arxiv: 2604.17121 · v2 · submitted 2026-04-18 · 💻 cs.LG · cs.AI

Recognition: unknown

The Topological Trouble With Transformers

Michael C. Mozer , Shoaib Ahmed Siddiqui , Rosanne Liu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:31 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords transformersstate trackingfeedforward networksrecurrent architecturesdynamic depthsequence modelingtemporal cognition

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The pith

Transformers push evolving state representations deeper into their layers with each new input, exhausting depth and limiting dynamic tracking.

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

The paper argues that transformers' purely feedforward architecture creates a fundamental limit on dynamic state tracking. State tracking requires iterative updates to latent variables as an environment evolves, but sequential dependencies force these representations deeper into the layer stack. Shallow layers then lose access to prior state, and the model eventually runs out of effective depth. A sympathetic reader would care because this explains why current transformers struggle with tasks needing ongoing state maintenance, such as tracking changes over long sequences, and why the authors advocate shifting toward recurrent designs that support implicit activation dynamics.

Core claim

Transformers encode structure in sequences via an expanding contextual history. However, their purely feedforward architecture fundamentally limits dynamic state tracking. State tracking involves inherently sequential dependencies that feedforward networks struggle to maintain. Consequently, feedforward models push evolving state representations deeper into their layer stack with each new input step, rendering information inaccessible in shallow layers and ultimately exhausting the model's depth.

What carries the argument

The mechanism of pushing evolving state representations deeper into the layer stack with each new input step, which renders prior state inaccessible to shallow layers.

If this is right

Dynamic depth models and explicit or latent thinking can bypass the depth limit but remain computationally and memory inefficient.
Temporally extended cognition requires refocusing from explicit thought traces to implicit activation dynamics via recurrent architectures.
Recurrent and continuous-thought transformers can be taxonomized by recurrence axis (depth versus step) and the ratio of input tokens to recurrence steps.
Enhanced state-space models and coarse-grained recurrence offer paths to integrate state tracking into foundation models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the depth-exhaustion mechanism holds, scaling feedforward transformers alone will not resolve state-tracking failures on long-horizon tasks.
Recurrent extensions could allow models to handle evolving environments with fixed depth by reusing activations across steps rather than stacking new layers.
This framing suggests testing whether hybrid recurrent-feedforward designs reduce the need for explicit chain-of-thought scaffolding in reasoning tasks.

Load-bearing premise

Alternatives such as dynamic depth models, explicit thinking traces, and latent thinking are too computationally and memory inefficient to scale, while recurrent architectures can integrate state tracking without introducing comparable costs.

What would settle it

A feedforward transformer that maintains accurate, accessible state tracking over arbitrarily long sequences without exhausting depth or relying on external mechanisms, or a recurrent architecture that fails to integrate state tracking more scalably than feedforward ones.

Figures

Figures reproduced from arXiv: 2604.17121 by Michael C. Mozer, Rosanne Liu, Shoaib Ahmed Siddiqui.

**Figure 2.** Figure 2: Two examples from the literature: Li et al. (2025a) and Lindsey et al. (2025). The details of each Figure are not critical, but in each case, the upward flow of information to deeper layers is depicted. et al., 2026; Shai et al., 2024). Essentially, when the state update function, f is of a certain form, the sequence of state updates may be composed into a simpler one-step function, e.g., there exists a fu… view at source ↗

**Figure 3.** Figure 3: The depth of a state representation in a transformer can limit its utility for inference (adapted [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Figure 5: Unrolling a transformer. Each rectangle represents a transformer layer. The colored boxes [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Unrolling a latent-thought model, where the model feeds back its latent thoughts as input to [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: Unrolling an SSM, where information from the previous input step at layer [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

read the original abstract

Transformers encode structure in sequences via an expanding contextual history. However, their purely feedforward architecture fundamentally limits dynamic state tracking. State tracking -- the iterative updating of latent variables reflecting an evolving environment -- involves inherently sequential dependencies that feedforward networks struggle to maintain. Consequently, feedforward models push evolving state representations deeper into their layer stack with each new input step, rendering information inaccessible in shallow layers and ultimately exhausting the model's depth. While this depth limit can be bypassed by dynamic depth models and by explicit or latent thinking that externalizes state representations, these solutions are computationally and memory inefficient. In this article, we argue that temporally extended cognition requires refocusing from explicit thought traces to implicit activation dynamics via recurrent architectures. We introduce a taxonomy of recurrent and continuous-thought transformer architectures, categorizing them by their recurrence axis (depth versus step) and their ratio of input tokens to recurrence steps. Finally, we outline promising research directions, including enhanced state-space models and coarse-grained recurrence, to better integrate state tracking into modern foundation models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that transformers' purely feedforward architecture fundamentally limits dynamic state tracking—the iterative updating of latent variables for evolving environments—because sequential dependencies cause state representations to be pushed deeper into the layer stack with each input step, rendering them inaccessible in shallow layers and exhausting depth. It argues that alternatives like dynamic depth models or explicit/latent thinking are inefficient, advocates refocusing on recurrent architectures for implicit activation dynamics, introduces a taxonomy of recurrent/continuous-thought variants categorized by recurrence axis (depth vs. step) and input-token-to-recurrence-step ratio, and sketches research directions including enhanced state-space models and coarse-grained recurrence.

Significance. If the conceptual argument holds, this discussion paper could usefully frame architectural limitations for temporally extended tasks and organize emerging recurrent transformer variants via its taxonomy, potentially steering research toward more integrated implicit state tracking. The work explicitly credits the role of recurrence in avoiding externalized thought traces and provides a structured categorization that may aid comparison of models.

major comments (2)

[Abstract and Introduction] Abstract and opening sections: the core claim that feedforward networks 'push evolving state representations deeper into their layer stack with each new input step' and thereby exhaust depth is advanced as an architectural intuition without a formal model, layer-wise information-flow analysis, or even a small illustrative example, which is load-bearing for dismissing feedforward transformers and motivating the recurrent turn.
[Taxonomy of recurrent and continuous-thought architectures] Section introducing the taxonomy: the categorization by recurrence axis and input-to-recurrence ratio is presented at a high level but lacks concrete mappings to existing models, pseudocode, or complexity comparisons, undermining its utility as a framework for the research directions that follow.

minor comments (2)

[Title and Introduction] The phrase 'topological trouble' is used in the title and text but never given a precise topological or graph-theoretic definition; a short clarifying sentence or reference would improve precision.
[Research directions] The research-directions paragraph lists several promising avenues but does not indicate relative priority or suggest minimal experiments that could falsify the inefficiency claims about dynamic-depth alternatives.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our discussion paper. We address the two major comments point by point below, indicating where revisions will be made to strengthen the manuscript while preserving its conceptual focus.

read point-by-point responses

Referee: [Abstract and Introduction] Abstract and opening sections: the core claim that feedforward networks 'push evolving state representations deeper into their layer stack with each new input step' and thereby exhaust depth is advanced as an architectural intuition without a formal model, layer-wise information-flow analysis, or even a small illustrative example, which is load-bearing for dismissing feedforward transformers and motivating the recurrent turn.

Authors: We agree that the core intuition would be clearer with a concrete illustration. The argument stems from the feedforward, parallel processing of transformers, where each new input step incorporates prior context but shifts the evolving state representation deeper without recurrent carry-over. In revision, we will add a brief illustrative example in the introduction (e.g., a step-by-step textual depiction for a short sequence of 3-4 inputs showing depth progression). As this remains a discussion paper rather than a theoretical one, we will not introduce a formal model or full layer-wise analysis, which would exceed the intended scope; the example will serve to make the intuition more accessible. revision: yes
Referee: [Taxonomy of recurrent and continuous-thought architectures] Section introducing the taxonomy: the categorization by recurrence axis and input-to-recurrence ratio is presented at a high level but lacks concrete mappings to existing models, pseudocode, or complexity comparisons, undermining its utility as a framework for the research directions that follow.

Authors: We accept that the taxonomy's utility can be improved with greater concreteness. In the revised manuscript, we will add explicit mappings to representative existing models (e.g., linking step-recurrence variants to models like Mamba or RWKV), include high-level pseudocode sketches for the primary categories, and provide brief qualitative notes on computational trade-offs. These additions will remain concise to fit the discussion format and will directly support the subsequent research directions section. revision: yes

Circularity Check

0 steps flagged

No significant circularity in conceptual critique

full rationale

The paper is a discussion manuscript presenting an architectural argument and taxonomy without any equations, formal derivations, fitted parameters, or predictions. The central claim about feedforward transformers pushing state representations deeper into layers is framed as a high-level intuitive observation about sequential dependencies, not derived from or reduced to prior results by construction. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps. The argument is self-contained as a critique and research outline.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a conceptual position paper. No free parameters are fitted, no new axioms are stated, and no invented entities are postulated; the argument relies on standard descriptions of feedforward and recurrent neural network properties.

pith-pipeline@v0.9.0 · 5474 in / 1135 out tokens · 57321 ms · 2026-05-10T06:31:05.070398+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

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