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Reward Value-Based Gain Control: Divisive Normalization in Parietal Cortex
Open accessAbstract
The representation of value is a critical component of decision making. Rational choice theory assumes that options are assigned absolute values, independent of the value or existence of other alternatives. However, context-dependent choice behavior in both animals and humans violates this assumption, suggesting that biological decision processes rely on comparative evaluation. Here we show that neurons in the monkey lateral intraparietal cortex encode a relative form of saccadic value, explicitly dependent on the values of the other available alternatives. Analogous to extra-classical receptive field effects in visual cortex, this relative representation incorporates target values outside the response field and is observed in both stimulus-driven activity and baseline firing rates. This context-dependent modulation is precisely described by divisive normalization, indicating that this standard form of sensory gain control may be a general mechanism of cortical computation. Such normalization in decision circuits effectively implements an adaptive gain control for value coding and provides a possible mechanistic basis for behavioral context-dependent violations of rationality.
Overview
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TL;DR
Neurons in monkey lateral intraparietal cortex (LIP) encode saccadic value relative to the values of other available alternatives, not as absolute values. Full divisive normalization best describes this context-dependent modulation, suggesting a canonical cortical gain-control mechanism for value coding.
Key findings
- In a two-target task, LIP activity increased with reward inside the response field (Vin) and decreased with reward outside it (Vout): 12/16 neurons (75.0%) were positively correlated with Vin, and 18/27 (66.7%) were negatively correlated with Vout; population mean correlations were 0.33 and −0.21, respectively.
- In a three-target task, stimulus-driven activity was suppressed by summed extra-RF value: 33/62 neurons (53.2%) were modulated, with 30/33 showing suppression; population mean correlation was −0.155 (p = 2.6×10−6). Activity in the absence of an RF target was also suppressed: 27/62 (43.6%) modulated, 21/27 suppressed; mean correlation −0.087 (p = 0.0019).
- Full divisive normalization best fit individual neurons (MED-RF: 53/62, 85.5%; HIGH-RF: 16/17, 94.1%; LOW-RF: 26/41, 61.9%) and the combined population dataset (R² = 0.961) versus fractional (0.730), difference (0.601), and simple normalization (0.219); it also had the lowest cross-validated mean squared error (0.0393).
- Suppression depended on extra-RF target value but not relative target distance (ANCOVA: value p = 0.004; distance p = 0.058; interaction p = 0.793), and behavioral measures such as fixation breaks, error rates, and reaction times showed no consistent dependence on Vout.
Methods
- Three male rhesus monkeys performed two-target and three-target saccade tasks with water reward magnitudes assigned to targets inside or outside the LIP neuron’s response field. Two-target task: 27 LIP neurons (monkey D n = 17; monkey W n = 10), with a subset (n = 16) also tested with RF value varied. Three-target task: 62 neurons under MED-RF (monkey W n = 31; monkey B n = 31), plus 45 neurons under HIGH-RF or LOW-RF conditions.
- Single-unit electrophysiology in LIP; activity analyzed mainly 0–1000 ms after peripheral target presentation and normalized to peak firing in single-target RF mapping trials.
- Analyses included Pearson correlations, multiple regression with Vout and saccade latency, ANCOVA on a suppression index, and model fitting of fractional, difference, simple normalization, and full normalization models using AIC and leave-one-out cross-validation.
Limitations
- Stated: the circuit mechanisms generating divisive normalization remain unknown, the biophysical implementation of the semisaturation term σ is unknown, and the causal role of normalized value coding in context-dependent choice remains to be explored.
- Stated: visuospatial parameters may influence suppression when alternative targets are very close to the RF (distance effect p = 0.058, not significant here), and attention cannot be fully excluded as an alternative explanation, though the authors argue the parametric value effects are not easily reconciled with simple attentional modulation.
- Evident: findings are restricted to macaque LIP, specific saccade tasks, and water reward magnitudes; some neurons were recorded under multiple value conditions, so across-condition analyses were restricted to population responses rather than individual-neuron comparisons.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Examination of the AIC values confirmed that the full divisive normalization model was the most likely of these underlying value representations in the vast majority of LIP neurons (MED-RF condition: n = 53/62, 85.5%; HIGH-RF condition: n = 16/17, 94.1%; LOW-RF conditions: n = 26/41, 61.9%).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As seen in Figure 7, the full normalization equation (Rmax = 3.86, σ = 1541 µl, β = 87.6 µl) characterized LIP responses in both conditions, which is evident when the best-fit normalization model (black lines) is compared to the population responses (red and blue points).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Examination of AIC values confirmed that the full normalization model best explained the MED-RF condition data (AICfract = −31.8, AICdiff = −26.5, AICnorm_simp = −21.9, AICnorm_full = −70.9).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In contrast, the average correlation coefficient in RF target-absent trials remained significantly negative.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Consistent with previous reports, many LIP neurons in this task possessed motor-related activity: a presaccadic increase in firing rate selective for saccades into the RF.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As shown in Figure 5, population activity in the three-target task also depended on the value of the RF target, with progressively higher firing rates at larger levels of Vin.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Across the population of neurons, the average correlation coefficient was significantly negative for most of the cue presentation interval in both RF target-present and RF target-absent conditions (p < 0.05, t-test).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As shown for the example neuron in Figure 2B, activity in trials without a target in the RF also varied as a function of Vout (r = −0.161, p = 0.037).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Finally, reaction times for saccades towards the RF target across the different value contexts did not differ across different Vout conditions in either monkey (Monkey D: p = 0.97; Monkey W: p = 0.20; one-way ANOVA).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Two-alternative neural data
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In the paper
“We observed that stimulus-driven activity, elicited by the appearance of the target in the RF, was a consistent function of the total amount of reward available, despite the fact that RF target value remained constant.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
- It may state two separate claims as one. 37
- Probably not a substantial claim. 11
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, the simple normalization model failed to predict the suppression below baseline levels observed in the absence of RF stimulation; only the full normalization model fully predicted the modulation of both RF-driven and baseline activity.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, examination of the relative target positions (distance from RF target) of small and large value alternative targets showed no discernible difference in the average relative position (distancesmall = 35.43 deg, distancelarge = 35.10 deg; p = 0.77, t-test) or the relative position distributions (p = 0.98, two-sample Kolmogorov-Smirnov test; Figure 4 inset).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The majority of LIP neurons were modulated by value context, with almost all neurons showing suppression (modulation: n = 33/62, 53.2%; suppression n = 30/33, 90.9%); furthermore, suppression was significant across the population of neurons (mean correlation −0.155; p = 2.6×10−6, t-test) and evident in the mean population activity (Figure 2C).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As shown in Figure 3, the population of LIP neurons displayed Vout-dependent suppression in both RF target-present and RF target-absent conditions across much of the trial, with peak modulation occurring approximately 200–300 ms after peripheral target onset.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Of the recorded neurons, firing rate was significantly dependent on only value in 29 neurons, on both value and latency in 3 neurons, and on only latency in 1 neuron, suggesting that the observed modulation of LIP activity was primarily driven by the value context.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In contrast, the difference model predicted suppression even in RF target-absent conditions; however, it could not adequately model both the RF target-driven and RF target-absent effects simultaneously.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For saccades to the small target, error rates varied by target configuration (Monkey B, χ2(3) = 13.4, p = 0.004; Monkey W, χ2(3) = 17.2, p = 0.0006) but were correlated with total value in only one monkey (Monkey B: r = 0.83, p = 0.167; Monkey W: r = 0.95, p = 0.047) and uncorrelated across the combined data (r = 0.35, p = 0.401).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
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In the paper
“This value modulation in the absence of RF stimulation was significant for a large fraction of LIP neurons (modulation n = 27/62, 43.6%; suppression 21/27, 77.8%) and significant across the population (mean correlation −0.087; p = 0.0019, t-test).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Similarly, the rate of incorrect saccadic choices did not vary consistently with Vout; both monkeys exhibited high success rates (> 90%), with error rates independent of Vout condition in Monkey W (χ2(4) = 4.5, p = 0.34) and dependent but not significantly related to Vout in Monkey D (χ2(4) = 14.4, p = 0.006; r = −0.40, p = 0.51).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Two-alternative neural data
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Despite constant Vin levels, activity in trials with a target in the RF (solid red symbols) was suppressed as Vout increased. Similarly, in trials without a target in the RF (solid blue symbols), activity decreased as a function of alternative target values.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both monkeys had low fixation break frequencies during cue presentation (Monkey W: 2.8%; Monkey B: 4.0%) that were uncorrelated with total value in both monkeys individually (Monkey W: r = −0.36, p = 0.42; Monkey B: r = 0.28, p = 0.54) and combined across animals (r = 0.04, p = 0.90).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“consistent with the timepoint analysis, average LIP activity is suppressed by Vout in RF target-absent conditions (mean r = −.0.071, p = 3.7×10−4) and unmodulated in RF target-present (mean r = 0.024, p = 0.302) conditions.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
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- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Consistent with the results described above, increasing the value of the target outside the RF in the two-target conditions decreased LIP firing rates (red, orange). Furthermore, activity was also a function of target number, decreasing from single target (black) to double target (red, orange) to triple target (yellow) conditions.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
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- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Fixation break frequencies were low in both monkeys (Monkey D: 9.2%; Monkey W: 1.6%); in Monkey W, these frequencies did not differ across Vout conditions (Monkey W: χ2(4) = 5.6, p = 0.23), while in Monkey D, these frequencies differed across conditions (χ2(4) = 20.6, p = 0.0004) but were not significantly correlated with Vout magnitudes (r = −0.87, p = 0.06).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Two-alternative neural data
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In the paper
“The fractional and simple normalization models failed to account for suppression in the absence of a RF target; because both models incorporate only the quantity Vin in the numerator, they predicted constant levels of activity in all RF-target absent conditions (simple normalization: R = 0; fractional: R = a).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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In the paper
“Across the population, suppression was independent of the relative spatial location of the extra-RF target, supporting a modulation driven primarily by target value rather than spatial location.”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
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In the paper
“Targets at these locations did not activate the recorded neuron when presented alone, consistent with a contralateral visual bias in LIP (Ben Hamed et al., 2001; Patel et al., 2010).”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
What the sources say
- Not checked yetcites Ben Hamed et al., 2001
- Not checked yetcites Patel et al., 2010
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In the paper
“As noted previously, the fractional model failed to account for background suppression in the absence of a RF target, evident as a horizontal line in predicted activity (Figure 6, top); furthermore, the predicted linear responses correspond poorly to the observed nonlinear activity.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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In the paper
“These results show that the value of targets situated far from the RF can modulate both stimulus-driven activity and activity in the absence of direct feed-forward RF drive.”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
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In the paper
“The value of σ derived from the present study is ~1000 µl, a quantity large enough at normal volumes of reward to significantly shift value coding away from a strict fractional representation and towards a richer function of value context.”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
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In the paper
“First, we find a monotonic relationship between the value of the target in the RF and LIP activity, as well as a parametric suppression related to the value of extra-RF targets.”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
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In the paper
“In the three-target task, extra-RF targets were far from the RF center (average 35 deg) and located primarily in the opposite visual hemifield.”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
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In the paper
“When examined across all data conditions, the full divisive normalization model explained the full dataset (R2 = 0.961) far better than the fractional (R2 = 0.730), difference (R2 = 0.601), or simple normalization (R2 = 0.219) models (Figure 6, right column).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The difference model predicted some RF target-absent suppression, but performed particularly poorly in characterizing the range of responses to different Vin conditions.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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In the paper
“While such linear models accurately characterized basic visual neuron responses such as orientation and direction selectivity, they could not explain more complicated, nonlinear phenomena such as contrast saturation and nonspecific suppression.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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In the paper
“More recently, motivated by computational models of two-alternative choice behavior, some researchers have suggested that the difference in option values may better describe LIP activity (Corrado et al., 2005).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
What the sources say
- Not checked yetcites Corrado et al., 2005
Strength:hedged· not yet calibratedCausal:correlational· not yet calibratedTests✗ Asserted: fails✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The authors may not put it forward as true. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Together, these results suggest that LIP encodes a context-dependent value representation, where the value configuration of the entire choice set controls both stimulus-driven and target-absent activity early in the valuation process.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, while both the fractional and difference models are consistent with LIP value modulation, neither theoretical proposal is directly based on the structure and function of cortical circuits.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Such normalization in decision circuits effectively implements an adaptive gain control for value coding and provides a possible mechanistic basis for behavioral context-dependent violations of rationality.”
§ Value-based gain control: divisive normalization in parietal cortex > Abstract
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In the paper
“Early models of striate cortex described visual neuron function as a linear operation, producing responses that are weighted sums of relevant inputs (Hubel and Wiesel, 1962, 1968; Movshon et al., 1978).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
What the sources say
- Not checked yetcites Hubel and Wiesel, 1962, 1968
- Not checked yetcites Movshon et al., 1978
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Initial studies of value coding in LIP (Platt and Glimcher, 1999; Sugrue et al., 2004) focused on a fractional representation of value due to its association with classic matching law behavior (Herrnstein, 1961).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
What the sources say
- Not checked yetcites Platt and Glimcher, 1999
- Not checked yetcites Sugrue et al., 2004
- Not checked yetcites Herrnstein, 1961
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Analogous to extra-classical receptive field effects in visual cortex, this relative representation incorporates target values outside the response field and is observed in both stimulus-driven activity and baseline firing rates.”
§ Value-based gain control: divisive normalization in parietal cortex > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Notably, activity positively related to Vout was absent in the two-target task (Figure 1C), suggesting that such activity may be a salience effect related to the instructional offset of the peripheral targets which only occurred in the three-target task.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Three-alternative neural data
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“This epoch represents the entire period of target array presentation prior to the signal identifying the saccade target; the general results presented here are not sensitive to the exact definition of this epoch.”
§ Value-based gain control: divisive normalization in parietal cortex > MATERIALS AND METHODS > Data analysis
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus, activity was both an increasing function of Vin and a decreasing function of Vout, suggesting that LIP value representation is relative rather than absolute; we explore the specific algorithm underlying this relative representation below.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Two-alternative neural data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The value of a given target is equated with the associated reward magnitude.
None of the sources cited for this claim have been checked yet.
In the paper
“Furthermore, normalization-style models yield efficient coding of natural signal statistics in both visual and auditory modalities (Schwartz and Simoncelli, 2001; Valerio and Navarro, 2003) and may play a role in attentional processing (Reynolds et al., 1999; Reynolds and Heeger, 2009), suggesting that divisive normalization may serve as a canonical computational algorithm in cortical circuits.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
What the sources say
- Not checked yetcites Schwartz and Simoncelli, 2001
- Not checked yetcites Valerio and Navarro, 2003
- Not checked yetcites Reynolds and Heeger, 2009
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“In sensory cortices, stimuli outside the classical receptive field can nonetheless significantly modulate neuronal activity. Many of these extra-classical effects are well-described by models where response is specified by the sensory properties of the stimulus inside the receptive field, divided by the weighted sum of the sensory properties of stimuli both outside and inside the receptive field (”
§ Value-based gain control: divisive normalization in parietal cortex > INTRODUCTION
What the sources say
- Not checked yetcites Heeger, 1992
- Not checked yetcites Carandini et al., 1997
- Not checked yetcites Cavanaugh et al., 2002
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Given the relatively small number of neurons recorded in multiple Vin conditions, we restricted analyses across all value conditions to the population responses.”
§ Value-based gain control: divisive normalization in parietal cortex > MATERIALS AND METHODS > Electrophysiological recording
Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“To address these issues, Heeger proposed that visual cortical function involves a normalization stage, where a given cell’s response is divided by a quantity representing the pooled activity of a large number of other similar neurons (Heeger, 1992).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
What the sources say
- Not checked yetcites Heeger, 1992
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
None of the sources cited for this claim have been checked yet.
In the paper
“This divisive normalization model explains a number of nonlinear phenomena in striate and extrastriate cortex (Carandini et al., 1997; Britten and Heuer, 1999; Cavanaugh et al., 2002; Heuer and Britten, 2002) as well as responses in the ventral visual stream (Zoccolan et al., 2005).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
What the sources say
- Not checked yetcites Carandini et al., 1997
- Not checked yetcites Britten and Heuer, 1999
- Not checked yetcites Cavanaugh et al., 2002
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“For both tasks, the initial ten trials in a block were discarded to avoid learning effects.”
§ Value-based gain control: divisive normalization in parietal cortex > MATERIALS AND METHODS > Data analysis
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Together, these results indicate that full divisive normalization outperformed the alternative models in terms of both response characterization and predictive power.”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Due to nonlinearity introduced by the semisaturation term (σ), the divisive normalization representation can produce responses on a continuum between absolute and relative value coding; this form of adaptive gain control depends on the relative balance between total value and σ.”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, at intermediate total values (V ~ σ) the denominator in the normalization model depends on both total value and σ, and activity grows increasingly sensitive to choice context, similar to a fractional model (angled shading and angled contour lines).”
§ Value-based gain control: divisive normalization in parietal cortex > RESULTS > Divisive normalization and value coding
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Our results provide the first example of normalization outside a strictly sensory area, and the most anterior extension of divisive normalization coding in the dorsal stream.”
§ Value-based gain control: divisive normalization in parietal cortex > DISCUSSION
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper relies on this without support.
The neural basis of context-dependent valuation is unknown.
“However, the neural basis of such context-dependent valuation is unknown.”
The paper relies on this without support.
The specific form of value representation in LIP and how it arises out of cortical circuit interactions remains largely unexplored.
“Current evidence suggests that parietal neurons are modulated by the value of their associated saccade, but the specific form of value representation and how it arises out of cortical circuit interactions remains largely unexplored.”
The paper relies on this without support.
LIP neurons have a circumscribed response field and many have a similarly tuned response to upcoming saccade amplitude and direction.
“LIP neurons, like those in visual cortex, respond to stimulus presentation in a circumscribed region of visual space termed the response field (RF); many of these neurons also possess a similarly tuned response to upcoming saccade amplitude and direction.”
The authors state this as an assumption.
The value of a given target is equated with the associated reward magnitude.
“The value of a given target was equated with the associated reward magnitude.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Similar results are obtained in tasks that manipulate the desirability of a target using different methods, for example by controlling the relative magnitude, probability or delay of its expected reward (Bernacchia et al., 2011; Louie et al., 2011; Sugrue et al., 2004; Yang and Shadlen, 2007).”
From Attention, learning, and the value of information (2012) · cites this paper as Louie et al., 2011
Statistics recomputed
Every reported test result, recomputed from its test statistic and degrees of freedom. A result shows as not adding up only once an independent check has confirmed it.
- Consistentχ²(4) = 5.6reported p = .23 · recomputed p = .231
“χ2(4) = 5.6, p = .23”
- Consistentχ²(4) = 20.6reported p = .0004 · recomputed p < .001
“χ2(4) = 20.6, p = .0004”
- Consistentχ²(4) = 4.5reported p = .34 · recomputed p = .343
“χ2(4) = 4.5, p = .34”
- Consistentχ²(4) = 14.4reported p = .006 · recomputed p = .006
“χ2(4) = 14.4, p = .006”
- Consistentχ²(3) = 13.4reported p = .004 · recomputed p = .004
“χ2(3) = 13.4, p = .004”
- Consistentχ²(3) = 17.2reported p = .0006 · recomputed p < .001
“χ2(3) = 17.2, p = .0006”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
LOW-RF neuron percentage does not match its count
MinorThe reported 26 of 41 neurons is 63.4%, not 61.9%.
Reported 61.9 · recomputed 63.414634
“LOW-RF conditions: n = 26/41, 61.9%”
Citations
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“To quantify the relative performance of the different models, we calculated the AIC for each neuron under every model; the AIC provides an information theoretic basis for model comparison that considers both goodness of fit and parsimony (Akaike, 1974).”
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Hubel, D. H., & Wiesel, T. N. (1962) · The Journal of Physiology · doi:10.1113/jphysiol.1962.sp006837 · Cited by 13,680 · cited 1×
“Early models of striate cortex described visual neuron function as a linear operation, producing responses that are weighted sums of relevant inputs (Hubel and Wiesel, 1962, 1968; Movshon et al., 1978).”
BackgroundReceptive fields and functional architecture of monkey striate cortex
Hubel, D. H., & Wiesel, T. N. (1968) · The Journal of Physiology · doi:10.1113/jphysiol.1968.sp008455 · Cited by 6,685 · cited 1×
“Early models of striate cortex described visual neuron function as a linear operation, producing responses that are weighted sums of relevant inputs (Hubel and Wiesel, 1962, 1968; Movshon et al., 1978).”
BackgroundTheory of Games and Economic Behavior
N., E., von Neumann, J., & Morgenstern, O. (1945) · The Journal of Philosophy · doi:10.2307/2019327 · Cited by 4,095
When choice is demotivating: can one desire too much of a good thing?
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“Under larger choice sets, human decision makers report greater difficulty choosing and lower outcome satisfaction, and they often choose the default option or opt not to choose at all (Iyengar and Lepper, 2000).”
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“Reward Value-Based Gain Control: Divisive Normalization in”
BackgroundRELATIVE AND ABSOLUTE STRENGTH OF RESPONSE AS A FUNCTION OF FREQUENCY OF REINFORCEMENT 1, 2
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“Initial studies of value coding in LIP (Platt and Glimcher, 1999; Sugrue et al., 2004) focused on a fractional representation of value because of its association with classic matching law behavior (Herrnstein, 1961).”
BackgroundShadlen, M. N., & Newsome, W. T. (1998) · The Journal of Neuroscience · doi:10.1523/jneurosci.18-10-03870.1998 · Cited by 2,178 · cited 1×
“Cortical neurons exhibit considerable variability in their spiking activity, and information is likely represented by distributions of neurons and spiking rates (Tolhurst et al., 1983; Shadlen and Newsome, 1998; Pouget et al., 2003).”
BackgroundNormalization of cell responses in cat striate cortex
Heeger, D. J. (1992) · Visual Neuroscience · doi:10.1017/s0952523800009640 · Cited by 1,835 · cited 4×
“…well described by models in which response is specified by the sensory properties of the stimulus inside the receptive field, divided by the weighted sum of the sensory properties of stimuli both outside and inside the receptive field (Heeger, 1992; Carandini et al., 1997; Cavanaugh et al., 2002).”
BackgroundInfluential
Flagged first, then by citations
5 of the 60 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- Stephens DW Krebs JR Foraging theory 1986 Princeton, NJ Princeton University Press
Cited by
Sorted by citations
Items 201–300 of 314
Neurocomputational Nosology: Malfunctions of Models and Mechanisms
Barack, D. L., & Platt, M. L. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.00602 · Cited by 6
“Another example is divisive normalization, a neurocomputation involved in such diverse cognitive functions as attention (Reynolds and Heeger, 2009), value encoding (Louie et al., 2011), multisensory integration (Ohshiro et al., 2011), and others.”
BackgroundXu, T., Chen, Z., & Feng, T. (2019) · Behavioural Brain Research · doi:10.1016/j.bbr.2019.112111 · Cited by 4
Toward Understanding the Role of Reward in Attentional Selection
Fan, L., Qi, S., Guo, R., HUAGN, B., & Yang, D. (2014) · Advances in Psychological Science · doi:10.3724/sp.j.1042.2014.01573 · Cited by 5
Moore, B., Khang, S., & Francis, J. T. (2020) · Frontiers in Behavioral Neuroscience · doi:10.3389/fnbeh.2020.541920 · Cited by 5
Methods for statistical analysis and prediction of discrete choices
Daviet, R. (2018) · TSpace (University of Toronto) · Cited by 5
Double Decoys and a Possible Parameterization: Empirical Analyses of Pairwise NormalizationPreprint
Daviet, R., & Webb, R. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3374514 · Cited by 4
Donut-like organization of inhibition underlies categorical neural responses in the midbrainPreprint
Mahajan, N. R., & Mysore, S. P. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2019.12.24.887810 · Cited by 5
Wong, J. J., Bongioanni, A., Rushworth, M. F., et al. (2024) · eLife · doi:10.7554/elife.91102.2.sa2 · Cited by 5
Park, J., Holmes, C. D., & Snyder, L. H. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.02.25.640211 · Cited by 9
“Represen@ng two targets at once is known to reduce coding amplitude, likely through a process of mutual inhibi@on or divisive normaliza@on 38,39 .”
How is emotional evidence from multiple sources used in perceptual decision making?
Ngai, H. H. T., Hsiao, J. H., Luhmann, C. C., Mohanty, A., & Jin, J. (2024) · Psychophysiology · doi:10.1111/psyp.14727 · Cited by 4
“…sampling of emotional evidence through eye movement may involve the lateral intraparietal area, which is known to be a hub for directing overt visual attention and integrating visual input driven by values in decision making (Louie et al., 2011; Mohanty et al., 2009; Reynolds & Desimone, 2003).”
Perkins, A. Q., & Rich, E. L. (2025) · PLoS Biology · doi:10.1371/journal.pbio.3003281 · Cited by 6
“Divisive normalization of value representations has been described in the lateral intraparietal cortex for cues in versus out of a receptive field [51], as well as in medial OFC for risky and safe options [52], suggesting this is a potential mechanism in OFC as well.”
Smarter than humans: rationality reflected in primate neuronal reward signals
Schultz, W., Stauffer, W. R., Lak, A., & Pastor‐Bernier, A. (2021) · Current Opinion in Behavioral Sciences · doi:10.1016/j.cobeha.2021.03.021 · Cited by 4
Region-Specific Summation Patterns Inform the Role of Cortical Areas in Selecting Motor Plans
Chang, S. W. C., Calton, J. L., Lawrence, B. M., Dickinson, A. R., & Snyder, L. H. (2015) · Cerebral Cortex · doi:10.1093/cercor/bhv047 · Cited by 3
“Perceptual decisions regarding the stochastic distribution of events (Shadlen and Newsome 2001) or the worth of those events (Louie et al. 2011) do not require integrating spatial and effector information.”
BackgroundFidelity of the representation of value in decision-making
Bays, P. M., & Dowding, B. A. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005405 · Cited by 7
Rational Imprecision: Information-Processing, Neural, and Choice-Rule PerspectivesPreprint
Steverson, K., Brandenburger, A., & Glimcher, P. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.3056332 · Cited by 31
“In work with primates, Louie, Grattan, and Glimcher (2011) showed that this representation of value is well described by a computation called (divisive) normalization (Carandini and Heeger, 2012) which is known to describe neural activity in a variety of brain regions and modalities.”
Self-citationLieder, F., Griffiths, T. L., & Hsu, M. (2016) · doi:10.31219/osf.io/kxxag · Cited by 4
Normative principles for decision-making in natural environmentsPreprint
Summerfield, C., & Parpart, P. (2021) · doi:10.31234/osf.io/s2wvz · Cited by 4
de Hollander, G., Grueschow, M., Hennel, F., et al. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.08.23.609296 · Cited by 4
Action repetition biases choice in context-dependent decision-making
Wagner, B., Wolf, H. B., & Kiebel, S. J. (2025) · Communications Psychology · doi:10.1038/s44271-025-00363-x · Cited by 7
“The other models performed worse, with WAIC values of 2487.6; 28% (ABS), 2854.7; 4% (RANGE) and 3438.6; 2% (DIV).”
InfluentialChapman, A. F., & Denison, R. N. (2025) · PLoS Biology · doi:10.1371/journal.pbio.3003546 · Cited by 3
“…property in cortex, as predicted by DSTN. Spatial normalization across local neuronal populations has been proposed as a canonical computation in the brain that may provide benefits to coding efficiency [12,44], and evidence for it has been found in a variety of cortical regions [26,45–49].”
Context effects on probability estimation
Lin, W.-H., Gardner, J. L., & Wu, S. (2020) · PLoS Biology · doi:10.1371/journal.pbio.3000634 · Cited by 5
“Recent neurobiological research also has begun to investigate how context impacts subjective-value representations in the brain [6,28,29,31,32,39,40,64,65] and how context-dependent value signals relate to choice behavior [8,66].”
BackgroundResultThe biological and behavioral computations that influence dopamine responses
Stauffer, W. R. (2018) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2018.02.005 · Cited by 3
“This result indicates that dopamine neurons perform subtraction of expected reward value from actual value, as opposed to using divisive operations that are more commonly observed in neural circuits [38,39].”
Normalization by Valence and Motivational Intensity in the Sensorimotor Cortices (PMd, rM1, and cS1)Preprint
Yao, Z., Hessburg, J. P., & Francis, J. T. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/702050 · Cited by 3
Adventures of human planners in Maze Search TaskPreprint
Kryven, M., Yu, S., Max Kleiman-weiner, A., & Tenenbaum, J. B. (2021) · doi:10.31234/osf.io/r5hd4 · Cited by 3
Attention biases preferential choice by enhancing an option's value.Preprint
Pleskac, T., Yu, S., Grunevski, S., & Liu, T.-S. (2021) · Journal of experimental psychology. General · doi:10.31234/osf.io/n3ghb · Cited by 12
“Indeed, neuroeconomic studies have found normalized neural representations of value in a number of key brain areas involved in decision making, such as the orbitofrontal cortex, anterior cingulate cortex, and posterior parietal cortex (Cai & Padoa-Schioppa, 2012; Louie et al., 2011; PadoaSchioppa, 2009).”
BackgroundPlans or Outcomes: How do we attribute intelligence to others?Preprint
Kryven, M., Ullman, T. D., Cowan, B., et al. (2021) · doi:10.31234/osf.io/ja3p6 · Cited by 3
Neuronal heterogeneity of normalization strength in a circuit model
Song, D., Ruff, D. A., Cohen, M. R., & Huang, C. (2026) · Science Advances · doi:10.1101/2024.11.22.624903 · Cited by 3
“Normalization has been observed across brain regions ( 1 – 3 ), sensory modalities ( 4 , 5 ), and species ( 6 – 8 ) and has been regarded as a canonical computation in nervous system ( 9 ).”
Neuronal normalization in monkey MT is an intensity-weighted average
Cherian, C., & Maunsell, J. H. R. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2522104122 · Cited by 3
“It has also been implicated in context - dependent modulation of neuronal representations of cognitive factors, such as spatial attention ( 2 – 4 ), pairwise noise correlations ( 5 ), working memory ( 6 , 7 ), and value ( 8 , 9 ).”
Systems Neuroscience: Shaping the Reward Prediction Error Signal
Stauffer, W. R. (2015) · Current Biology · doi:10.1016/j.cub.2015.09.057 · Cited by 2
Approximate planning in spatial search
Kryven, M., Yu, S., Max Kleiman-weiner, A., Ullman, T. D., & Tenenbaum, J. B. (2024) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1012582 · Cited by 2
LIP activity in the interstimulus interval of a change detection task biases the behavioral response
Arcizet, F., Mirpour, K., Foster, D. J., Charpentier, C. J., & Bisley, J. W. (2015) · Journal of Neurophysiology · doi:10.1152/jn.00604.2015 · Cited by 2
“…can be thought of as representing priority (Bisley and Goldberg 2010), salience (Gottlieb 2007), or a form of value (Kubanek and Snyder 2015; Louie et al. 2011; Louie and Glimcher 2010; Sugrue et al. 2004), but in all cases it is used to decide where to place covert (Bisley and Goldberg…”
MethodWong, J. J., Bongioanni, A., Rushworth, M. F. S., & Chau, B. K. H. (2023) · eLife · doi:10.7554/elife.91102 · Cited by 4
“In humans and monkeys, a positive distractor effect was found in decision signals in the mPFC ( Chau et al., 2014 ; Fouragnan et al., 2019 ), whereas divisive normalization was found in decision signals in the PPC ( Chau et al., 2014 ; Louie et al., 2011 ).”
BackgroundOn multiple sources of value sensitivity
Pirrone, A., & Tsetsos, K. (2022) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2207053119 · Cited by 2
Reward value revealed by auction in rhesus monkeysPreprint
Al-Mohammad, A., & Schultz, W. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2019.12.11.872564 · Cited by 2
Efficiently Irrational: Illuminating the Riddle of Human ChoicePreprint
Glimcher, P. W. (2022) · doi:10.31234/osf.io/zhymg · Cited by 2
Self-citationPlanning ahead in spatial searchPreprint
Kryven, M., Max Kleiman-weiner, A., Tenenbaum, J. B., & Yu, S. (2022) · doi:10.31234/osf.io/epmxf · Cited by 2
Decision bias and sampling asymmetry in reward-guided learningPreprint
Cao, Y., & Tsetsos, K. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.09.10.557023 · Cited by 2
Explaining decision biases through context-dependent repetitionPreprint
Wagner, B., Wolf, H. B., & Kiebel, S. J. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.10.09.617399 · Cited by 2
Perkins, A. Q., & Rich, E. L. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.11.12.623291 · Cited by 2
A dynamic spatiotemporal normalization model for continuous visionPreprint
Chapman, A. F., & Denison, R. N. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.03.06.641906 · Cited by 2
“…may provide benefits to coding efficiency (Carandini & Heeger, 2012; Louie & Glimcher, 2012), and evidence for it has been found in a variety of cor-cal regions (Busse et al., 2009; Carandini et al., 1997; Louie et al., 2011; Rabinowitz et al., 2011; Simoncelli & Heeger, 1998; Zoccolan et al., 2005).”
Perceptual Support for Temporal Normalization Across Hundreds of MillisecondsPreprint
Epstein, M. L., Kovacevich, S., & Denison, R. N. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.08.28.672950 · Cited by 2
Neural substrates on the judgment of sequential benefits and losses
Noda, M., Tanabe, H. C., Yoshioka, A., & Kimura, M. (2023) · Cognitive Affective & Behavioral Neuroscience · doi:10.3758/s13415-023-01087-3 · Cited by 1
“, 1996) or present contexts (Louie et al., 2011) as a reference point (Bartra et al.”
BackgroundIs the Whole the Sum of its Parts? Neural Computation of Consumer Bundle Valuation in Humans
Cross, L., Webb, R., & O’Doherty, J. P. (2025) · Journal of Neuroscience · doi:10.1523/jneurosci.0983-25.2025 · Cited by 1
Neuroeconomics and Agent-Based Computational Economics
Chen, S. (2014) · International Journal of Applied Behavioral Economics · doi:10.4018/ijabe.2014040102 · Cited by 1
Early versus late noise differentially enhances or degrades context-dependent choice
Shen, B., Nguyen, D., Wilson, J., Glimcher, P. W., & Louie, K. (2025) · Nature Communications · doi:10.1038/s41467-025-59140-3 · Cited by 2
“One promising explanation for context-dependent choice is the divisive normalization computation, a widely documented nonlinear neural computation seen in diverse species, brain regions, and cognitive processes, that has been proven to be optimal for many environments 18 .”
InfluentialSelf-citationStabilization of recurrent neural networks through divisive normalization
Morone, F., Rawat, S., Heeger, D. J., & Martiniani, S. (2026) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2601841123 · Cited by 6
“…in the responses of neurons in the primary visual cortex [1, 2], it was later invoked to interpret a larger body of physiological data in the olfactory [3] and auditory [4] cortical areas, as well as in cognitive processes such as attention, working memory and value-based decision making [5–8].”
Computational Principles of Value Coding in the Brain
Louie, K., & Glimcher, P. W. (2016) · Elsevier eBooks · doi:10.1016/b978-0-12-805308-9.00010-5 · Cited by 2
Self-citationVisual-Motor Integration in the Primate Brain
Hagan, M. A., Wong, Y. T., & Pesaran, B. (2020) · Elsevier eBooks · doi:10.1016/b978-0-12-809324-5.24265-x · Cited by 2
Neuronal Response to Reward and Luminance in Macaque LIP During Saccadic Choice
Wu, Z., Chen, A., & Cai, X. (2022) · Neuroscience Bulletin · doi:10.1007/s12264-022-00948-0 · Cited by 1
“6F), which is consistent with divisive normalization in the LIP [12, 25].”
BackgroundNi, Y., Su, J., Wang, S., & Wan, X. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3155882 · Cited by 1
Dorsal anterior cingulate cortex neurons only partially integrate determinants of valuePreprint
Azab, H., & Hayden, B. Y. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.01.01.892380 · Cited by 1
“For example, competitive inhibition models, the dominant models of economic choice, involve separate pools of integrated (i.e. post-evaluation) value neurons competing (Chau et al., 2014; Rustichini and Padoa-Schioppa, 2015; Hunt et al., 2012; Hunt et al., 2015; Louie et al., 2011).”
BackgroundWittmann, M. K., Scheuplein, M., Gibbons, S. G., & Noonan, M. P. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.01.14.426647 · Cited by 1
“We test this hypothesis by examining a type of decision-making bias that occurs in multi-option environments and depends on medial prefrontal cortex: how the comparison of two option is influenced by an irrelevant third alternative (Ray, 1973; Noonan et al., 2010; Louie et al., 2011; Louie et al., 2013; Chau et al., 2…”
BackgroundMethodInfluentialKohl, C., Wong, M., Rushworth, M. F. S., & Chau, B. K. H. (2021) · Research Square · doi:10.21203/rs.3.rs-148214/v1 · Cited by 1
Uncertainty modulates visual maps during non-instrumental information demandPreprint
Li, Y., Daddaoua, N., Horan, M., et al. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.07.20.453107 · Cited by 1
Asymmetric and adaptive reward coding via normalized reinforcement learningPreprint
Louie, K. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.11.24.469880 · Cited by 1
Self-citationContrast effect of emotional context on interpersonal distance with neutral social stimuliPreprint
Cartaud, A., Lenglin, V., & Coello, Y. (2021) · doi:10.31234/osf.io/b54kd · Cited by 1
Reply to Pirrone and Tsetsos: Robust evidence for enhanced high-value sensitivity
Shevlin, B. R. K., Smith, S. M., Hausfeld, J., et al. (2022) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2209521119 · Cited by 1
Wong, J. J., Bongioanni, A., Rushworth, M. F. S., & Chau, B. K. H. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.08.20.554013 · Cited by 1
Modulation of input sensitivity and output gain by retinal amacrine cellsPreprint
Nategh, N., Manu, M., & Baccus, S. A. (2023) · doi:10.7554/elife.90862.1 · Cited by 1
The timescale and functional form of context-dependence during human value-learningPreprint
Tohidi-Moghaddam, M., & Tsetsos, K. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.02.01.578398 · Cited by 1
Wong, J. J., Bongioanni, A., Rushworth, M. F. S., & Chau, B. K. H. (2024) · eLife · doi:10.7554/elife.91102.2 · Cited by 1
Neuronal normalization in monkey MT is an intensity-weighted averagePreprint
Cherian, C., & Maunsell, J. H. R. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.07.21.665985 · Cited by 1
Efficient Learning of Predictive Maps for Flexible PlanningPreprint
Bazarjani, A., & Piray, P. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.02.11.705395 · Cited by 2
Context dependent modulation of value processing in the human brain
Park, S. Y. Q. (2012) · Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver · doi:10.17169/refubium-12810
“Furthermore, a recent study has shown that the primate lateral intra‐parietal cortex codes saccade values of the same option depending on other available choice options (Louie et al., 2011).”
BackgroundA fresh approach to vector graphics
Wonka, P. (2013) · Communications of the ACM · doi:10.1145/2483852.2483872
Effects of numeric magnitude on the cortical valuation network
Kanayet, F. J., Opfer, J. E., & Cunningham, W. A. (2013) · eScholarship (California Digital Library)
The neural correlates of intentional control
Wisniewski, D. (2016) · edoc Publication server (Humboldt University of Berlin) · doi:10.18452/17500
Mechanisms of attention in visual cortex and the amygdala
Baruni, J. (2016) · doi:10.7916/d83t9h70
Normalization models of cue combination in touchPreprint
Rahman, M. S., & Yau, J. M. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/283218
Modulation of input sensitivity and output gain by retinal amacrine cellsPreprint
Nategh, N., Manu, M., & Baccus, S. A. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/273730
Contextual Influences on Value-based ChoicePreprint
Man, V. Y., Kovacheff, C., & Cunningham, W. A. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/340695
“We tested a divisive normalisation mechanism (Louie et al., 2011; 2013) to account for choice set effects, or the local context of an alternative against other available options (Tversky and Simonson, 1993).”
MethodExpectation in motor planning and execution
Weinberg, I. (2018) · UCL Discovery (University College London)
Context-Dependent Probability Estimation and its Neurocomputational SubstratesPreprint
Lin, W.-H., Gardner, J. L., & Wu, S. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/624163
“…representations in the brain (Tremblay & Schultz, 1999; Sallet et al., 2007; Elliot et al., 2008; Padoa-Schioppa, 2009; Kobayashi et al., 2010; Louie et al., 2011, 2013; Cox & Kable, 2014; Yamada et al., 2018) and how context-dependent value signals relate to choice behavior (Khaw et al.,…”
BackgroundMethodResultSaccadic foraging reveals mechanisms of value-based decision-making in primate superior colliculusPreprint
Zhang, B., Kan, J. Y. Y., & Dorris, M. C. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/764357
Adaptive Economics: A neuroethological approach to the study of preferences, biases, and choice
Bujold, P. M. (2019) · Apollo (University of Cambridge) · doi:10.17863/cam.48007
Reaction Time And Subjective Value-Based Decision-Making
Rady, N. A. (2019) · UA Campus Repository (The University of Arizona)
Lin, L. (2020) · Journal of Behavioral and Experimental Economics · doi:10.1016/j.socec.2020.101618
Bounded Rationality in C. elegansPreprint
Cohen, D., Volovich, M., Zeevi, Y., Elbaum, L., Louie, K., Levy, D. J., & Rechavi, O. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/257535
“…experimental results and normalization-based mathematical model are aligned with previous studies on cortical computation which showed that IIA violations can be explained by a divisive normalization framework (Louie, Grattan, and Glimcher 2011; Louie et al. 2013; Webb, Glimcher, and Louie 2014).”
Self-citationA new scaling rule for context-dependent moral judgments.Preprint
Gomis-Pont, S., Navarro-Plaza, M. C., Navajas, J., Quiroga, R. Q., Sala, S., & Martinez, L. M. (2020) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/rbhqd · Cited by 1
Neural correlates of individual differences in aversion to risk and choice inconsistencyPreprint
Jaquerod, M. E., Lintas, A., Gratton, G., et al. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.05.10.443362
Reward Value Revealed by Auction in Rhesus MonkeysPreprint
Al-Mohammad, A., & Schultz, W. (2020) · SSRN Electronic Journal · doi:10.2139/ssrn.3598157
Normalization Models of Contextualized TouchPreprint
Rahman, M. S., & Yau, J. M. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3219287
van Wingerden, M., & Tobias Kalenscher, A. (2013) · Springer eBooks · doi:10.1007/978-1-4614-7320-6_311-1
Computational mechanisms underlying latent inverse value updating of unchosen actionsPreprint
Ben-Artzi, I., Kessler, Y., Nicenboim, B., & Shahar, N. (2022) · doi:10.31234/osf.io/sxjez
van Wingerden, M., & Tobias Kalenscher, A. (2022) · Springer eBooks · doi:10.1007/978-1-0716-1006-0_311
Modulation of sensory processing under different modes of reward cueing
Antono, J. E. (2023) · eDiss (Georg-August-Universität Göttingen) · doi:10.53846/goediss-9824
Modulation of input sensitivity and output gain by retinal amacrine cellsPreprint
Nategh, N., Manu, M., & Baccus, S. A. (2023) · doi:10.7554/elife.90862
Sustained attention operates via dissociable neural mechanisms across different eccentric locationsPreprint
Phangwiwat, T., Punchongharn, P., Wongsawat, Y., Chatnuntawech, I., Wang, S., Chunharas, C., Sprague, T. C., Woodman, G. F., & Itthipuripat, S. (2023) · Research Square · doi:10.21203/rs.3.rs-3562186/v1
Distractor effects in decision making depends on individual’s style of integrating choice attributesPreprint
Wong, J. J., Bongioanni, A., Rushworth, M. F. S., & Chau, B. K. H. (2023) · eLife · doi:10.7554/elife.91102.1
Cultural contributions to cognitive aging
Barber, N., Valoumas, I., Chunharas, C., Itthipuripat, S., & Gutchess, A. H. (2023) · Elsevier eBooks · doi:10.1016/b978-0-12-820480-1.00042-5 · Cited by 1
Approximate Planning in Spatial SearchPreprint
Kryven, M., Yu, S., Kleiman‐Weiner, M., et al. (2024) · doi:10.31234/osf.io/bja7f
Adaptive value coding and choice behavior
Louie, K., & Glimcher, P. W. (2024) · Elsevier eBooks · doi:10.1016/b978-0-12-820480-1.00149-2
Self-citationWong, J. J., Bongioanni, A., Rushworth, M. F., et al. (2024) · eLife · doi:10.7554/elife.91102.2.sa1
Wong, J. J., Bongioanni, A., Rushworth, M. F., et al. (2024) · eLife · doi:10.7554/elife.91102.2.sa3
Wong, J. J., Bongioanni, A., Rushworth, M. F. S., & Chau, B. K. H. (2024) · eLife · doi:10.7554/elife.91102.2.sa0
A Tale of Two Environments: Divisive Normalization and the (In)Flexibility of ChoicePreprint
Kurtz-David, V., Sinha, S., Alladi, V., Bucher, S., Brandenburger, A. M., Louie, K., Glimcher, P. W., & Tymula, A. A. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.08.25.609561
Self-citationNeural and behavioral probability weighting functionPreprint
Tymula, A. A., & Yamada, H. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4971546
Shen, X., Li, F., & Min, B. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.12.10.627688
Metadata
- Authors
- Louie, K., Grattan, L. E., & Glimcher, P. W.
- Affiliations
- New York University (US)
- Venue
- Journal of Neuroscience
- Publisher
- Society for Neuroscience
- Published
- 2011-07-20
- Volume
- 31
- Issue
- 29
- Pages
- 10627-10639
- ISSN
- 0270-6474 (ISSN-L)
- 1529-2401
- PMC
- PMC3285508
- OpenAlex
- W2069815761
- Semantic Scholar
- 2c68a342adf5dd25439ef7f3f553afd1e9a0d1d4
- Cited by
- 308
- References
- 60
- Citations by year
- 2026: 7 · 2025: 13 · 2024: 20 · 2023: 22 · 2022: 18 · 2021: 29 · 2020: 19 · 2019: 25 · 2018: 23 · 2017: 22 · 2016: 16 · 2015: 24 · 2014: 23 · 2013: 24 · 2012: 19
- FWCI
- 11.36
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Neuroscience (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Eye Institute (R01EY010536)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Keywords
- divisive normalization, gain control, context-dependent choice, comparative analysis, decision-making, monkey visual cortex
- MeSH terms
- Action Potentials, Analysis of Variance, Animals, Choice Behavior, Macaca mulatta, Male, Models, Neurological, Neurons, Parietal Lobe, Photic Stimulation, Predictive Value of Tests, Reference Values, Reward, Time Factors, Chi-Square Distribution
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