While Haueis and Colaço successfully highlight the relevance of metabolic considerations in neuroscientific modeling, they focus, primarily, on intracellular biochemical processes (e.g., costs in terms of number of ATP molecules spent). Most modeling of cognitive phenomena in neuroscience operates at a different level of abstraction, framed in terms of computational processes across populations of neurons. Haueis and Colaço do consider information-theoretic measures of efficiency applicable to such models, but dismiss them as too generic to adjudicate between competing cognitive models. I argue that this dismissal is premature: abstract considerations about the efficiency of information processing are broadly applied to evaluate and generate specific cognitive models in neuroscience. Yet the rationale for expecting efficiency in biological cognitive systems often remains implicit. By foregrounding metabolic considerations, Haueis and Colaço make explicit one reason to expect efficient information processing in such systems.
A neural code is efficient for transmitting information about a stimulus feature if it conveys as much information as possible using as short a message as possible (e.g., with few spikes) (Shannon, Reference Shannon1948). This information-theoretic notion has been applied to computational neuroscience (Borst & Theunissen, Reference Borst and Theunissen1999). Bialek et al. (Reference Bialek, DeWeese, Rieke and Warland1993) operationalized the coding efficiency in terms of the mutual information between a stimulus feature and a neural response, normalized by the entropy of the neural response. The normalization is key: coding efficiency measures what proportion of the neural variability (measured by its entropy) actually carries information about the stimulus. One natural motivation for considering this proportion is metabolic. Maintaining neural variability (e.g., the firing of neurons) is metabolically costly; variability that carries no information about the stimulus is therefore metabolically wasteful. An efficient neural code allows spending limited metabolic resources with the greatest benefit for information transmission.
Let us consider a few cases in which coding efficiency has been used to evaluate and generate specific cognitive models.
Rieke, Warland, and Bialek (Reference Rieke, Warland and Bialek1993) showed that receptors in the bullfrog inner ear, transmitting information about the acoustic waveform, and filiform hairs of the cricket, transmitting information about airflow velocity, both achieve coding efficiencies of 50–60%. This establishes that these systems exploit a substantial proportion of their response variability. Rieke, Bodnar, and Bialek (Reference Rieke, Bodnar and Bialek1995) used the same measure to show that neural coding is optimal for natural stimuli: primary auditory afferents in the bullfrog, transmitting information about acoustic waveform, respond with ∼80% efficiency to stimuli resembling natural advertisement calls, but only with ∼20% efficiency to white noise. This supports the hypothesis that the neural code is specifically organized around the statistics of ecologically relevant stimuli and rules out models in which the code is stimulus-agnostic.
Coding efficiency can also help to resolve questions about the temporal structure of the neural code. In a rate-based code, only the firing rate across a relatively large time window is computationally relevant. In a timing-based code, the spike timing down to a small temporal resolution is relevant. De Ruyter van Steveninck et al. (Reference de Ruyter van Steveninck, Lewen, Strong, Koberle and Bialek1997) and Strong et al. (Reference Strong, Koberle, de Ruyter van Steveninck and Bialek1998) measured how much information H1 motion-sensitive neurons in the fly visual system transmit about visual flow as a function of the temporal resolution of spike counts. Efficiency remains near 50% even at 3 ms resolution, supporting a timing-based rather than rate-based code. Here, the measure is doing exactly the discriminative work Haueis and Colaço suggest it cannot: choosing between two specific, competing hypotheses about neural representation.
Considerations about the efficiency of information processing in cognitive neuroscience extend far beyond the literature on coding efficiency alone. As Pohl et al. (Reference Pohl, Walker, Barack, Lee, Denison, Block, Meyniel and Ma2026) note, standard goodness-of-fit measures for encoding models are closely related to coding efficiency. Most notably, the proportion of variance explained is a variance-based analogue of coding efficiency as defined by Bialek et al. (Reference Bialek, DeWeese, Rieke and Warland1993), where the neural variability not explained by the stimulus is measured in terms of the remaining variance of the error of an encoding model rather than the remaining entropy of the neural response given the stimulus. The interpretation of the measure remains largely the same: Since maintaining variability is costly, we can expect that a true model of the computational process leaves little variance unexplained. A model that fails to explain a large proportion of variance is probably missing something about what the neural response is doing.
Measures of the goodness-of-fit of encoding models are applied even more broadly across cognitive neuroscience than information-theoretic measures of coding efficiency. Pohl et al. (Reference Pohl, Walker, Barack, Lee, Denison, Block, Meyniel and Ma2026) argue that encoding model performance, under the label “specificity,” is one of the four core characteristics of neural representations that structure how evidence for neural representations is gathered and link this explicitly to measures of coding efficiency.
What remains underexplored – and what Haueis and Colaço’s framework usefully foregrounds – is why we should expect biological cognitive systems to implement efficient information processing in the first place. Metabolic cost is one compelling answer: unexploited variability is energetically expensive, and we may expect evolution to select against it. But this is unlikely to be the only answer. Efficient neural codes may also be faster, affording quicker reaction times (Gautrais & Thorpe, Reference Gautrais and Thorpe1998), or they may be less complex and therefore favored by learning or ontogenesis (Grünwald, Reference Grünwald2007; Simoncelli & Olshausen, Reference Simoncelli and Olshausen2001).
Notably, in the line of literature following Bialek et al. (Reference Bialek, DeWeese, Rieke and Warland1993) and Rieke, Warland, and Bialek (Reference Rieke, Warland and Bialek1993), the benefits of efficient coding are rarely discussed explicitly. Here, efficiency of coding may be seen as a mere theoretical virtue much like mathematical elegance or simplicity. In contrast, the line of literature on efficiency that Haueis and Colaço draw on (Attwell & Laughlin, Reference Attwell and Laughlin2001; Laughlin, Reference Laughlin2001) does consider metabolic cost as an explicit motivation for efficiency. There are surprisingly few crossreferences between these lines of literature, which may be an instance of a broader sociological divide between more biology-adjacent and more physics-adjacent groups of neuroscientists (De Schutter, Reference De Schutter2008). By drawing our attention to metabolic considerations, Haueis and Colaço help to bridge this gap.
While Haueis and Colaço successfully highlight the relevance of metabolic considerations in neuroscientific modeling, they focus, primarily, on intracellular biochemical processes (e.g., costs in terms of number of ATP molecules spent). Most modeling of cognitive phenomena in neuroscience operates at a different level of abstraction, framed in terms of computational processes across populations of neurons. Haueis and Colaço do consider information-theoretic measures of efficiency applicable to such models, but dismiss them as too generic to adjudicate between competing cognitive models. I argue that this dismissal is premature: abstract considerations about the efficiency of information processing are broadly applied to evaluate and generate specific cognitive models in neuroscience. Yet the rationale for expecting efficiency in biological cognitive systems often remains implicit. By foregrounding metabolic considerations, Haueis and Colaço make explicit one reason to expect efficient information processing in such systems.
A neural code is efficient for transmitting information about a stimulus feature if it conveys as much information as possible using as short a message as possible (e.g., with few spikes) (Shannon, Reference Shannon1948). This information-theoretic notion has been applied to computational neuroscience (Borst & Theunissen, Reference Borst and Theunissen1999). Bialek et al. (Reference Bialek, DeWeese, Rieke and Warland1993) operationalized the coding efficiency in terms of the mutual information between a stimulus feature and a neural response, normalized by the entropy of the neural response. The normalization is key: coding efficiency measures what proportion of the neural variability (measured by its entropy) actually carries information about the stimulus. One natural motivation for considering this proportion is metabolic. Maintaining neural variability (e.g., the firing of neurons) is metabolically costly; variability that carries no information about the stimulus is therefore metabolically wasteful. An efficient neural code allows spending limited metabolic resources with the greatest benefit for information transmission.
Let us consider a few cases in which coding efficiency has been used to evaluate and generate specific cognitive models.
Rieke, Warland, and Bialek (Reference Rieke, Warland and Bialek1993) showed that receptors in the bullfrog inner ear, transmitting information about the acoustic waveform, and filiform hairs of the cricket, transmitting information about airflow velocity, both achieve coding efficiencies of 50–60%. This establishes that these systems exploit a substantial proportion of their response variability. Rieke, Bodnar, and Bialek (Reference Rieke, Bodnar and Bialek1995) used the same measure to show that neural coding is optimal for natural stimuli: primary auditory afferents in the bullfrog, transmitting information about acoustic waveform, respond with ∼80% efficiency to stimuli resembling natural advertisement calls, but only with ∼20% efficiency to white noise. This supports the hypothesis that the neural code is specifically organized around the statistics of ecologically relevant stimuli and rules out models in which the code is stimulus-agnostic.
Coding efficiency can also help to resolve questions about the temporal structure of the neural code. In a rate-based code, only the firing rate across a relatively large time window is computationally relevant. In a timing-based code, the spike timing down to a small temporal resolution is relevant. De Ruyter van Steveninck et al. (Reference de Ruyter van Steveninck, Lewen, Strong, Koberle and Bialek1997) and Strong et al. (Reference Strong, Koberle, de Ruyter van Steveninck and Bialek1998) measured how much information H1 motion-sensitive neurons in the fly visual system transmit about visual flow as a function of the temporal resolution of spike counts. Efficiency remains near 50% even at 3 ms resolution, supporting a timing-based rather than rate-based code. Here, the measure is doing exactly the discriminative work Haueis and Colaço suggest it cannot: choosing between two specific, competing hypotheses about neural representation.
Considerations about the efficiency of information processing in cognitive neuroscience extend far beyond the literature on coding efficiency alone. As Pohl et al. (Reference Pohl, Walker, Barack, Lee, Denison, Block, Meyniel and Ma2026) note, standard goodness-of-fit measures for encoding models are closely related to coding efficiency. Most notably, the proportion of variance explained is a variance-based analogue of coding efficiency as defined by Bialek et al. (Reference Bialek, DeWeese, Rieke and Warland1993), where the neural variability not explained by the stimulus is measured in terms of the remaining variance of the error of an encoding model rather than the remaining entropy of the neural response given the stimulus. The interpretation of the measure remains largely the same: Since maintaining variability is costly, we can expect that a true model of the computational process leaves little variance unexplained. A model that fails to explain a large proportion of variance is probably missing something about what the neural response is doing.
Measures of the goodness-of-fit of encoding models are applied even more broadly across cognitive neuroscience than information-theoretic measures of coding efficiency. Pohl et al. (Reference Pohl, Walker, Barack, Lee, Denison, Block, Meyniel and Ma2026) argue that encoding model performance, under the label “specificity,” is one of the four core characteristics of neural representations that structure how evidence for neural representations is gathered and link this explicitly to measures of coding efficiency.
What remains underexplored – and what Haueis and Colaço’s framework usefully foregrounds – is why we should expect biological cognitive systems to implement efficient information processing in the first place. Metabolic cost is one compelling answer: unexploited variability is energetically expensive, and we may expect evolution to select against it. But this is unlikely to be the only answer. Efficient neural codes may also be faster, affording quicker reaction times (Gautrais & Thorpe, Reference Gautrais and Thorpe1998), or they may be less complex and therefore favored by learning or ontogenesis (Grünwald, Reference Grünwald2007; Simoncelli & Olshausen, Reference Simoncelli and Olshausen2001).
Notably, in the line of literature following Bialek et al. (Reference Bialek, DeWeese, Rieke and Warland1993) and Rieke, Warland, and Bialek (Reference Rieke, Warland and Bialek1993), the benefits of efficient coding are rarely discussed explicitly. Here, efficiency of coding may be seen as a mere theoretical virtue much like mathematical elegance or simplicity. In contrast, the line of literature on efficiency that Haueis and Colaço draw on (Attwell & Laughlin, Reference Attwell and Laughlin2001; Laughlin, Reference Laughlin2001) does consider metabolic cost as an explicit motivation for efficiency. There are surprisingly few crossreferences between these lines of literature, which may be an instance of a broader sociological divide between more biology-adjacent and more physics-adjacent groups of neuroscientists (De Schutter, Reference De Schutter2008). By drawing our attention to metabolic considerations, Haueis and Colaço help to bridge this gap.
Financial support
There was no funding for this work.
Competing interests
None.