories of the Attentional Blink, showing distinct processing phases for T1 and T2 and reduced engagement when T2 is missed.
Tool availability: The method is provided as a general-purpose software tool (PupilDeconvolve) for investigating temporal attention dynamics in rapid visual tasks, offering a non-invasive alternative or complement to neuroimaging methods like EEG and MEG.

The authors maintain a modest stance regarding the emotional valence results, acknowledging that while behavioral effects were present, the model did not detect corresponding differences in attentional episode amplitude, potentially due to methodological constraints (trial aggregation and temporal resolution limits of the RSVP window). They emphasize that the estimated episodes are approximations based on an LTI assumption and should be interpreted as model-derived estimates rather than direct physiological measurements.