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Analog Cognition and Consciousness

Earl K. Miller, Scott L. Brincat, and Jefferson E. Roy The Picower Institute for Learning & Memory and Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology

Corresponding Author: Earl K. Miller, MIT, 77 Massachusetts Ave, Cambridge, MA 02139 USA Email: ekmiller@mit.edu

All authors approve the paper.

Competing interest statement: The authors declare no conflict of interest.

Keywords: cognition, consciousness

Abstract

Cognition and consciousness may arise from bidirectional interactions between neuron spiking and large-scale brain waves. We propose that, while synapses store memories, brain waves provide an executive-like control process that organizes millions of neurons into lowerdimensional, coordinated patterns in real time. These waves can implement analog computation, generating new patterns of neural excitation according to underlying computational principles. Their top-down influences can flexibly route and organize neural signals, allowing multifunctional neurons to assume different roles depending on context. This flexibility is the sine qua non of cognition. Goal-directed thought, action, and unified consciousness may thus emerge from organized, cortex-wide wave patterns that both reflect and transform the information expressed by spiking, thereby shaping it into organized brain states.

Introduction

Cognition is the brain’s use of internal representations (e.g., schemas, goals, and memories) to mediate between stimuli and responses. To do so, we evolved top-down feedback mechanisms that filter and modulate feedforward sensory inputs, control actions, and retrieve stored memories and, at the highest levels, include executive functions that align thought and action with future goals (Desimone and Duncan, 1995; Miller and Cohen, 2001; Buschman and Miller, 2007; Bastos et al., 2012). Many top-down processes are unconscious, but they can become conscious to support deliberation, long-term planning, and the inhibition of automatic yet counterproductive impulses. This kind of flexible, self-directed neural processing requires a control system that can coordinate hundreds of millions of neurons within fractions of a second.

This is hard to reconcile with traditional models that view brain function as arising only from brief electrical impulses (“spikes”) transmitted through networks shaped by the synaptic connections between neurons. Spiking and synaptic connections are, of course, critical and fundamental. However, synaptic changes are likely too cumbersome for flexible top-down control. That would require a control system to “know” which synapses and neurons were employed for any given neural representation and selectively coordinate them with subsecond precision, a seemingly implausible computational demand.

A biologically plausible mechanism may involve an emergent level of influence from electric field oscillations, i.e., brain waves. These waves reflect reverberating activity in neural circuits coordinated over millimeter-to-centimeter scales, providing a basic internal organization beyond simple feedforward reactions to the environment. Evolution could exploit this default organization by developing mechanisms that control oscillatory dynamics. Crucially, brain waves do not merely mirror spiking activity. They alter the electrical field environment that is itself critical for generating spikes. Spikes shape brain waves, while the waves in turn influence when and where spikes occur. We outline evidence for a complementary framework in which synaptic connections and spikes interact with brain wave dynamics to support the coordination and computation underlying cognition and consciousness.

20th century neuroscience: The classical model of neural information processing

A useful starting point is to contrast our hybrid spike/wave view of cortical function with traditional connectionist models. Classic models emphasize computation and memory through changes in synaptic weights driving spiking activity in specialized neurons. Drawing on logic-

Feedforward

Higher cortex

Features, objects, and categories

Intermediate cortex

Details combine and generalize across location

Primary and secondary sensory cortex

Low-level details in specific locations

Figure 1 – The connectionist view of cortical processing. Lower visual areas detect simple features such as lines and edges, then feed this information forward along the cortical hierarchy, where neurons combine these features into increasingly complex and specialized representations (e.g., limbs, paws, nose, whiskers), until the brain constructs a representation [Image: Image25]of a holistic category or concept (e.g., cat, dog).

gate metaphors from early sensory physiology, they describe hierarchical feedforward circuits in which neurons become tuned to progressively more complex features (Fig. 1). This was thought to result in a modular set of brain networks and areas with discrete, non-overlapping functions.
In this view, each neuron serves a stable, specialized function, i.e., a given neuron’s spikes always “mean” the same unique thing. The thought was that if we could decode each neuron’s message, their connections, and their collection into a functional patchwork of cortical areas, we could, in principle, understand the brain.

This framework is not wrong, but it is incomplete. The connectionist approach was foundational and remains a good account of feedforward processing in the sensory cortex. But it cannot explain many observations. An early example was the consistent finding that any given task engages around a third of all neurons in the prefrontal cortex (Asaad et al., 2000; Freedman et al., 2001; Wallis et al., 2001; Xiang et al., 2025). Under the traditional connectionist model, this would imply that we can only learn about three different cognitive functions before essentially all prefrontal neurons have been “assigned a function”, and its computational capacity is saturated.
Alternatively, many cortical neurons may be multifunctional, rather than specialized (Duncan and Miller, 2013, 2002). Subsequently, it was confirmed that many cortical (and subcortical) neurons do indeed multiplex different kinds of information in their activity (Asaad et al., 2000; Warden and Miller, 2007; Cromer et al., 2010; Akam and Kullmann, 2014; Lankarany et al., 2019; Ramakrishnan et al., 2017; Rigotti et al., 2013). This phenomenon has come to be called nonlinear “mixed selectivity” (Fusi et al., 2016; Rigotti et al., 2013; Tye et al., 2024)

Mixed Selectivity: Multifunctional neurons enable flexible cognition

To understand mixed selectivity, consider a task in which two objects and their order (first vs second) must be remembered (Fig. 2A) (Warden and Miller, 2007). Classical “pure” selectivity for object identity would predict similar neural responses to the same objects, regardless of their order in the sequence (Fig. 2B), as well as neurons whose sole function was to keep track of order. Mixed selectivity instead predicts that neurons reflect nonlinear combinations of

A Object sequence memory task

PanelPhaseObject shownTime (relative)Recall (correct)
A — Object sequence memory task1st object (encoding)Butterfly (1)Early—
A — Object sequence memory task2nd object (encoding)Green latch (2)Later—
A — Object sequence memory taskRecallButterfly (1)—Yes
A — Object sequence memory taskRecallGreen latch (2)—Yes
A — Object sequence memory taskRecallBlue flower (3)—No
Series (color)1st stimulus (green ring) — peak time (approx.)1st stimulus — peak activity (approx.)2nd stimulus (blue flower) — peak time (approx.)2nd stimulus — peak activity (approx.)3rd stimulus (orange butterfly) — peak time (approx.)3rd stimulus — peak activity (approx.)
Green (1st)~1.0~1.0~2.0~1.0~2.0~0.8
Blue (2nd)~1.2~0.8~1.8~0.8~2.0~0.6
Orange (3rd)~1.4~0.5~2.0~0.5~2.2~0.4
Series (color)1st sequence order – peak (relative)1st sequence order – trough (relative)2nd sequence order – peak (relative)2nd sequence order – trough (relative)
Green (top)~1.00~0.30~0.15~0.05
Blue (middle)~0.75~0.35~0.55~0.25
Orange (bottom)~0.30~0.20~0.90~0.35

Figure 2 – Schematic illustration of pure vs mixed selectivity in an example task. (A) Task structure. Subjects were required to briefly remember the identity and order of a sequence of two objects, then reproduce the sequence from memory. (B) A neuron with “pure” selectivity for object identity would show the same responses to objects, regardless of their order. (C) A neuron with nonlinear mixed selectivity might show different object preferences, depending on the context of the objects’ sequential order. [Image: Image48]

variables, often integrating contextual information (like order) with sensory inputs (like objects) and motor actions. In our example, this corresponds to selective spiking to objects that changes depending on the context of their sequence order (Fig. 2C), as we observed in many prefrontal neurons (Rigotti et al., 2013; Warden and Miller, 2007). A neuron might spike to object A, but only when it was seen first, and to object B, but only when it is seen second.

Thus, these neurons embody the flexible, context-dependent behavior associated with higher cognition (Rigotti et al., 2013; Fusi et al., 2016; Tye et al., 2024). Modeling studies show that such neurons greatly expand a network’s computational power by providing a higher-order representational space (Rigotti et al., 2013; Fusi et al., 2016; Tye et al., 2024). Further, they also greatly expand a network’s capacity to store information because information is multiplexed across many multifunctional neurons rather than segregated into specialist neurons (Rigotti et al., 2013). But they are not merely the “icing on the cake” of cortical processing. Instead, nonlinear mixed selectivity seems to reflect a core computational principle (Johnston et al., 2020). They are prevalent in higher areas like prefrontal cortex (Abbass et al., 2025; Dang et al., 2022; Mouille et al., 2025; Parthasarathy et al., 2017; Warden and Miller, 2007) but also in primary sensory and motor cortex (Grunfeld and Likhtik, 2018; Kaufman et al., 2022; Kira et al., 2023; Tseng et al., 2022; Tye et al., 2024).

Because mixed selectivity neurons blend sensory, motor, and contextual information, they are inherently multifunctional, sending different messages in different situations. This indicates the cortex is not a mosaic of isolated, specialized, circuits of specialized areas. This means that cortical neurons have the capacity to participate in multiple networks, shifting membership as needed.

A control system therefore has the challenge of dynamically routing signals through a dense web of overlapping networks, allowing the same neurons to contribute to different computations in different contexts. Such flexible routing is difficult to reconcile with a purely connectionist framework based solely on changing synaptic weights. A more computationally tractable mechanism seems to be needed. Neural oscillations, i.e., brain waves, could serve that role.

Oscillations organize neural information

Neural oscillations are rhythmic fluctuations in intracellular potential that reflect coordinated neural activity over a mesoscale range of millimeters to centimeters (Buzsáki, 2006). Their phases reflect alternating periods of relative neural excitation and inhibition and thus change the electric field environment in the tissue surrounding neurons. This can be measured extracellularly within the brain as local field potentials (LFPs) or externally as the EEG.

Neural oscillations are not just a passive byproduct of spiking activity, they help actively shape it. Evidence shows that oscillations have several well-established computational roles: organizing information, routing it between circuits, and coordinating memory and control processes (Buzsáki, 2006; Sejnowski and Paulsen, 2006; Miller et al., 2024; Singer and Effenberger, 2025). In both cortex and hippocampus, information is organized by segregating spiking to different phases of local oscillations (Lisman and Jensen, 2013; Siegel et al., 2009; Skaggs et al., 1996). Oscillations are also thought to route information locally (Odean et al., 2023) and selectively facilitate long-range cortical communication by creating temporal windows when target regions are more vs less receptive to inputs (Fries, 2015; Womelsdorf et al., 2007).
Further, cortical feedforward and feedback processing are associated with oscillations in distinct frequency bands, gamma (~30–80 Hz) vs alpha/beta (~10–30 Hz), respectively (Buschman and Miller, 2007; Van Kerkoerle et al., 2014; Bastos et al., 2015; Mendoza-Halliday et al., 2024).

In all of these cases, brain waves both reflect and instantiate a coordination of large populations of spiking neurons. These oscillations are particularly suited for a role in top-down control because they can have direct, rapid influence on neuronal activity via extra-synaptic means, by ephaptic coupling effects.

Oscillations directly influence spiking via ephaptic coupling

Oscillatory fluctuations in extracellular electric fields have direct field effects on the intracellular potentials and spiking activity of nearby neurons. Ephaptic coupling in the brain is the influence of neuronal electric fields on nearby neurons’ membrane potentials, allowing interaction and coordination independent of synapses (Anastassiou and Koch, 2015; Chiang et al., 2019; Faber and Pereda, 2018; Han et al., 2020; Katz and Schmitt, 1940; Pinotsis and Miller, 2023; Schmidt et al., 2021a; Hunt and MacIver, 2026). For example, cerebellar Purkinje cells generate extracellular potentials that are large enough to drive synchrony in nearby cells, even when chemical synapses and gap junctions are blocked (Han et al., 2018). Externally applied electric fields with strength in the range of endogenous fields can modulate and propagate neural waves, alter spike timing, and synchronize neurons (Anastassiou et al., 2011; Fröhlich and McCormick, 2010; Jæger and Tveito, 2026; Radman et al., 2007; Ruffini et al., 2020; Schloetter et al., 2025). Because many cortical neurons operate with membrane potentials fluctuating near the spike threshold, even weak oscillatory extracellular fields can induce small subthreshold voltage changes that significantly modulate both spiking probability and spike timing in local populations of neurons (Buzsáki and Draguhn, 2004; Ladenbauer and Obermayer, 2019; Radman et al., 2007). Individual ephaptic interactions, when synchronized and summed across neurons, create effects large enough to shape and coordinate neuron spiking at the mesoscale (Goldwyn and Rinzel, 2016; Cunha et al., 2024). This feedback of electric field effects onto spiking activity can thus recruit neurons into an activated population, as well as spatially and temporally coordinate their activity.

Neural organization and communication via electric fields potentially offers key advantages over traditional spiking and synaptic mechanisms. While spiking activity is itself very localized, the electric fields it helps create can spread across millimeters or more, due to correlated activity (Łęski et al., 2013; Xing et al., 2009). This could coordinate large cortical neighborhoods simultaneously. Individual spikes are brief, and cortical firing is sparse in space and time, with most neurons firing only a few spikes per second on average in brief bursts followed by longer periods of no spiking (Levenstein and Okun, 2023). In contrast, electric fields are continuous population activity and influence essentially all neurons within a local volume (Anastassiou and Koch, 2015). Further, the speed of spike-based synaptic signalling is limited by conduction along axons and transmission across synapses. By contrast, changes in electric fields arise essentially concurrently with the underlying transmembrane currents and spread through the local tissue at the speed of electromagnetic propagation, making them effectively instantaneous on neuronal timescales (Han et al., 2008; Schmidt et al., 2021b; Teleńczuk et al., 2017). This speed makes electric fields well suited for rapidly coordinating local activity (Pinotsis and Miller, 2023). Beyond effects at the level of spiking activity, electric field oscillations may also tune neural circuitry at a molecular level, improving network efficiency (Pinotsis et al., 2023).

These properties make oscillatory electric fields excellent candidates for rapid, large-scale control. They can align spike timing, activate or suppress ensembles, and flexibly route information across overlapping networks to support adaptive top-down control (Hunt and MacIver, 2026).

Spatial Computing: A theory of oscillatory control of neural information

The “Spatial Computing” model builds on this idea by proposing how spatially-structured oscillations can exert flexible executive control over neural computation (Lundqvist et al., 2023). It also exploits the distinct functional roles and push-pull relationship between gamma (~30–80 Hz) vs alpha and beta (~13–30 Hz) rhythms (see “Organization by Oscillations”).

Gamma rhythms are associated with net excitation and thus increased spiking, while alpha/beta

A Executive control Spatially-structured top-down connectivity Alpha/beta 1st 2nd

B Sensory information Random feedforward/current connectivity Gamma & spiking activity

determines population neural activity

1st

2nd

Figure 3 – Schematic illustration of Spatial Computing theory. (A) Spatially-structured alpha/beta oscillations convey signals related to context, goals, and control. Here, the blue and purple regions represent spatial locations of strong alpha/beta reflecting the contextual sequential order of objects in our example task. (B) Spatially-random feedforward and recurrent connections convey the sensory “contents” of cognition via gamma oscillations and spiking. Activation (colored “neurons”) induced by two object stimuli is illustrated. (C) The interaction of these two signals determines where information is expressed in neural activity. Here, the same object induces two different spatial patterns of population response, depending on the sculpting effects of alpha/beta. [Image: Image100]

rhythms are linked to reduced activity. In the motor cortex, for example, beta acts like a brake on movement execution. When alpha/beta decreases locally, gamma and spiking increase, and movement becomes more likely (Barone and Rossiter, 2021; Engel and Fries, 2010; Khanna and Carmena, 2017). A reasonable hypothesis is that top-down control in general evolved from this basic mechanism for regulating action.
Indeed, we found these gamma vs alpha/beta oscillations form a specific laminar pattern conserved across four species (mouse, marmoset, macaque, and human) and multiple (14+) cortical areas: Gamma is highest in cortical superficial (feedforward) layers, while alpha/beta is

strongest in deep (feedback) layers (Mendoza-Halliday et al., 2024).

Spatial computing theory (Fig. 3) proposes that alpha/beta rhythms convey internally-generated signals whose spatial patterning reflects top-down information (Fig. 3A). They function as temporary inhibitory “stencils” across the surface of cortex. This regulates gamma and spiking in the feedforward and local recurrent circuits that carry sensory-related cognitive contents (Fig. 3B) and drive actions. Alpha/beta rhythms thus dampen or suppress gamma and associated spiking in targeted locations, creating a push-pull dynamic that determines where feedforward signals are suppressed. Feedforward signals are then permitted to emerge in the remaining “open” regions, where alpha/beta is weaker. Where spiking is expressed thus depends on the interaction between spatially random feedforward inputs and spatially organized alpha/beta suppression (Fig. 3C).

This scheme allows for flexible control over the neural expression of information in spiking, without the control system needing to know the precise neurons and synapses employed for any specific information (Badre et al., 2021; Chandrasekaran et al., 2025; MacDowell et al., 2022). It also allows for compositional reuse of the same control signals for any arbitrary information. Conversely, the same neuronal population can be reused for any arbitrary task demands, simply by changing the control “stencil” imposed on it (Tafazoli et al., 2026; Xie et al., 2022). This flexible push-pull interaction between alpha/beta and gamma/spiking signals provides a mechanism by which control systems can dynamically organize and shape thought and action.

We recently confirmed several key predictions of Spatial Computing theory by examining prefrontal cortex activity in non-human primates during complex cognitive tasks (Chen et al., 2026). Alpha/beta rhythms reflected learned, internally generated contextual and categorical information, organized into spatial patterns across the cortical surface. These patterns inversely mirrored the spatial distribution of sensory information in spiking activity and predicted behavioral errors through mismatches in contextual representation.

Why the alpha/beta range for top-down control? The spatial scale of influence of waves covaries with temporal frequency (Łęski et al., 2013). Gamma is higher frequency and thus has a finer spatial scale. This is well-suited for forming smaller scale ensembles that carry detailed feedforward information (Berens et al., 2008; Liu and Newsome, 2006). Lower frequency (delta and theta) oscillations can extend over the scale of a cortical area, and thus may be involved in inter-area cortical communication (Adams et al., 2019; Bonnefond et al., 2017; Liebe et al., 2012; Nácher et al., 2013; Womelsdorf and Everling, 2015). Oscillations in the intermediate alpha/beta range, which extend over a range of a few millimeters, might be just the right spatial scale for top-down control (Miller et al., 2024).

Explaining mixed selectivity with spatial computing

Spatial Computing theory provides a straightforward, concrete way for nonlinear mixed selectivity to emerge from wave-based control acting on a large multifunctional population of neurons. Each goal or context creates a unique, temporary alpha/beta “stencil” that suppresses gamma and spiking in some locations while sparing others (e.g. first vs second sequence order in our example; Fig. 3A). Because the neurons have overlapping connectivity, the same neuron may receive many different sensory signals and may lie inside the inhibitory stencil in one context and outside it in another. This context-dependent gating can make a neuron effectively change its selectivity, producing the nonlinear mixed selectivity observed by many studies (Fig. 4A). This account predicts that prefrontal cortex neurons should exhibit spatial organization for goals and contexts, as suggested by recent work (Fang et al., 2025).

In this view, there is no requirement for specialized “context neurons” or “object neurons” with fixed tuning predicted by classical connectionists views of cortex. Instead, mixed selectivity arises from the interaction between broadly responsive neurons and mesoscale wave patterns that control when and where spiking is expressed. Synaptic connectivity provides a rich representational space, while alpha/beta vs gamma dynamics determine which subpopulations are active under each condition, enabling flexible computation.

Mixed selectivity

A

Object

1st

Order

2nd

neuron 2 2nd 1st neuron n neuron 3 neuron 1

Figure 4 – Spatial computing offers mechanistic explanations for mixed selectivity and subspace coding. (A) Schematic of spatial computing for two objects (rows) x two sequential contexts (columns). The neuron labeled ‘1’ lies outside of the suppressive alpha/beta “stencil” in both contexts, resulting in “pure” context-independent object selectivity, as in Fig. 1B. Neuron ‘2’ receives signals for both objects, which are differentially affected in the two contexts, resulting in the context-dependent mixed selectivity in Fig. 1C. (B) Under this scheme, oscillations induce structure in population activity, which is distinct for different contexts. This may also underlie the segregation of different types of information, such as distinct contexts, into orthogonal population activity subspaces. [Image: Image123]

Explaining subspace coding with spatial computing

Mixed selectivity means that single neurons have access to a rich, high-dimensional set of nonlinear features. This information is spread across a population of neurons whose activity is not independent, but instead exhibits structured patterns of coordination. As a result, population spiking tends to occupy a lower-dimensional “subspace” or “manifold” within the highdimensional space defined by all possible population activity patterns (Ebitz and Hayden, 2021). Note that neural coding can be both low-dimensional compared to the high-dimensional code implied by independent activity and high-dimensional compared to the low-dimensional code implied by “pure” unmixed selectivity. This is consistent with broad anatomical gradients in the cortex, which compress signals to create functional equivalences, establishing the anatomical substrate for low dimension representations distributed across a wide population of mixed selectivity neurons (Barrett and Miller, 2026).

Structuring activity via subspace coding is thought to organize information processing, for example by segregating different computations into independent (orthogonal) subspaces to minimize interference (Fig. 4B) (Yoo and Hayden, 2020; Tang et al., 2020; Johnston et al., 2023; Libby and Buschman, 2021; Panichello and Buschman, 2021; Maggi and Humphries, 2022; Xie et al., 2022; Weber et al., 2023; Kaufman et al., 2014; Genkin et al., 2025). Spatial Computing theory also provides a potential neural mechanism for subspace coding. Alpha/beta control signals segregate spiking activity into partially overlapping active subsets, each of which exhibits structured patterns of correlation (Fig. 4A). This is essentially a description of the organization of spiking activity into orthogonal activation subspaces (Fig. 4B).

Notably, over short timescales, population spiking traces smooth trajectories through its activity subspace, consistent with the temporal evolution of a dynamical system (Churchland et al., 2012; Ebitz and Hayden, 2021; Vyas et al., 2020). Different sensory stimuli, cognitive operations, and behaviors follow distinct paths. Distractions may briefly nudge trajectories off course, but the population state usually returns smoothly, such that cortical neurons move together according to shared dynamics. As elaborated below (“Traveling Waves and Representational Change”), these smooth population trajectories may be related to wave dynamics. As traveling waves sweep continuously over the cortex, they may “pull” population spiking activity along, creating repeatable smooth trajectories (Batabyal et al., 2026).

This framework reconciles two observations: Single neurons are noisy and context dependent, yet populations exhibit structured, low-dimensional behavior. Rather than independent units driven solely by local, specialized connections, cortical populations behave like a coordinated flock governed by shared dynamics. Brain waves offer a tractable mechanism for this coordination. Low-dimensional spiking trajectories in subspace can be seen as the spiking-level expression of broader wave-based control signals that impose global structure on neural activity.

Traveling Waves and Representational Change

Brain waves typically do not stand in place. They often sweep across the cortical surface, tracing complex, but highly organized, spatiotemporal patterns referred to as traveling waves (Bhattacharya et al., 2022; Ermentrout and Kleinfeld, 2001; Muller et al., 2018; Sato et al., 2012). Traveling waves have been observed at temporal frequencies ranging from the delta to gamma bands (~1–80 Hz) and move at speeds consistent with propagation via the extensive long-range horizontal connections in superficial layers of cortex (Bringuier et al., 1999; Davis et al., 2021; Grinvald et al., 1994). As they pass over a patch of cortex, traveling waves modulate the excitability of local neurons. There is mounting evidence for a role for traveling waves in a variety of functions, including perception (Aggarwal et al., 2022; Davis et al., 2020; Muller et al., 2014; Townsend et al., 2017), attention (Alamia et al., 2023; Fiebelkorn and Kastner, 2019; Han et al., 2026), memory (Mohan et al., 2024; Patel et al., 2012; Zhang and Jacobs, 2015), and motor planning/execution (Balasubramanian et al., 2020; Best et al., 2016; Rubino et al., 2006; Zanos et al., 2015).

In the motor system, beta rhythms, which are thought to act as a “brake” on movement, typically manifest as traveling waves. In the motor cortex, they are prominent during stable postures and while movements are withheld. They decrease prior to and during movement execution and rebound after movement cessation (Barone and Rossiter, 2021; Engel and Fries, 2010; Khanna and Carmena, 2017). Both the onset of beta rhythms evoked by a movement target (Rubino et al., 2006), and their offset just prior to movement onset (Balasubramanian et al., 2020; Best et al., 2016), have been shown to form a spatiotemporal wave across the surface of motor cortex.
Likewise, in the prefrontal cortex, beta traveling waves are evoked by sensory stimuli and movement. They are also evident at the start of the “memory delay period” in working memory paradigms, when sensory information is loaded into working memory (Bhattacharya et al., 2022). These are also times, not coincidentally we suggest, when prefrontal population spiking activity forms new representations (stimulus and movement onset) or transforms representations between orthogonal coding subspaces (memory delay) (Parthasarathy et al., 2017; Stokes et al., 2013).

We propose that one role of traveling waves, particularly in the alpha/beta band, may be in instantiating state changes in neural coding. That is, by moving patterns of inhibition vs excitation across the surface of cortex, alpha/beta waves can alter which subsets of neurons are permitted to spike and their correlational structure. Thus, we propose that alpha/beta waves may constitute a control mechanism that transitions cortical population activity from one subspace to another. This can be thought of as a dynamic, spatiotemporal extension of Spatial Computing theory, Spatial Computing in motion. In our running example, we suggest traveling waves might be involved in transitioning activity between orthogonal subspaces for the objects presented in the two sequential orders (Fig. 5).

1st 2nd

Figure 5 – Spatiotemporal computing theory suggests traveling waves instantiate coding dynamics. Depicted is the transition between the alpha/beta control “stencil” for the first vs second sequential order context, and the resulting changes in the neural code for a given object. We propose this shift may be driven by alpha/beta traveling waves transitioning from one static pattern to the other. [Image: Image161]

This hypothesis predicts that wave incidence should correlate with the overall temporal dynamics of population activity, but show little variation with specific sensory conditions. This is broadly consistent with the aforementioned wave dynamics, and with the lack of clear differences in wave incidence or direction across task conditions. This hypothesis is also complementary to the traditional view of static beta oscillations as having a role in maintaining stable neural representations (Engel and Fries, 2010). This is usually taken to imply that the inverse situation, representational change, correlates with an overall reduction of beta rhythms.
We suggest that this process, when viewed across a larger spatial region, is better characterized as a shift of beta from one spatial pattern to another, that is a spatiotemporal traveling wave.

Theta (~3–8 Hz) traveling waves, given their lower frequency and spatial scale, may organize and coordinate neural activity on a larger scale. Theta oscillations modulate attentional states (Fiebelkorn and Kastner, 2019) and organize higher-frequency beta (Han et al., 2026) and gamma oscillations (Lisman and Jensen, 2013) via phase-amplitude coupling. Evidence suggests theta traveling waves “drag” coupled beta and gamma (in different theta phases) across the surface of the cortex, influencing readout of information from working memory (Han et al., 2026) and long-term memory (Mohan et al., 2024). Theta waves also travel with alpha waves and appear to form large-scale structures that organize activity across widespread regions of the cortex (Zhang et al., 2018).

Analog Computation with Waves

Here, we consider another function of traveling waves in not just organizing neural activity, but in performing actual computation to create new brain states. [Image: Image175]

SpaceWave 1 (blue)Wave 2 (yellow)Sum (1+2) (black dashed)
00.00.00.0
10.80.81.6
21.01.02.0
30.80.81.6
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5-0.8-0.8-1.6
6-1.0-1.0-2.0
7-0.8-0.8-1.6
80.00.00.0
90.80.81.6
101.01.02.0
110.80.81.6
120.00.00.0

Figure 6 – Analog computing with two sine waves. The sum of two sine waves depends on their relative phase in time and space, producing different resultant values at each point. Each variable is encoded as an amplitude at a specific phase of its respective wave. When the waves interact, all phase-encoded values are processed in parallel. [Image: Image176]

Analog computing uses continuous physical quantities, such as voltages or mechanical motion, to directly represent and solve mathematical problems (Bournez and Pouly, 2018; Hughes et al., 2019; Tzarouchis et al., 2025). Unlike digital systems that rely on binary on/off signals, analog systems combine information continuously. When waves meet, they naturally add together, cancel out, or form new patterns through their superposition and interference (Fig. 6). Simple examples like overlapping sine waves show how addition, subtraction, and thus filtering can

Analog Cognition and Consciousness

emerge directly from wave physics. But analog computation with waves can perform complex math. Early analog machines such as mechanical tide predictors and differential analyzers used wheels and disks to even solve complex 18-variable differential equations. Electric field waves can compute using the same principles (Muller et al., 2018; Singer and Damasio, 2025).

Importantly, analog computing is computationally efficient. In an analog system, the physical medium itself evolves all at once. How the waves interact (e.g., their geometry, frequencies, and phase relationships) model the equation. The variables are all encoded as a continuous physical quantity in different phases of the wave. Because the wave interactions occur everywhere simultaneously, the computation is inherently parallel. An analog system does not loop through variables but settles into a solution as a whole. This is in contrast to digital computing, which is inherently sequential, solving problems one step at a time. Brain‑inspired neuromorphic hardware, motivated by the energy efficiency of biological neural systems, has shown that analog computation can improve energy efficiency over digital by more than an order of magnitude (Ambrogio et al., 2023; Ye et al., 2025).

In the cortex, oscillating electric fields provide a similar medium. Waves of different frequencies move in different directions and at different speeds across the cortical sheet. As they overlap, their interactions can result in temporary excitation of some neuron groups and suppression of others. This might be employed to route and shape neural activity. Slower rhythms can also modulate faster ones, allowing multiple interacting streams of information at once (see below).

Multi-context object sequence memory task

A 1st object 2nd object match recall Time

Analog computing Computation via wave interaction

B 1st + match = 1st & match

C 1st + recall = 1st & recall

Figure 7 – Schematic illustration of analog computing. (A) Extension of example task requiring combination of contextual signals (sequential order and mode of behavioral report–cued recall vs matching). (B,C) Each context is proposed to instantiate a specific spatiotemporal wave as a control signal. The summation of these waves (right) constrains neural activity to a specific pattern unique to [Image: Image193] each combination of contexts.

As a simple concrete example, consider an extension to the previous task that requires combining control signals reflecting two distinct types of task context (Fig. 7A) (Warden and Miller, 2010). The idea is that each of these control signals would correspond to a distinct wave pattern across the cortex (Fig. 7B,C). Their wave summation would essentially compute an intersection of constraints, resulting in a unique spatiotemporal pattern of neural activation for every possible combination of contexts (Fig. 7B,C, right). Of course, this idea is not restricted to only simple combinations of control signals reflecting categorical variables. Waves might also be used to represent continuous

physical quantities (e.g. speed, distance, spatial relationships) or mental constructs (e.g. value, emotion, social relationships). Their interactions might be used for neural computations underlying such complex cognitive functions as spatial causal reasoning or evaluating interpersonal relationships.

In this view, synapses define the network’s structure, but moment to moment computation can be carried out by evolving wave patterns rather than by spikes alone. The efficiency of analog computation could explain how the brain performs vast amounts of computation while consuming only about 20 watts, roughly the power of a dim light bulb (Kováč, 2010). By contrast, modern digital AI systems require enormous energy.

Thus, the brain could rely heavily on efficient, parallel, wave-based computation layered on top of synaptic mechanisms that store long-term information and perform some level of computation. Wave patterns are patterns of different levels of neural excitation. Analog wave dynamics can thus create new patterns of excitation in a computationally principled fashion.
This could be key to the mesoscale organization needed for cognition and the unified neural representations needed for consciousness.

Altered Cortical Waves and Unconsciousness

General anesthesia further supports a central role for brain waves in cognition and consciousness. Anesthetics do not simply shut off the cortex. Instead, they profoundly alter wave dynamics (Redinbaugh et al., 2020; Bastos et al., 2021).

Despite acting on different molecular targets, different anesthetic agents, such as propofol (GABAergic), ketamine (NMDAergic), and dexmedetomidine (alpha-2 adrenergic), all converge on similar large-scale electrical effects in the cortex (Bardon et al., 2025; Eisen et al., 2026). The mixed, low-amplitude higher-frequency activity of wakefulness transitions to high-power slow delta (~1–4 Hz) oscillations across frontal, parietal, and sensory regions. These slow waves are often temporally misaligned, disrupting coordinated communication. The result may be a destabilized, fragmented cortex.

The main point here is that different pharmacological routes of different drugs nonetheless converge on the same systems-level outcome: Slow, desynchronized cortical waves. This suggests that consciousness depends less on specific receptors or cell types and more on the integrity of large-scale wave organization.

A Hybrid Synapse/Wave Framework for Cognition and Consciousness

In this framework, wave interactions, through analog computing, generate organized patterns of brain waves. These patterns, through Spatial Computing, in turn shape cortical activity.

The idea is that synapses and brain waves play complementary roles (Fig 8). Synaptic connections, shaped by experience, store long‑term information and define potential activity patterns. When neurons fire spikes, they generate electric fields that influence nearby neurons through ephaptic coupling, i.e., electrical interaction without direct synaptic contact. This creates a feedback loop: Synapses shape spiking, spiking contributes to brain waves, and waves shape spiking. Spikes and gamma, by virtue of their higher frequency, represent higher‑resolution (smaller‑spatal scale) sensory and motor information. Lower‑frequency rhythms such as alpha/beta and theta instead exert larger‑scale control, organizing where sensory and motor spiking/gamma occur according to top‑down schemas, goals, plans, and memories.

Series (line color)Cycle 1Cycle 2Cycle 3Cycle 4Cycle 5Cycle 6Cycle 7
Black (upper trace)0.000.000.000.000.000.000.00
Purple (middle trace)0.000.000.000.000.000.000.00
Red (lower trace)0.000.000.000.000.000.000.00
SeriesCycle 1Cycle 2Cycle 3Cycle 4Cycle 5Cycle 6Cycle 7Cycle 8Cycle 9
Sunspot (black)0.00.51.00.50.0-0.5-1.0-0.50.0
Two‑year (purple)0.00.51.00.50.0-0.5-1.0-0.50.0
Nine‑year (red)0.00.51.00.50.0-0.5-1.0-0.50.0
Other (blue)0.00.51.00.50.0-0.5-1.0-0.50.0

Figure 8 – A hybrid system of synapses, spikes, and waves.

Schematic illustrating our proposed framework. Synapses define a network’s structure and thus its set of possible activity patterns. Different contexts and goals instantiate distinct patterns of traveling waves across cortex, which interact via wave summation. The resulting pattern, combined with feedforward/recurrent drive conveyed via synapses, determines moment-to-moment what information is actually expressed in highfrequency gamma and spiking activity, and thus communicated to downstream regions. The shaded columns represent both time and cortical [Image: Image202]space.

Experience effectively “bakes” information about the world into the brain’s synaptic wiring (Barrett and Miller, 2026). When neurons spike (and gamma power increases) in response to sensory input or internal drive, they integrate with ongoing lower frequency traveling wave patterns. This generates patterns that reflect this stored knowledge and the current state of the world. The waves interact via the principles of analog computation, combining and transforming that information in predictable ways to generate new and unique brain states. Through the downward influence of the waves on spikes, these new thoughts can be “baked” into synaptic wiring, adding new information.

Moment‑to‑moment coordination underlying cognition and consciousness is thus dominated by brain waves rather than rapid synaptic changes. Different wave types coordinate activity at different scales: Slower waves can suppress some regions while enabling spiking in others, effectively routing information. Synapses provide representational capacity for storing information, while brain waves determine which representations are active at any given moment.

Brain waves can thus help solve the binding problem by dynamically linking distributed neural representations into a unified conscious experience. Derived from knowledge stored in synapses, they filter and shape conscious perception and thought according to our internal models of the world. Their interactions can generate new brain states that update these models via top-down influences on spiking and synaptic plasticity.

Comparison to other theories of consciousness and executive control

Our analog theory shares key themes with major theories of consciousness but diverges in its mechanism.

Like Global Workspace (GW) and Global Neuronal Workspace Theory (GNWT), our model holds that a distributed cortical network supports flexible, global integration (Baars, 1997; Dehaene et al., 1998; Mashour et al., 2020). We, however, emphasize how this integration occurs via dynamic field interactions rather than broadcasting of information (GW) and spikes alone (GWNT). Similarly, our framework resembles Integrated Information Theory (IIT) in treating organization and self-influence as essential to consciousness (Tononi et al., 2016). However, we locate its mechanisms not in a “hot zone,” but in the large‑scale wave dynamics that organize cortical computation.

Our framework closely aligns with Higher‑Order Theories (HOTs) that stress top‑down model or schema influences in which a brain state becomes conscious when it is the target of a higherorder representation, typically from frontal cortex (Rosenthal, 2005; Lau and Rosenthal, 2011; Graziano, 2022; LeDoux, 2023; Riddle and Schooler, 2024). As such, it also aligns with predictive coding theories of cortical function and perceptual awareness (Friston and Kiebel, 2009; Bastos et al., 2012; Seth et al., 2012; Bastos et al., 2020). In our framework, we conceptualize consciousness as emerging naturally when higher‑order predictive models, implemented through oscillatory wave patterns, impose organized structure on lower‑level cortical processes. This is similar to the nested observer model in which oscillatory dynamics impose a hierarchy of consciousness (Riddle and Schooler, 2024). Rather than a separate observer system making representations “conscious,” we emphasize the very act of top‑down organization in generating conscious integration.

Our framework also connects with neural theories of executive control that posit the influence that top-down signals from the frontoparietal cortex and anterior cingulate exert on sensory cortex (Desimone and Duncan, 1995; Miller and Cohen, 2001; Botvinick et al., 2004; Banich, 2009; Rossi et al., 2009; Funahashi and Andreau, 2013). The influences have been thought to involve excitatory influences that selectively gate spiking via winner-take-all dynamics (Desimone and Duncan, 1995; Miller and Cohen, 2001). In our framework, we instead place emphasis on top-down influences exerted by wave dynamics. In this way, our theory grounds the higher‑order, top‑down architecture of cognition in a specific physical mechanism, analog wave computation and the organizing influence of wave dynamics across the cortex.

Conclusion

Our framework shares with others the general idea that cognition and consciousness involve large‑scale coordination and top‑down control across the brain. But instead of describing function mainly in terms of information exchange between discrete neurons, circuits or regions, we emphasize brain‑wide wave dynamics as the organizing principle.

In this view, rhythmic electric fields unify and structure cortical activity, allowing analog computation to take place across space and time. These wave interactions not only bind distributed neural populations into coherent states but also carry out computations that support flexible thought and control. Consciousness, then, emerges when these dynamic wave patterns bring the cortex into an organized, globally integrated state, one that naturally links and influences widespread activity.

This framework is not only conceptually plausible but biologically feasible. Cortical circuits naturally generate oscillatory dynamics and propagate waves through recurrent connectivity across scales. The dynamics we emphasize thus require no special machinery. These waves are energetically efficient, leveraging continuous field interactions rather than metabolically costly, all‑or‑none spiking at every step. In this sense, the brain exploits its own physics: Electric field dynamics offer a low‑overhead substrate for organizing and coordinating information across cortical networks. Given strong evolutionary pressure to maximize computation per unit energy, it would be surprising if evolution did not exploit such a built‑in analog computing substrate.

Acknowledgements

This work was supported by Office of Naval Research MURI N00014-23-1-2768, Army Research Office W911NF2410228, NIMH 1R01MH131715-01, NEI 1R01EY033430-01A1, NEI 1R01EY033430-01A1, The Freedom Together Foundation, The Picower Institute for Learning and Memory, and The Simons Center for the Social Brain

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