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REVIEW 4 major objections 4 minor 23 references

Finding Similar Objects and Active Inference for Surprise in Numenta Neocortex Model

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Small changes to a neocortex inference algorithm give it similarity search and surprise response, both framed as Bayesian or non-Bayesian updates.

desk verdict Clean, honest extension of the Numenta inference algorithm with two new capabilities, but the similarity result is conditional on an assumed distance function and the toy validation is weak. read the letter →

arxiv 2506.21554 v1 pith:PYKQWI26 submitted 2025-06-11 q-bio.NC

Hajime Kawakami This is my paper · ORCID
classification q-bio.NC
keywords thousand-brainsmodelneocortexsimilaritysearchsparsedistributedrepresentationactiveinferencesurprisenon-Bayesianupdatingassociation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that the thousand-brains neocortex model, built around prediction, can also handle association: given an object the model has already recognized, it can search the stored objects for ones whose features are similar. The proposed Algorithms 4.1 and 4.2 accomplish this by replacing the sensed feature's sparse distributed representation with a neighborhood of similar representations under a fixed feature distance, so that objects sharing similar features remain active as the model moves along the object. The paper further claims that a third algorithm, Algorithm 5.1, lets the model actively respond to surprise—sensory input most of its mini-columns did not predict—by either rewriting its prior state or zeroing its movement, and that this response can be written as a non-Bayesian updating process. The author is explicit that the setting is restricted and not validated against brain recordings; the contribution is the algorithmic bridge showing these capabilities are compatible with the model's existing machinery. If the claim holds, the model gains two of the brain's most basic cognitive operations without abandoning its core inference routine.

What carries the argument

The load-bearing objects are: (1) the cortical column with its three layers—location (grid-cell modules acting as reference frames), sensory (mini-columns whose sparse activity is the SDR of a feature), and output (whose sparse activity represents objects); (2) the inference Algorithm 3.2, which iterates prediction and observation until one object's output representation stays active; (3) the feature-distance neighborhood $N_d(W)$ on SDRs, which is the sole change that turns inference into similarity search; and (4) the non-Bayesian updating equation (5.6) with switching coefficient $\gamma_t$, which expresses Algorithm 5.1's response to surprise as a mixture of standard Bayesian updating and a reset of the prior. The argument works by showing that each proposed algorithm is a literal edit of Algorithm 3.2's steps, so convergence and recognition behavior of the original carry over essentially unchanged.

What would settle it

Implement Algorithms 4.1 and 4.2 on a dataset of objects whose pairwise similarity is independently known (for example, human judgments). If, for a fixed $D$, the objects returned are those with $D$-similar features rather than those judged similar by the independent measure in a significant fraction of runs, the claim that the algorithm 'finds similar objects' would be falsified in the sense of similarity as a brain-relevant relation. For Algorithm 5.1, feed a sensory sequence with a known Bayesian posterior: if the algorithm's active-object trajectory diverges from the posterior of the non-Bayesian process (5.6) with the same $\gamma_t$ sequence, the interpretation as Bayesian/non-Bayesian updating fails.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the inference algorithm of the thousand-brains model can be reused almost unmodified for two further cognitive operations. For similarity, the paper defines a distance $D$ on the SDRs of sensory features and replaces each sensed feature $W_t^{\mathrm{in}}$ in the inference cycle with a neighborhood $N_d(W_t^{\mathrm{in}})=\{W': D(W,W')\le d\}$. Objects whose paths of movement vectors visit locations whose features fall in these neighborhoods remain active, so the model converges not to the observed object but to a similar stored object; Algorithm 4.2 adds a reactivation rule that handles the two ways a candidate can drop out (missing location or missing feature). For surprise, the paper flags an observation as surprising when the fraction of unpredicted mini-columns exceeds $\theta_w$ (condition (5.1)); Algorithm 5.1 then either sets the previous output activity $\rho^{\mathrm{out}}_{k,t-1}=1$ so the surprising input is treated as the new prior (type I), or keeps the movement vector at zero so the next observation re-fixates on the surprising location (type II). The paper formalizes this as a non-Bayesian updating process with a switching coefficient $\gamma_t$, connecting the model's inference to the free-energy principle's active-inference story.

Load-bearing premise

The similarity search presupposes a fixed, pre-specified distance function $D$ on feature SDRs that already agrees with true object similarity; if the brain (or the model) has no way to learn or calibrate that distance, the 'similar objects' it returns are only as valid as that externally injected measure.

Editorial extensions

If this is right

  • Similarity search is a drop-in extension: with $d=0$, Algorithm 4.1 reduces to ordinary inference, so the model does not lose its original recognition behavior when the new capability is added.
  • Association between objects can be recorded in the location layer of a higher cortical column by arranging similar objects close together, giving the model a learned 'similarity' relation rather than just a one-shot query.
  • Algorithm 4.2's reactivation makes similarity search robust to the two failure modes (missing location, missing feature), so candidates are not permanently lost on the first mismatch.
  • Algorithm 5.1 gives a concrete implementation of two types of active inference: updating one's model of the world (the coffee-pot example) and orienting toward the surprising stimulus (the eye-movement example), both expressed through the same reset mechanism.
  • The non-Bayesian formulation provides a probabilistic counterpart to the algorithm's internal states, so the model's surprise response can in principle be compared with Bayesian posterior updates on the same sensory sequence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The fixed distance $D$ is doing the real cognitive work; a more complete model would learn $D$ from co-occurrence statistics of features across objects, making the similarity judgment emerge from experience rather than being injected.
  • The neighborhood trick could be applied in the location layer as well, turning the search into a location-tolerant matching that would allow analogies between objects with different spatial layouts.
  • Algorithm 5.1's reset can be read as a minimal model of attentional capture: the surprising input overrides the current motor plan, which is a testable behavioral prediction if the algorithm is embedded in a simulated agent.
  • The distance function's thresholds ($d$, $\theta_w$, $\Gamma$) control a precision/recall trade-off; measuring that trade-off on a standard object dataset would give a clean benchmark for how much 'similarity' the model can extract per unit of path length.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes two extensions of the Numenta neocortex model. Algorithms 4.1 and 4.2 search a learned object set Ω for objects similar to a given object O by replacing the sensory SDR W_t^in with a neighborhood N_d(W_t^in) defined through an external distance function D; Algorithm 5.1 responds to prediction failures (surprise) by resetting past output activity and setting the movement vector to zero. The paper further claims that Algorithm 5.1 can be interpreted as a Bayesian or non-Bayesian updating process for the latent location L_t(O), and formalizes this as Definition 5.1 together with Assumption 5.1.

Significance. If the claims held, the paper would add two capabilities—similarity-based association and surprise-driven active inference—to a biologically motivated model, with clear pseudo-code that aids reproducibility. The strength of the manuscript is its explicitness: algorithms are stated step-by-step, thresholds are listed, and the toy experiments are honest in reporting low success rates. However, the central claims are only conditional at present: the similarity algorithms rely on an externally supplied distance function whose origin is unexplained, and the non-Bayesian interpretation is constructed to match the algorithm rather than derived from it. These issues directly affect the main assertions of the paper.

major comments (4)
  1. [§4, Eq. (4.1)] The central claim that Algorithms 4.1 and 4.2 'find objects in Ω similar to O' is conditional on an external distance function D, with the assertion that 'the brain knows that these are similar' (text following Eq. (4.1)). The algorithms propagate this externally injected similarity measure; no learning rule for D is proposed, and no experiment compares the output against an independent ground-truth similarity ranking. Table 4.1 only tests whether a randomly chosen O' remains active under random feature placements, not whether the active objects correspond to semantically similar objects. As written, the association capability is assumed at the input level rather than implemented in the model.
  2. [§5, Definition 5.1 and Assumption 5.1 (Eqs. (5.5)–(5.6))] The non-Bayesian updating process is reverse-engineered to match Algorithm 5.1: γ_t is defined in (5.5) exactly by the algorithm's condition (5.2), and Assumption 5.1 forces the first term in (5.6) to vanish whenever γ_t=1, leaving only the second term. The claimed correspondence between algorithm steps and probabilities (Table 3.1) is therefore asserted by construction rather than derived or independently validated. The paper should either weaken the claim to a definitional correspondence or provide a derivation that starts from the algorithm's actual mechanisms.
  3. [§5, Eq. (5.6)–(5.7)] The proposed state-space model is formally incomplete: the sums in (5.6) are over the sets Ω_{t,L}∩Ω_{t-1,+} and Ω_{t,L}∩Ω_{t-1,0}, which depend on the informal threshold 'P>0' introduced before (5.5), and no explicit transition distribution for L_t(O)→L_{t+1}(O) is specified beyond the phrase 'by the movement vector' in (5.7). Without these probabilistic primitives, the claim that Algorithm 5.1 'can be interpreted as Bayesian or non-Bayesian updating' is not precise enough to be checked.
  4. [§4, Table 4.1] The experiments show that with Γ=1, which the paper notes is exactly Algorithm 4.1, the probability that O' is active at the end is only 7.0%, 0.4%, and 0.1% for T=3, 4, 5; for Γ=2 the probabilities also decay quickly (59.6%, 10.2%, 1.6%). These are high failure rates for the central similarity-search claim, yet the paper reports them without discussing why they are acceptable or providing a performance criterion. Moreover, the experimental setup excludes the (NL) case, making the results optimistic. The simulations therefore do not currently support the claim that the algorithms reliably find similar objects.
minor comments (4)
  1. [§3.4, Definition 3.1] The two thresholds in Definition 3.1 are both rendered as θ_out^o in the text (with and without an overbar); the notation should be distinguished explicitly, e.g., θ^out_o and θ̄^out_o, to avoid confusion.
  2. [§1] The sentence 'Real systems almost always encounter errors, and in the following, the equations contain few of such errors, unless otherwise noted' is unclear and should be rephrased or removed.
  3. [§4, Eq. (4.1)] The assumption that the brain 'knows that these are similar' should be listed as a formal assumption with the other parameters (d, Γ, θ_w, θ'_w, θ''_w, D), rather than appearing only in the prose.
  4. [§5, Remark 5.1] The statement that setting δ_i,t=0 'takes no time' is trivially true but does not clarify how the active-inference mapping Φ_move_{i,t-1} → Φ_move_{i,t} is realized in discrete time; this deserves a more precise explanation.

Circularity Check

2 steps flagged · score 6.0 of 10

Active-inference 'non-Bayesian updating' interpretation is constructed from Algorithm 5.1's own surprise flag; the similarity search is conditional on an externally stipulated distance D.

  1. self definitional [Section 4, Eq. (4.1), Algorithms 4.1 and 4.2 (steps 3 and 11)]
    "We introduce a distance function D on F such that D(W in(f ), Win(g)) is small if and only if features f and g are similar. For instance, colors with similar wavelengths, such as blue and purple, are often considered as similar features. Then, we assume that the brain knows that these are similar, that is, D(W in(blue), Win(purple)) is small."

    The algorithm's 'similarity' output is fixed by the same distance function that defines similarity. Eq. (4.1) sets N_d(W) = {W' in F: D(W,W') <= d}, and Algorithm 4.1's only essential change is 'the replacement of W in_t with Nd(W in_t)'. Hence an object O' is active exactly when the features along the observed path on O are within d of the corresponding features of O' under D. Since D was stipulated to be small iff features are similar, 'find similar objects' is equivalent by construction to 'propagate D through the Numenta inference machinery'. No learning rule or independent similarity benchmark is offered for D, so the similarity judgment is relocated into an input assumption rather than derived from the model.

  2. self definitional [Section 5, Eqs. (5.5)-(5.6), Definition 5.1, Assumption 5.1]
    "γt = γ (St) := 1 if (5.2) is satisfied, 0 if (5.2) is not satisfied ... Pt (Lt(O)|St) = (1 − γt) ... + γt ... As described below, we consider Algorithm 5.1 to correspond to the non-Bayesian updating process in Definition 5.1."

    The mixing parameter γ_t is not independent; it is literally the algorithm's own surprise flag from (5.2). Assumption 5.1 is then inserted to force the first (Bayesian-prior) term of (5.6) to zero whenever γ_t=1, exactly reproducing Algorithm 5.1's reset (5.3) of ρ^out_{k,t−1} to 1 and the zero movement vector in step 9. Thus Definition 5.1 is an annotated copy of Algorithm 5.1. The claimed 'correspondence' is guaranteed by how the definition was written, not derived from the Numenta inference steps or from Friston's free-energy principle. Any two-mode algorithm could be represented in this form with a suitable γ_t and P, so the headline 'can also be interpreted as Bayesian or non-Bayesian updating processes' is a by-construction restatement rather than an explanatory result.

full rationale

The paper is largely a proposal of algorithms rather than a fitted-data study: Algorithms 4.1, 4.2, and 5.1 are explicit procedures, and the author openly restricts the similarity setting. The similarity claim is not circular in the fitting sense, but the headline 'find objects similar to O' is weakly definitional because D is stipulated to be small iff features are similar and the algorithms only propagate N_d(W_in^t). The more substantial circularity is in Section 5: Definition 5.1 and Assumption 5.1 are constructed from Algorithm 5.1's own test (5.2), reset (5.3), and zero-movement step 9, so the stated Bayesian/non-Bayesian interpretation is true by construction rather than derived. Since that interpretation is one of the paper's declared contributions, the central framing has partial circularity, but the algorithms themselves may still stand as engineering proposals. Overall score 6 reflects one or more claims that reduce by construction while the underlying algorithmic content retains independent form.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central additions rest on an externally supplied distance metric D and on inherited Numenta convergence properties; no new physical entities are introduced. The probabilistic interpretation relies on assumptions chosen to match Algorithm 5.1.

free parameters (4)
  • d (neighborhood radius in N_d(W)) = nonnegative real, user-chosen
    Controls how many features count as similar; the entire similarity search depends on this threshold. Not fitted to data.
  • Gamma (reactivation tolerance) = positive integer <= T; experiments use 1 and 2
    Determines how long an object can be inactive before reactivation in Algorithm 4.2; strongly affects the probability of selecting the correct object.
  • theta_w, theta'_w, theta''_w = hand-chosen, theta_w close to 1
    Thresholds in Algorithm 5.1 that decide when a surprise is declared and when the reset is applied.
  • distance function D on features = not learned; input
    The similarity relation between features is assumed known ('the brain knows that these are similar'). The algorithms do not learn D.
assumptions (5)
  • domain assumption Numenta model structure and Algorithms 3.1/3.2 are taken as given from [9] and [14].
    The proposed algorithms build directly on the reviewed learning and inference algorithms without re-deriving them.
  • domain assumption The convergence property of Algorithm 3.2 carries over to Algorithms 4.1 and 4.2.
    Section 4 asserts 'the convergence property of Algorithm 4.1 is essentially the same as that of Algorithm 3.2' without proof.
  • ad hoc to paper Similar features correspond to small D(W_in(f), W_in(g)).
    Section 4 states 'the brain knows that these are similar, that is, D(W_in(blue), W_in(purple)) is small.' This is the bridge between the distance function and real similarity.
  • ad hoc to paper Assumption 5.1: if gamma_t=1 and P(S_t|L_t(O))>0 then P_{t-1}(L_t(O)|S_{t-1})=0.
    This assumption is introduced to make the non-Bayesian updating process consistent with Algorithm 5.1, but it is not derived from the model or data.
  • domain assumption A generative model with probabilities P(S_t|L_t(O)) exists and the algorithm steps correspond to likelihood, posterior, and prior (Table 3.1).
    The probabilistic interpretation treats the Numenta inference as Bayesian updating, an analogy asserted rather than demonstrated.

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Cite this review

Pith. "Pith review of Finding Similar Objects and Active Inference for Surprise in Numenta Neocortex Model." pith.science (2026). https://pith.science/paper/PYKQWI26

@misc{pith2026250621554,
  author       = {Pith},
  title        = {Pith review of: Finding Similar Objects and Active Inference for Surprise in Numenta Neocortex Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PYKQWI26}},
  note         = {Machine review of arXiv:2506.21554}
}
read the original abstract

Jeff Hawkins and his colleagues in Numenta have proposed the thousand-brains system. This is a model of the structure and operation of the neocortex and is under investigation as a new form of artificial intelligence. In their study, learning and inference algorithms running on the system are proposed, where the prediction is an important function. The author believes that one of the most important capabilities of the neocortex in addition to prediction is the ability to make association, that is, to find the relationships between objects. Similarity is an important example of such relationships. In our study, algorithms that run on the thousand-brains system to find similarities are proposed. Although the setting for these algorithms is restricted, the author believes that the case it covers is fundamental. Karl Friston and his colleagues have studied the free-energy principle that explains how the brain actively infers the cause of a Shannon surprise. In our study, an algorithm is proposed for the thousand-brains system to make this inference. The problem of inferring what is being observed from the sensory data is a type of inverse problem, and the inference algorithms of the thousand-brains system and free-energy principle solve this problem in a Bayesian manner. Our inference algorithms can also be interpreted as Bayesian or non-Bayesian updating processes.

Figures

Figures reproduced from arXiv: 2506.21554 by the authors.

Figure 2.1
Figure 2.1. An object and a movement vector (A) (B) ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ ✁ ✁ ✁ ✁✕ O O As described below, the inference is also performed by observing and sensing pairs (location, feature) individually (by Algorithm 3.2). Assume that the model has already learned objects O, O′ , and O′′ of [PITH_FULL_IMAGE:figures/full_fig_p003_2_1.png] view at source ↗
Figure 2.3
Figure 2.3. Convergence onto a representation for O (A) ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ ✛✲ ❄ ✻ ✷ ◦ ✷ ✷ ⋆ ◦ ◦ ⋆ ⋆ ✛✲ ❄ ✻ • ◦ ✷ ◦ ✷ • ◦ ✷ • • O O′ O′′ ❄ ✻ (B) ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ ✲ ✻ ✷ ◦ ✷ ✷ ⋆ ◦ ◦ ⋆ ⋆ ✻ ✛ • ◦ ✷ ◦ ✷ • ◦ ✷ • • O O′ O′′ (C) ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ ✲ ✻ ✛ ✷ ◦ ✷ ✷ ⋆ ◦ ◦ ⋆ ⋆ • ◦ ✷ ◦ ✷ • ◦ ✷ • • O O′ O′′ 4 [PITH_FULL_IMAGE:figures/full_fig_p004_2_3.png] view at source ↗
Figure 3.1
Figure 3.1. Numenta cortical column location layer sensory layer (input layer) output layer • • • • • • • • • • • • • • • mini-column ❅ [PITH_FULL_IMAGE:figures/full_fig_p006_3_1.png] view at source ↗
Figures from the paper (6 more)
Figure 3.2
Figure 3.2. Figure 3.2: Numenta cortical columns ✲ ✲ ✲ ✲ ✲ ✲ ✻ ❄ ✻ ❄ ✻ ❄ ✻ ❄ ✻ ❄ ✻ ❄ ✲ ✲ ✲ ✲ ✛ ✛ ✛ ✛ ❄ ❄ In §3.1 and §3.2, we consider learning and inference/recognition algorithms for objects. Fig￾ure 2.1 shows an example of such an object. This object O comprises ten pairs of (location, f…
Figure 4.1
Figure 4.1. Figure 4.1: Example of objects (they are the same objects as in Figure 2.2) [PITH_FULL_IMAGE:figures/full_fig_p018_4_1.png]
Figure 4.2
Figure 4.2. Figure 4.2: Example of movement vectors (A) ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ O ❄ ❅ ❅❘ ✁ ✁ ✁ ✁✕ ❄ (B) ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ O ✻ ✠ [PITH_FULL_IMAGE:figures/full_fig_p021_4_2.png]
Figure 4.3
Figure 4.3. Figure 4.3: Paths connecting movement vectors ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✻ T = 3 T = 4 T = 5 [PITH_FULL_IMAGE:figures/full_fig_p022_4_3.png]
Figure 4.4
Figure 4.4. Figure 4.4: Example of movement vectors (A) ⋆ ◦ ✷ ◦ ◦ ⋆ ✷ ✷ ⋆ ⋆ O ❄ ❄ ✲ ✒ ✻ (B) ✷ ◦ ✷ ✷ ⋆ ◦ ◦ ⋆ ⋆ E′ O′ ✛ ✲ ✻ (C) ✷ ◦ ✷ ✷ ⋆ ◦ ◦ ⋆ ⋆ E′ O′ [PITH_FULL_IMAGE:figures/full_fig_p022_4_4.png]
Figure 4
Figure 4. Figure 4: (B) are active at [PITH_FULL_IMAGE:figures/full_fig_p022_4.png]

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Works this paper leans on

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