Updates & Issues

Version 1 (April 2026)

Published on Preprints.org: 10.20944/preprints202604.1390.v1

Known Issues & Imprecisions

The following issues have been identified in the current version of the paper based on community feedback (e.g., via Reddit discussions). These will be addressed in the next revision:

• 2026-04-27: Lack of clear policy for individuating variables in worked examples: The Waymo calculation takes state variables at face value and assigns a fixed 14-bit depth without directly measuring mutual information. While the metric definition is clear that only variables with genuine mutual information count, a rigorous application would measure it directly. The ±order-of-magnitude confidence interval in the paper partly acknowledges this limitation, but the worked examples could be more rigorous in application.
• 2026-04-27: Definition 3 (R) is not explicit enough about information bottleneck and compression: A naïve "sum over variables" formulation of representational capacity (R) could over-reward fine-grained, low-level descriptions over compressed, higher-level abstractions. While FC intends to outsource this to Bialek et al. (variables only contribute if they participate in prediction), restricting R to predictively relevant information should be stated as a formal constraint in Definition 3, rather than just implied.
• 2026-05-05: FCS is not "slice-invariant" under the product formula for perfect cross-reasoning:
  "Slice invariance" is a desired property of the FC score. When a system's internal variables are partitioned or regrouped, the representation should ideally remain consistent.
  However, the product formula P_agent = ∏_j P(m_j) is sensitive to how self-model boundaries are drawn: subdividing one self-model into two multiplies P_agent by an extra factor of P; merging two models into one collapses it. The score changes under re-partitioning of the same underlying variable set, which is undesirable.
  
  Root cause. The product formula correctly computes the joint conclusion space of independent reasoning processes (a Cartesian product argument). But perfect cross-reasoning is precisely the case where independence breaks down: a single global reasoning engine drawing inferences across self-models is the opposite of independent per-model processes.
  
  Where the problem does not arise. R_agent = ∑_i I(m_i; s_i) is slice-invariant by construction. The no-cross-reasoning formula FCS_agent = ∑_j FCS(m_j) is unaffected, since independence is there definitional, not assumed. Only the perfect cross-reasoning paragraph requires correction.
  
  The correction. Replace P_agent = ∏_j P(m_j) with reasoning power computed over the full variable set — either via Bialek scaling applied globally:
  P_agent = (K/2) log₂ N
  where K is the total number of self-model variables and N inference steps; or more fundamentally, as the joint predictive mutual information:
  P_agent = I(ℳ ; 𝒮_future)
  Both are invariant to regrouping of variables. Self-models remain essential as enumerative units — they are how an evaluator identifies which variables to include — but do not enter the score formula as separate multiplicative factors.
  
  Practical impact. Single-domain scores (e.g., Waymo kinematic) are unaffected. Agent-level scores combining multiple self-models under cross-reasoning assumptions (Generative Agents, human working memory) should be treated as illustrative of ordering rather than precise values until the agent-level formula is revised.
• 2026-05-13: Contested claim regarding self-modeling and Theory of Mind (ToM): The manuscript states that self-modeling is a requirement for ToM as a fact, but this is contested in cognitive science literature. While model-theoretic accounts (Theory-Theory) support this requirement, simulation-theoretic accounts suggest ToM can function via direct simulation without an explicit self-model. The text should be revised to acknowledge this theoretical debate.
• 2026-05-13: Lack of formal derivation for multiplicative aggregation: The multiplicative aggregation for perfect cross-reasoning (P_agent = ∏_j P(m_j)) is not derived, only asserted as analogous to IIT's high-Φ regime. The product of local reasoning powers is not generally a well-defined quantity without a formal account of how cross-model inference combines them. This theoretical gap is the underlying cause for the missing slice-invariance in the current formulation (see 2026-05-05).
• 2026-05-13 (fixed 2026-05-27): Missing confidence intervals in Figure 1: Figure 1 currently plots agents using point estimates for Representational Capacity (R) and Reasoning Power (P). To accurately reflect the uncertainty in the current measurement techniques and variable individuation, the plot should include confidence intervals for both axes.
• 2026-05-13: Justification for applying Bialek et al. scaling across diverse substrates: The manuscript uses the scaling law from Bialek et al. (2001) as a universal model for Reasoning Power (P). However, the applicability of this information-theoretic bound across widely different architectures—such as Model Predictive Control (MPC) in robotics versus transformer-based inference in LLMs—requires more explicit justification. The next revision should address whether the logarithmic scaling of predictively relevant information holds uniformly or if architectural constants significantly alter the functional comparison.
• 2026-05-13: Need for additional FSMA evaluation on diverse datasets: The current demonstration of FSMA only uses one text (Mark on the Wall) with SBR top-down priors. To prove the generalizability of the metric, future revisions should include evaluations on wildly different text sources, ensuring the assessment is not over-fitted to the specific characteristics of the SBR instantiation.
• 2026-05-13: Weak theoretical connection to Predictive Processing (PP): The manuscript currently claims a link between Functional Consciousness (FC) and Predictive Processing (PP), primarily mediated by the use of Bialek et al.'s predictive information. However, this connection is theoretically thin as it stands. Future revisions should either establish a more defensible bridge to the PP framework or scale back the claimed alignment with PP.
• 2026-05-13: Formal constraint for Definition 3 (R): Definition 3 requires a formal constraint explicitly restricting R to predictively relevant variables. This is currently only implied by the reference to Bialek et al. Future revisions should add this constraint directly to the definition, accompanied by a justification citing the Information Bottleneck literature to clarify the functional boundaries of the representation.
• 2026-05-13: Reproducibility and variable individuation policy: To ensure the FCS metric is applied consistently across different systems, a clearer variable individuation policy is required. Future revisions should include a formal checklist of decisions an evaluator must make before calculation (defining the temporal horizon, information depth, ...) to improve the reproducibility of the worked examples.
• 2026-05-13: Expansion of the theoretical comparison section: The current in-text treatment of major consciousness theories (GWT, IIT, AST, etc.) is too compressed, leading to potential overclaiming of theoretical alignment. Future revisions should integrate the Covers / Sticks Out structural framework into the manuscript. Specifically, incorporating the FAQ's comparison table as a formal figure or table would provide more nuance regarding how FC overlaps with or deviates from existing theories.
• 2026-05-13: Addition of a Limitations and Validation Agenda for a "Metric": To address the current gap between the proposed metric and a validated scientific instrument, a new "Limitations and Validation Agenda" section needs to be added to the manuscript. This section should explicitly outline the specific studies required for full validation: convergent validity, criterion validity, and inter-rater reliability, transforming the "proxy" nature of the metric into an explicit scientific research program and preempting reviewer concerns about validation status.
• 2026-05-20: Theoretical boundaries of recurrence and "stateless" LLM scoring:
  Commentary on the 2025 Trends in Cognitive Sciences paper (e.g., by Christian et al. on Astral Codex Ten) argues that the feedforward versus recurrent distinction is a category error when applied to transformer generation. When a transformer's output is fed back as input (or accessed via a key-value cache), it implements recurrence. There is no principled functional difference between "unrolling N layers with feedback" and "N+1 layers of feedforward with shared weights."
  
  This is highly relevant to where FC draws its architectural boundaries. If recurrence-via-KV-cache or active auto-regressive generation counts as recurrence, then an LLM performing chain-of-thought reasoning has a non-zero representational capacity (R), contradicting the manuscript's current "stateless LLM → FCS = 0" claim.
  
  Proposed refinement. Future revisions should clarify that it is a system's session-level statelessness (the lack of a persistent, dynamically updated self-model between separate conversations or interactions) that produces FCS = 0, rather than the complete lack of token-by-token recurrence during active inference.