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Grid Long Short-Term Memory

Architectures AIMech:GridLongShortTermMemory DRAFT

Aliases: Grid LSTM

A neural architecture family whose grid blocks couple hidden representations across computational dimensions while maintaining separate gated memory flows along their LSTM-equipped axes, including depth and data dimensions.

Identity Notes & Concept Scope Compared all 442 pinned AIO and 609 native IDs, names, aliases and scoped synonyms; no normalized identity match. Ignored- and hidden-inclusive fixed-string searches of the recovery, older discovery and original Documents checkouts returned 6, 0, 0 lines. All distinct match contents were inspected. Semantic matching covered 54 AIO and 68 native definitions, with every matched definition read. 6 full annotated AIO node/edge/generated contexts and 2 full native records were inspected. Grid LSTM couples per-dimension hidden context while retaining distinct memory flows. It is not a grid-search optimizer, Neural GPU convolutional GRU grid, DMN episodic memory, or the memory-summing multidimensional LSTM formulation it contrasts with. Named task-specific instantiations are kept within explicit scope.

Claims & Grounded Evidence

6 Claims

Mechanism #separate-dimensional-memory

An N-dimensional grid block receives one hidden vector and one memory vector from each incoming dimension. It concatenates the hidden vectors and computes a separate LSTM transform for each dimension using that common hidden context and the corresponding dimension-specific memory. The outputs remain N distinct hidden-memory pairs. Unlike the multidimensional LSTM update discussed in the paper, this construction does not directly sum all incoming memory vectors into one memory; the dimensions still interact through hidden features and their learned gates.

supports Source: Grid Long Short-Term Memory · Locator: Sections 2.3 and 3.1, PDF pp. 4–5, Equations 4–6 and Figure 1

Scope #axis-priority-and-sharing

The framework includes a priority schedule that updates other dimensions before computing a selected output dimension from their updated hidden states. It also permits ordinary nonlinear or identity connections on selected axes instead of LSTM cells. Parameters may be tied across positions along chosen axes; this does not require direction-specific transforms to share identical weights. One-dimensional feed-forward and higher-dimensional sequential or spatial instantiations are members of the family, so neither a single scan order nor temporal sequence input is mandatory for every instance.

supports Source: Grid Long Short-Term Memory · Locator: Sections 3.2–3.5, PDF pp. 5–6, Equations 7–8; translation instantiation, pp. 9–10

Scope #printed-cell-convention

Equation 1 prints the hidden output as tanh of the output-gated memory, tanh(g_o multiplied by m_new). That is generally different from multiplying the output gate after tanh. This record follows the displayed formula when illustrating that distinction and does not infer author-code behavior. Separate additive memory paths and gating are architectural mechanisms, not a proof that gradients remain stable for every parameter setting or arbitrary grid extent.

supports Source: Grid Long Short-Term Memory · Locator: Section 2.1, PDF p. 3, Equations 1–3; Sections 2.2–3.1, pp. 4–5; constructed output-gate example

Limitation #fixed-length-algorithmic-tests

The reported algorithmic experiments include fixed fifteen-digit addition, memorization of twenty-symbol sequences, and whole-vector parity at selected input lengths up to 250 bits. Addition and memorization report per-digit or per-symbol accuracy; selected parity runs meet a stopping criterion of one hundred correct unseen examples of the same length. These finite tests do not certify every input or demonstrate one learned model extrapolating to arbitrary unseen lengths. Training examples being newly sampled also does not by itself establish an absence of overfitting or selection effects.

supports Source: Grid Long Short-Term Memory · Locator: Sections 4.1–4.2, PDF pp. 6–8, Figures 4–5; Appendix 5.1, pp. 12–14, Figures 9–10

Limitation #character-model-protocol

The character-prediction experiment uses a tied two-dimensional model on the Hutter Wikipedia corpus, with a 205-character alphabet and the last five million characters held out. Hidden and cell state are carried across updates while gradients are backpropagated over fifty-character segments; carrying state is not full-length gradient propagation. Figure 6 reports 1.47 bits per character, but comparison rows differ in alphabet and test size. The text lists 8.82 million parameters while Figure 6 lists 16.8 million, so this source alone does not resolve one exact parameter count.

supports Source: Grid Long Short-Term Memory · Locator: Section 4.3 and Figure 6, PDF p. 8

Limitation #task-specific-instantiations

The Reencoder translation example repeatedly scans the source conditioned on the generated target prefix and reports an ensemble of seven models with beam decoding; it is a task-specific grid construction, not a single-model result for every Grid LSTM. The image example projects patches into depth hidden and memory vectors, scans spatial axes and concatenates final features without pooling. Its compared cell-depth and ReLU-depth configurations differ in patch size, cropping and classifier width, so their error difference does not isolate the causal effect of a depth memory cell. Selected activation visualizations likewise do not prove a unique learned algorithm.

supports Source: Grid Long Short-Term Memory · Locator: Section 4.4, PDF pp. 8–10, Figures 7–8; Appendix 5.1–5.2, pp. 13–15, Figures 10–12

⚠️ Curated Limitations & Negative Results

Distinct dimensional memories remain coupled through hidden-state computations; separate memory streams are not independent networks.
Optional non-LSTM axes, priority schedules and parameter-tying choices remain explicit variants, not interchangeable aliases.
The printed output-gate convention and inconsistent character-model parameter counts are recorded without inferring unseen implementation details.
Fixed-length tests, finite stopping samples, different comparison protocols and task-specific ensembles limit generalization claims. All fifteen pages of arXiv1507.01526v3 were visually read; no author code, other versions, training or benchmark replication. DRAFT remains.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:ArtificialNeuralNetwork` Artificial Neural Network	broad_match	The grid of learned gated transforms is a specific neural architecture family; the target is broader across its feed-forward, sequential and spatial instantiations.
`AIO:LongShortTermMemory` Long Short Term Memory	related_match	The grid generalizes LSTM memory transforms across computational axes. The pinned target specifically denotes a recurrent network processing sequences; this relation does not assert that every one-dimensional feed-forward Grid LSTM instance has that narrower temporal scope.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`kalchbrenner2016`	Grid Long Short-Term Memory Nal Kalchbrenner, Ivo Danihelka, Alex Graves	primary paper full_text	ID: arXiv:1507.01526v3 sha256:7993018d83f1…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-13T11:30:18Z

Updated: 2026-10-13T11:37:17Z

Source File: data/curated/GridLongShortTermMemory.yaml