Beyond the Parameter Monolith: Reconstructive Memories, Executable Skills, and Residual Assembly for Language Models

1. Introduction

• FEM-ASM combines locally optimized document states, deterministic executable elements, and a shared neural field that reconciles typed proposals at explicit interfaces.The finite-element name denotes architectural inspiration, not a claim that language obeys a physical partial differential equation or that the model discretizes a known weak form.Source: §1 · p. 1

2. Related work

• Prior work already covers visual or frozen inputs, external memory, tool use, shared computation, and set aggregation; this study focuses on their combination with managed artifacts and explicit interfaces.The paper does not claim reconstructive memory outperforms raw-text storage and retrieval, or that summation alone is novel.Source: §2 · p. 2

3.1. Implemented interface

• External elements specify a source state and type, while a shared adapter handles instances and support selects a target node rather than a general learned finite-element basis.A node without an external contribution receives exactly zero external residual.Source: §3.1 · p. 2

3.2. Consistency and neural correction

• Approximately 44% reduction in excess quadratic energy is expected from the deterministic interpolation rule; the complete learned iteration need not reduce consistency energy or language-model loss.The contraction checks implementation consistency, not reasoning or a learned convergence mechanism.Source: §3.2 · p. 3

3.3. Conditional causality

• Causal sequence operators provide only a conditional guarantee: attached proposals and attachment decisions must not depend on unavailable target information.Offline document memory may contain information about an entire stored document, so standalone language-model, external-memory, and oracle-coordinate evaluations are reported separately.Source: §3.3 · p. 3

4.1. Fixed observations and the Multi-Mesh prototype

• The Multi-Mesh prototype uses fixed Binary16 identity inputs plus visual-form, binary-tile, coarse-history, and scratch observations, and is distinct from the later modular core.The tile is not a QR code or a frequency-domain representation.Source: §4.1 · p. 3

4.2. Reconstructive document memory

• Workers optimize document-specific residuals over shared-codec initial cells, and a frozen decoder reconstructs slots without correct previous tokens as decoder inputs.Published elements carry immutable versions, codec identity, provenance, and checksums; reconstruction is incomplete, so the memory is not lossless exact memory.Source: §4.2 · p. 4

4.3. Executable elements

• The bounded frozen VM executes five controller-selected operations, while position-specific render observations expose intended output tokens for neural adoption rather than unaided arithmetic.The comparison also includes a global result vector repeated over output positions; termination uses the buffer's declared token count, not a learned stopping test.Source: §4.3 · p. 4

4.4. Retrieval and QA diagnostics

• The initial learned retriever mapped text-query states to mean-pooled memory keys and performed poorly, without showing that the cells contain no usable information or that pooling must always fail.The repaired candidate-generation tasks include prefix completion, masked-span restoration, value restoration, and quote continuation.Source: §4.4 · p. 4
• The repaired retriever uses fixed lexical sketches and a shared reranker, but coordinate-assisted cues use source token spans and stored offsets rather than arbitrary questions.The evaluated tasks are prefix completion, masked-span restoration, value restoration, and quote continuation.Source: §4.4 · p. 4

5.1. Data and separation

• Memory workers use odd-numbered training shards and the base modular stream uses even-numbered shards, while QA splits hold out element identities.That split does not rule out duplicate text under different identities or establish benchmark decontamination; R1 and QA supervision expose memory-source information to the reasoning network.Source: §5.1 · pp. 4–5
• Table 1 reports standalone Multi-Mesh results, not scores for the modular attachment core.The LM experiments use FineWeb-Edu and a SmolLM2-family tokenizer, but the tokenizer choice does not mean the models were initialized from SmolLM2 weights.Source: §5.1 · p. 4, Table 1 · p. 5

5.2. Separate ledgers

• The accounting distinguishes trainable parameters, frozen shared parameters, external state values, and derived caches.These categories are tracked separately rather than collapsed into one nominal parameter count.Source: §5.2 · p. 5
• A small trainable core alongside billions of frozen values is not a parameter-matched dense model of the same nominal size.The current latent cell uses 1,536 bytes versus 128 bytes for 64 uint16 token IDs, a factor of 12 before additional states, indices, and caches.Source: §5.2 · p. 5

5.3. Evaluation conventions

• Evaluation separates standalone benchmarks, memory and skill experiments, and fixed-core attachment demonstrations, with external memory and VM disabled for standalone benchmarks.Accuracy is a percentage, token NLL uses natural-log units, perplexity normalizations remain distinct, and single-run estimates are not multi-seed conclusions.Source: §5.3 · p. 5

6.1. Standalone Multi-Mesh evaluation

• The standalone Multi-Mesh prototype performs causal language modeling but does not establish competitive general reasoning, with MMLU point estimates around nominal four-choice chance.The standalone checkpoint is evaluated without external memory or VM.Source: §6.1 · p. 5

6.2. Memory construction and positional decoding

• 52,809 active element versions were produced near a 1.7-billion-floating-value budget, while the readout-cache audit showed repeatable decoding rather than lossless storage or successful answer generation.The audit covered 2,910 evidence blocks from 98 elements and 10,000 QA task references.Source: §6.2 · p. 6, Table 2 · p. 6

6.3. Controlled retrieval

• Approximately 99.6% test candidate recall and 97.7% test recall at one were achieved on provenance-controlled, lexically derived tasks, not arbitrary-question semantic retrieval.The coordinate-assisted protocol uses source token spans and stored offsets.Source: §6.3 · p. 6
• Answer-token losses were approximately 6.6930 with retrieved evidence, 6.7726 with wrong evidence, and 7.2544 without evidence; wrong evidence accounts for much of the no-evidence improvement.The smaller additional gain from correct evidence is consistent with a document-specific contribution but does not eliminate generic in-domain conditioning.Source: §6.3 · p. 6
• Free QA generation had zero measured greedy exact match, so successful retrieval and improved likelihood did not establish a functioning free-form QA system.Source: §6.3 · p. 6

6.4. Executable-result interfaces

• The positional-render comparison supports explicit output-slot correspondence over a repeated global result vector, while the small tokenizer-only versus combined difference does not establish a reliable character-channel benefit.The variants are external-result interfaces, not unaided arithmetic models.Source: §6.4 · p. 6, Table 3 · p. 7
• Changing the returned execution result changed answer likelihood, but mixed unchanged and substituted runs require stratifying intervention effects by whether the value actually changed.Source: §6.4 · p. 7

6.5. Bounded attachment demonstration

• The attachment demonstration measured a 3.7643-nat-per-target-token loss difference, but changing evidence coverage from zero to one does not isolate evidence quality or full-store serving costs.The package supplies selected evidence rather than the complete originating store.Source: §6.5 · p. 7, Table 4 · p. 7

• Storage, addressing, content extraction, and answer rendering are distinct problems: a cell can reconstruct tokens yet provide a poor retrieval key, or a skill can compute correctly while the neural head renders incorrectly.Source: §7 · p. 7
• Modularity allows key construction to change without retraining document cells, executable results to be replayed independently, and immutable states to be versioned without mutating the reasoning core.These are engineering properties, not proof of superior reasoning, fault isolation, or distributed-serving efficiency.Source: §7 · p. 7
• The FEM analogy is limited to weighted least-squares reconciliation at selected nodes, not a physical weak formulation; observed consistency contraction is largely determined by the update rule.Source: §7 · p. 7

• The memory is neither lossless nor compact relative to raw token storage, and its full cost includes codec weights, coarse cells, search keys, readout caches, and metadata.Source: §8 · p. 8
• Evidence-derived query spans and answer offsets are unavailable in unrestricted QA, while element-ID splitting alone does not guarantee content disjointness or absence of prior checkpoint exposure.Source: §8 · p. 8
• The successful controller covers a small arithmetic skill set with deterministic parsing and compilation; positional token buffers expose output identities, and buffer length controls termination.Source: §8 · p. 8
• Matched raw-text retrieval and storage, latency, and answer-quality measurements remain necessary, while finite-sample point estimates and single runs do not establish seed robustness or large-store efficiency.Large-store coverage, end-to-end latency, active state, failure localization, and replacement behavior require dedicated measurements.Source: §8 · p. 8

9. Conclusion

• FEM-ASM demonstrates working instances of separately managed contextual computation, reconstructive document state, and deterministic execution, while identifying failures in pooled retrieval, dense readout, privileged coordinates, and free QA.The evidence supports further investigation, not replacement of dense language models or equivalence between frozen stored values and trainable parameters.Source: §9 · p. 8

Reproducibility statement

• Runnable packaged paths and selected research code do not constitute a complete end-to-end reproduction of every reported experiment or reproduce a long-training checkpoint.Source: Reproducibility statement · p. 8

Ethics statement

• The experiments use web-derived text and research models not established as deployment-safe; rights, privacy, licensing, and future online-memory policies remain applicable concerns.The VM’s resource bounds are not a formal security audit, and no autonomous collection of user interaction histories is claimed.Source: Ethics statement · p. 8

A.1. Reported prototype configurations

• Table 5 summarizes the reported prototype configurations.Source: §A.1 · p. 10, Table 5 · p. 10

A.2. Training details required for reproduction

• The supplied runs specify Transformer and Multi-Mesh training settings alongside codec adaptation steps and worker publication thresholds.Source: §A.2 · p. 11

A.3. Counting trainable, frozen, and active state

• The ledger distinguishes trainable parameters from frozen storage and tracks active query values, HBM, and latency; freezing avoids optimizer state and backpropagation through storage, not serving costs.Source: §A.3 · p. 11

• A complete evaluation manifest links each result to checkpoint and configuration hashes, evaluation code and dependencies, and task, dataset, split, and sample-count details.Source: B. Evaluation reporting considerations · p. 11
• The manifest also records prompt and scoring conventions, tokenization and label-shift rules, memory and codec identities, and generation stopping and normalization rules.Source: B. Evaluation reporting considerations · p. 11
• For QA, confidence intervals should resample elements or documents rather than treating tasks from one evidence block as independent; paired interventions should reuse tasks and scoring rules.Source: B. Evaluation reporting considerations · p. 11

C. Consistency calculation

• The consistency calculation leaves a disagreement floor between fixed proposals, while the first term is scaled by (1 −ηi)2 after the consistency step.Source: C. Consistency calculation · p. 12
• Its guarantee is limited to fixed proposals, nonnegative weights, the selecting-node support, and the deterministic substep, not later neural correction or LM loss.Source: C. Consistency calculation · p. 12

D. Visual resource and licensing

• Visual observations use a fixed Unifont-based rendering pipeline, while token identity remains a separate Binary16 channel; the font is a third-party resource with retained license notices.Source: D. Visual resource and licensing · p. 12

E. Executable-element protocol

• The VM supports bounded operations and typed failures, but successful arithmetic experiments learn only operation selection over a fixed two-operand program skeleton.Source: E. Executable-element protocol · p. 12
• Replay records must bind the program and VM configuration, since a result checksum alone does not verify the intended semantics.Source: E. Executable-element protocol · p. 12

F. Research trajectory and negative results

• The reconstruction codec trained cells to recover associated blocks, making local memory useful while leaving reconstruction incomplete.Source: F. Research trajectory and negative… · pp. 12–13
• Mean-pooled document keys with learned queries were not useful in reported runs; fixed prefix sketches recovered literal cues, while internal quotes and missing spans needed support-aware charts.Source: F. Research trajectory and negative… · p. 13
• The generic VM-program controller failed to recover exact variable operands, so deterministic operand extraction isolated operation routing without demonstrating arbitrary long-range understanding.Source: F. Research trajectory and negative… · p. 13
• Positional output observations substantially improved rendering over a repeated global vector, under conditions that changed per-position information and used an externally declared output length.Source: F. Research trajectory and negative… · p. 13

G. Artifacts

• Supplementary materials include a Multi-Mesh preprocessing and training path and selected documented source files, distinguishing runnable paths from components requiring additional artifacts or datasets.Source: G. Artifacts · p. 13