NOTE-953: Sung, Rigotti & Lee — factorized goal and uncertainty codes in lateral PFC

Contribution

It reanalyses an existing dataset (Lee, Shimojo and O’Doherty 2014, its ref. 17) with the representational-geometry tools of Bernardi et al. 2020 (shattering dimensionality, cross-condition generalization, parallelism) and asks how goals and environmental uncertainty share a neural space. It finds a mostly linear (“factorized”) arrangement in vlPFC, dlPFC and OFC, in which the goal code does not measurably move when transition noise changes. Across 20 subjects, how separable and how transferable the goal code is correlates with behaviour. It adds simulations showing that model-free agents trade flexibility against stability, and model-based agents do not.

Key insight

A code in which one variable’s readout generalizes across the levels of another lets a system notice the second variable without disturbing its use of the first. “In such a factorized embedding structure, it is possible to detect uncertainty changes, while goal information remains consistently represented regardless of uncertainty levels” (p. 5). The paper’s closing gloss: “By maintaining separate codes for goal and uncertainty, the PFC preserves goal-directed action plans while selectively adjusting behavior in response to environmental variability” (p. 9).

Assumptions

• The task is an action–outcome learning task. “Goal-directed learning requires representing action-outcome contingencies and updating them to attain a goal” (p. 1). Participants make two left/right choices per trial through a tree of states to a coloured coin, and were told they “should learn, through experience, which choices were more likely to lead to each colored coin” (p. 9). Everything that changes their model arrives as the consequence of their own choices.
• The goal is cued from outside, per trial. A coloured box at trial start says which coin pays (specific goal); a white box says any coin pays (non-specific). The goal is not chosen, inferred or held by the participant across trials.
• “Uncertainty” is block-wise transition stochasticity of the environment: transition probabilities (0.9, 0.1) against (0.5, 0.5), alternating in short uncued blocks (3–5 and 5–7 trials, p. 9). It is not the subject’s uncertainty about a hypothesis, nor a reliability score attached to a piece of evidence.
• “Factorized” is operational, and linear. Three tests (pp. 5–7, 11):
  • Shattering. Six classes (3 goals × 2 uncertainty levels); every balanced dichotomy is decoded with a linear SVM, and dichotomies are grouped as goal (3), uncertainty (1), linear and nonlinear (9, those no random linear-mixing model y = W_g g + W_u u + b with N = 3 could separate). Factorized mixing is the profile goal, uncertainty and linear SD high, nonlinear SD “significantly lower”.
  • CCGP. Train a goal decoder in low-uncertainty trials, test in high, and the reverse; average. “If the target embedding is influenced by context, the decision boundary for decoding would shift, leading to a lower CCGP” (p. 7). Factorization is read off CCGP not differing from within-condition goal SD.
  • Parallelism. Cosine between goal-difference vectors in the two uncertainty conditions (Supplementary Fig. 9). CCGP was computed only for goal across uncertainty. No decoder for uncertainty was trained under one goal and tested under another.
• fMRI specifics. 3T, TR 2.8 s; each event’s pattern is the first volume after the event (p. 10), not a modelled response; leave-one- session-out cross-validation with 100 undersampling repeats; eight anatomical ROIs.
• Statistics. ROI decoding tests are uncorrected across ROIs, on the grounds that ROIs were chosen a priori (p. 11); neural–behaviour correlations are called exploratory and FDR-corrected over the eight ROIs. n = 20 throughout (22 scanned, 2 excluded).
• The simulated agents are not fitted to humans. MB and MF agents each run with 1000 random (learning rate, inverse temperature) pairs on each of the 20 humans’ trial and goal sequences (20,000 agents each), and the human–agent comparison is between scatter patterns (p. 10).

Key results

• Behaviour (p. 2, Fig. 1d). Uncertainty hurt choice only without a specific goal: optimality 0.850 ± 0.035 (low) against 0.619 ± 0.021 (high), t(19) = 5.975, p < 0.0001; consistency 0.897 against 0.847, t(19) = 5.294. With a specific goal neither changed (optimality t(19) = 0.887, p = 0.384; consistency t(19) = 0.891, p = 0.386). Response times were longer with a specific goal, and longer still under high uncertainty (Supplementary Fig. 1).
• Agents against humans (p. 3, Fig. 1f). Flexibility (choice versatility after a goal change) with performance: humans r = 0.827, MB r = 0.799, MF r = −0.035. Stability (choice consistency within a goal) with performance: humans 0.779, MB 0.963, MF 0.042. Flexibility with stability: humans 0.541 (p = 0.014), MB 0.829, MF −0.964. “MF agents suffer from a flexibility-stability trade-off …, whereas humans and the MB agents did not.”
• Decoding (pp. 4–5, Fig. 2). Goal (chance 33.3%): dlPFC 38.8%, vlPFC 37.2%, V1 36.9%, OFC 36.6%, ACC and preSMA 35.4%. Uncertainty (chance 50%), in the specific-goal condition only: OFC 53.4% (p = 0.0014), dlPFC 52.1% (p = 0.026), vlPFC 51.8% (p = 0.020), uncorrected; not decodable in the non-specific condition, and “Uncertainty was not decodable in ACC” (p. 8).
• Shattering (p. 5, Supplementary Table 3). vlPFC goal SD 0.530, uncertainty 0.518, linear 0.519, nonlinear 0.508; dlPFC 0.541, 0.521, 0.526, 0.511; OFC 0.527, 0.534, 0.521, 0.507. All above 0.5, nonlinear included. Nonlinear SD is below goal and linear SD in vlPFC and dlPFC, and below all three in OFC. In vlPFC and dlPFC the uncertainty SD is not distinguishable from the nonlinear SD (t(19) = 1.446, p = 0.164; t(19) = 1.175, p = 0.254).
• CCGP (p. 7, Fig. 4a, Supplementary Table 4). In every ROI, goal CCGP across uncertainty did not differ from goal SD within either uncertainty level (vlPFC t(19) = −0.337 and −0.827; dlPFC −0.072 and −0.372; OFC 0.109 and −0.395; all n.s.). Parallelism was above zero in vlPFC, dlPFC, OFC and preSMA.
• Neural–behaviour correlations, FDR-adjusted (Supplementary Tables 3 and 4).
  • Goal SD with flexibility: vlPFC r = 0.583, dlPFC 0.641 (q < 0.03); with stability: vlPFC 0.554, dlPFC 0.577 (q = 0.031); with performance: vlPFC 0.679, dlPFC 0.768, OFC 0.549.
  • Uncertainty SD with any behaviour: none (e.g. flexibility vlPFC r = −0.150, dlPFC −0.050). The text: “uncertainty separability was not significantly related to goal-directed behavior” (p. 6).
  • Goal CCGP with flexibility: vlPFC r = 0.576, dlPFC 0.551 (q = 0.047); with performance: vlPFC 0.628, dlPFC 0.713, ACC 0.564, preSMA 0.641; with stability: none after correction (vlPFC r = 0.559, dlPFC 0.543, q = 0.054; OFC 0.468, q = 0.075).

Claims

id	claim	strength	support
C1	With a cued specific goal, transition noise does not lower choice optimality or consistency; without one, it does	moderate	Fig. 1d, n = 20, paired t-tests
C2	Unfitted model-free agents trade flexibility against stability; model-based agents and humans show a positive relation	moderate for the agents, weak as a model of humans	Fig. 1f; agents not fitted
C3	Goal and transition uncertainty are linearly decodable from vlPFC, dlPFC and OFC	weak to moderate	Fig. 2; small effects (1.8–5.5 points over chance), uncorrected across ROIs
C4	Their joint geometry there is factorized (linear) rather than nonlinearly mixed	weak	Fig. 3b; nonlinear SD lower but above chance; in vlPFC and dlPFC uncertainty SD not separable from nonlinear SD
C5	The goal code is unaffected by uncertainty	weak	Fig. 4a; a null difference between CCGP and SD, with no equivalence test
C6	Goal separability and robustness in lateral PFC are associated with behavioural flexibility, stability and performance	moderate for flexibility and performance; not shown for CCGP and stability	Supplementary Tables 3–4, n = 20, exploratory, FDR over 8 ROIs
C7	The factorized code is the mechanism of stably flexible behaviour	weak	correlational only; no intervention or model linking geometry to choice

Method

1. Reuse Lee et al. (2014): 400 main-task trials over five sessions, 100 pretraining trials at (0.5, 0.5) with a white box.
2. Score each choice for optimality (against an oracle with true transitions and rewards), versatility (switch after a goal change) and consistency (same choice when the goal repeats).
3. Simulate MB agents (FORWARD transition learning with a state prediction error δ_SPE = 1 − T(s, a, s′), ΔT = η δ_SPE, and BACKWARD planning that recomputes Q_MB from the cued goal’s reward at once) and MF agents (SARSA on the reward prediction error), both with softmax choice (p. 10).
4. Decode goal, uncertainty and all six-class dichotomies per event with linear SVMs; compute SD, CCGP and parallelism; correlate per-subject pre-outcome averages (S1–A2) with the behavioural measures.

Concepts

• Choice versatility — on a trial whose goal differs from the last, 1 if the choice at the same state differs, else 0. The paper’s flexibility.
• Choice consistency — on a trial whose goal repeats, 1 if the choice at the same state is the same, else 0. The paper’s stability. In the high-uncertainty blocks a consistent choice is one not revised after a noisy transition.
• Shattering dimensionality (SD) — mean linear-decoder test accuracy over a set of dichotomies of the condition classes.
• CCGP — accuracy of a decoder for one variable trained in one level of another variable and tested in a different level (Bernardi et al. 2020).
• Factorized mixing — goal, uncertainty and linear dichotomies separable, nonlinear (interaction) dichotomies markedly less so.

Connections

The analysis is Bernardi et al.’s geometry of abstraction (Cell 2020; Rigotti is among its authors, which the paper’s reference, “Bernardi, S. et al.”, does not show), with Rigotti et al.’s mixed-selectivity and shattering apparatus (2013), applied to human BOLD patterns. The dataset and the MB agent’s FORWARD/BACKWARD scheme come from Lee, Shimojo and O’Doherty (2014) and Gläscher et al. (2010). The factorization-for- generalization reading follows Flesch et al. (2022) and Ito et al. (2022). The paper cites recent task-switching work that treats stability and flexibility as controlled by “independent mechanisms” (p. 8).

Bearing on the record

• CLAIM-341 (the loop runs between judgement and observation, without action). Nothing for or against. The task is an action–outcome loop in the sense the claim sets aside: what the subject learns, transitions and coins, arrives only as consequences of its own choices, and the paper defines its subject matter that way (p. 1). No condition holds action and its outcomes fixed, so defeat condition (a) is not touched. The goals are cued by the experimenter each trial, not judgements the subject forms.
• CLAIM-342 and QUESTION-121 (what scores evidence independently of the interpretation it tests). The LIT’s “Why this is here” offers factorized goal and uncertainty codes as “a candidate for how a mind keeps its scoring of evidence apart from its current goal”. The reading narrows that in four ways.
  • Wrong direction measured. CCGP was computed for the goal code across uncertainty levels: uncertainty does not bend the goal readout. What independent scoring would need is the converse, an uncertainty (or evidence) code that does not bend with the goal. The paper never trains an uncertainty decoder under one goal and tests it under another.
  • Uncertainty is coded only under a specific goal. vlPFC, dlPFC and OFC “significantly represented uncertainty information exclusively within the specific goal condition” (p. 5). Whether uncertainty is represented at all depends on the goal condition. Within that condition it is factorized from which goal, but the evidence-side code is gated by having a goal, which is the opposite of scoring that runs without reference to it.
  • The uncertainty axis is the weak one. In vlPFC and dlPFC uncertainty SD is not separable from the nonlinear SD (p = 0.164, 0.254), and uncertainty separability predicts no behaviour. The title’s “factorized embedding of goal and uncertainty in the lateral prefrontal cortex” rests in LPFC on goal and linear dichotomies.
  • Uncertainty is not evidence scoring. It is a block-level estimate of how noisy transitions are, a precision-like context. It is closer to QUESTION-121’s candidate 4 (processing signals, scoring “how the interpretation is going, not what it says”) than to Regime B’s independent score of operators, and the paper does not show it regulating learning rates.
  • My observation: the closer analogue is in the simulation. The MB agent’s transition model is scored by a state prediction error that does not involve the goal (δ_SPE = 1 − T(s, a, s′), p. 10); the goal enters only afterwards, in BACKWARD planning. The MF agent’s only error signal is the goal-defined reward, so its evidence is scored through what it currently wants, and it shows the trade-off (flexibility–stability r = −0.964). That is CLAIM-342’s shape, an anchor whose scoring does not pass through the current goal, in a two-parameter toy. Three cautions: the agents are not fitted to the humans; the goal here is a cued reward, not an interpretation under test; and the evidence that scores the MB model, the observed transition, arrives through the agent’s own choice. So it illustrates separation of scoring from goal, not evidence free of action.
• CLAIM-340 (commitment and κ′ against κ̄). No bearing beyond analogy. In the MB agent the cued goal bends neither the committed transition predictions nor the reading of the observed transition, so in the claim’s terms both weights are zero with respect to the goal, trivially. The paper measures nothing that could estimate κ′ or κ̄ in people.
• Checks of the current LIT against the text.
  • Summary, “In simulations model-free learning fails the flexibility–stability trade-off while model-based learning can be both flexible and stable”: correct, for unfitted agents with random parameters.
  • Summary, “goals and uncertainty are represented as factorized embeddings in lateral prefrontal and orbitofrontal cortex”: as the paper says, with the qualifications above (small effects, uncorrected ROI tests, nonlinear SD above chance, uncertainty side weak in LPFC, uncertainty coded only under specific goals).
  • Summary, “the separability of goals and their resilience to uncertainty correlated with participants’ flexibility and stability”: goal separability, yes. Goal resilience (CCGP) correlated with flexibility and performance after correction, not with stability. The main text says the goal CCGPs in vlPFC and dlPFC “were significantly correlated with behavioral flexibility, stability, and performance” (p. 7); Supplementary Table 4 gives the stability correlations q = 0.054, n.s., and Fig. 4b marks them only as “weak statistical significance (significant before multiple correction)”.
  • Tags: learning-and-conditioning fits; the task is instrumental learning with cued goals.
• For the anthology. No instruction for machine-learning practice. A closing suggestion to build β-VAE-like factorized RL agents (p. 8) is a research direction, not a practice.

Limitations

• n = 20, a reanalysis of a 2014 dataset, BOLD at TR 2.8 s with one volume per event.
• Decoding effects are a few points above chance and ROI tests are uncorrected across ROIs.
• “Unaffected by uncertainty” is a failure to find a difference, without an equivalence test or power analysis.
• The brain–behaviour link is across-subject correlation, called exploratory; nothing is manipulated.
• Agents are compared with humans by scatter pattern, not fitted; the human flexibility–stability correlation (0.541) is not shown to need an MB learner.
• The goal is cued every trial, so “goal pursuit” here does not include forming or holding a goal.

Open questions

• Is the uncertainty code invariant across goals (CCGP of uncertainty across goals)? That is the test the record’s question needs.
• Does the uncertainty code modulate learning from transitions, as an arbitration signal would, and is it present when no specific goal is cued?
• Does the human stability under noise come from goal-independent scoring of the transition model, as in the MB agent? Fitting the agents to the choices would say.