neural techniques for trident

Neural_Techniques_for_Trident
trident

Neural Network Techniques for Trident

Compilation, Execution, Proving — Prioritized Roadmap

Scope

Everything here lives strictly within the trident → TIR → TASM → Triton VM → STARK pipeline. No cybergraph dynamics, no consensus, no planetary-scale inference. Just the language, the compiler, the prover, and what neural networks can do for each of them.

Priority 1 — Foundation Layer

1.1 Field-Native Neural Network Library (nn.trd)

What: A Trident library implementing neural networks primitives — matrix multiply, dot product, layer normalization, activation functions (GELU via Padé approximant, ReLU via conditional), softmax approximation — all in Goldilocks field arithmetic ($p = 2^{64} - 2^{32} + 1$).

Why first: Every other technique on this list either IS a neural network running in Trident, or benefits from having one. This is the substrate for everything below.

Architecture:

nn.trd
├── field_signed.trd      — signed integer convention (x > p/2 → negative)
├── field_fixed.trd       — fixed-point arithmetic via scaling factor
├── linalg.trd            — matmul, dot product, vector ops
├── activations.trd       — GELU (polynomial), ReLU (conditional), tanh (Padé)
├── layers.trd            — linear layer, layer norm, residual connection
├── loss.trd              — MSE, cross-entropy (field approximations)
└── inference.trd         — forward pass orchestration

Key constraints:

  • No negative numbers natively → signed representation via convention
  • No fractions natively → fixed-point with configurable scale factor (e.g., 2^16)
  • No floating point → all activations are polynomial or rational approximations
  • Every operation is a field op → every inference produces a valid Triton VM trace

Size estimate: ~500 lines of Trident. A 3-layer MLP with 64-wide hidden layers compiles to ~2,000 TASM instructions.

The result: A neural network whose every inference is a STARK-proven computation, compiled from .trd source. World first.

Tier: 0+1 only. No hash/sponge (Tier 2) or recursive verification (Tier 3) needed for NN inference.

1.2 Field-Native Evolutionary Training

What: Train neural networks entirely within Goldilocks field arithmetic using evolutionary optimization — no gradients, no floats, no external frameworks.

Why: Gradient descent in field arithmetic is noisy (finite differences for gradients, field inverse for learning rate). Evolution sidesteps this entirely. Crossover = conditional copy. Mutation = random field element replacement. Both are pure Tier 0 ops.

Algorithm:

POPULATION: N = 16 weight vectors (each ≤91K field elements)
MEMORY:     16 × 728 KB = 11.6 MB total

FOR each generation:
  FOR each individual:
    FOR each training example:
      output = inference(individual.weights, input)
      individual.fitness += score(output, expected)
  
  SORT by fitness (descending)
  survivors = top 25%
  
  FOR i in 0..N:
    parent_a, parent_b = random_choice(survivors)
    child = uniform_crossover(parent_a, parent_b)
    child = mutate(child, rate=0.01)
    new_population[i] = child

Performance: ~2.5M field ops per generation. On M4 Pro Metal: ~50μs per generation. 1,000 generations in 50ms. Training a small model in seconds.

Hybrid path (optional later):

  • Phase 1: Gradient training via fixed-point finite differences (cold start, ~1M steps, ~5s)
  • Phase 2: Evolutionary refinement (continuous, discovers cliff-jumping strategies gradients miss)

Deliverable: A self-contained Trident program that trains a neural classifier, proves every training step, and outputs verified weights. The training loop IS provable computation.

1.3 Predictive Trace Analysis

What: A small neural network (trained via 1.2) that predicts the 9 AET table heights from TIR features, BEFORE compilation and execution.

Why: This is the cheapest way to learn the AET cost landscape empirically. Every other compilation optimization depends on understanding this landscape.

Input: TIR graph features — node count, operation type histogram, max nesting depth, branch count, loop bound sum, memory access count. Encode as ~32 field elements.

Output: 9 field elements — predicted height of each AET table (Processor, Op Stack, RAM, Jump Stack, Hash, Cascade, Lookup, U32, Degree Lowering).

Training data: Compile and execute N programs, record actual table heights. Start with ~1,000 programs (combinatorially generated from TIR primitives), scale to ~100,000 as the compilers matures.

Model: Single hidden layer, 64 units. ~6K parameters. Trains in seconds via evolutionary loop.

Uses:

  1. Fast cost estimation during compilation (no execution needed)
  2. Identifying "proof-expensive" programs before committing to proving
  3. Cost-aware TIR optimization — reject TIR transformations that increase predicted proof cost
  4. Training signal for the neural compiler (§2.1)

Accuracy target: Predict which table is the tallest (i.e., the bottleneck) correctly >90% of the time. Exact height prediction within 20% suffices.

Priority 2 — Compiler Intelligence

2.1 Differentiable STARK Cost Surrogate

What: A learned, differentiable approximation of the STARK (zero knowledge proofs) proving cost function. Feed it a TASM instruction sequence, get back a predicted proving time.

Why: The actual cost function — $\text{cost}(S) = 2^{\lceil \log_2(\max_t H_t(S)) \rceil}$ — is non-differentiable (power-of-2 ceiling, max over tables). A smooth surrogate enables gradient-based optimization of compilation strategies.

Architecture: 1D CNN over the TASM instruction sequence. Input: sequence of instruction IDs (vocabulary ~44) + operands, padded to fixed length 128. Output: scalar cost prediction. ~15K parameters.

Training: Run STARK prover on thousands of programs, record (TASM_sequence, proving_time) pairs. Train to minimize prediction error.

Key insight: The surrogate doesn't need to predict absolute proving time. It needs to correctly rank: "Is TASM sequence A cheaper to prove than sequence B?" Pairwise ranking accuracy >95% is sufficient for guiding compilation.

Backpropagation through cost: Once the surrogate exists, you can compute $\partial \text{cost} / \partial \text{compilation\_choices}$ and use this gradient to train the neural compiler. This turns compilation optimization from black-box search (evolution) into gradient-guided search (faster convergence for smooth improvements, combined with evolution for cliff-jumping).

2.2 Learned Instruction Scheduling

What: Given a correct TASM sequence with data dependencies, reorder instructions to minimize AET table heights. Only permutes — never adds, removes, or modifies instructions.

Why: Correctness is guaranteed by construction (dependency-respecting permutations preserve semantics). No verifier needed. Pure upside.

Architecture: graph neural network (GNN) on the TASM dependency DAG. Each node = one instruction. Edges = data dependencies. The GNN outputs a priority score per instruction. Schedule greedily by priority.

The GNN sees:

  • Instruction type (one-hot, 44 dimensions)
  • Current stack depth at this point
  • Which AET tables this instruction touches
  • Distance to nearest dependency predecessor/successor

The GNN learns:

  • "Cluster hash instructions together to avoid interleaving with arithmetic" (minimizes Hash table padding)
  • "Front-load RAM operations to allow pipeline filling" (reduces Processor table stalls)
  • "Delay U32 operations until after the main computation" (avoids U32 table height dominating)

Training: For each program, generate 1,000 random valid schedules. Measure actual table heights for each. Train the GNN to predict the table-height-minimizing ordering.

Model size: ~20K parameters. Tiny. Runs in microseconds.

Correctness guarantee: The scheduler only outputs permutations that respect the dependency DAG. This is enforced by the algorithm (topological sort with learned priorities), not by the model. The model cannot produce an incorrect schedule.

2.3 Multi-Objective Compiler Ensemble

What: Instead of one 80K-parameter TIR→TASM optimizer, run 8-16 specialist models. Each specialist is biased toward minimizing a different AET table. A meta-selector picks the best specialist's output per program.

Why: The cliff-discontinuity cost function means the bottleneck table shifts between programs. A specialist that excels at minimizing Hash table height may produce terrible RAM table profiles. No single model dominates across all programs.

Specialist training: Same evolutionary loop from §1.2, but with modified fitness functions:

specialist_0.fitness = -max(H_processor, H_opstack, ...)     # minimize overall max
specialist_1.fitness = -H_processor                           # minimize Processor
specialist_2.fitness = -H_hash                                # minimize Hash
specialist_3.fitness = -H_ram                                 # minimize RAM
specialist_4.fitness = -(H_processor + H_hash)                # minimize joint bottleneck
specialist_5.fitness = -(max_H - second_max_H)                # minimize gap (balance)
...

Meta-selector: Run all specialists. Use the trace predictor (§1.3) or the cost surrogate (§2.1) to pick the winner without actually proving all candidates. Only prove the selected one.

Memory: 16 specialists × 728 KB = 11.6 MB. Fits in L2 cache.

Performance: 16× inference cost → 16 × 50μs ≈ 800μs. Still <1ms total. Negligible compared to proving time (seconds).

2.4 Learned Peephole Patterns

What: A small 1D convolutional network that scans TASM instruction windows (size 3-8) and detects sequences where local substitution reduces proving cost.

Why: The evolutionary compiler discovers optimization patterns implicitly (encoded in weights). Peephole extraction makes these patterns explicit, composable, and transferable between compilation runs.

Architecture: 1D Conv (kernel size 5) → ReLU → 1D Conv (kernel size 3) → classifier. Input: sliding window of TASM instructions. Output: (should_rewrite: bool, replacement_pattern_id: int).

Training pipeline:

  1. Run evolutionary compiler on 10,000 programs
  2. For each program, diff the naive lowering vs. evolved output
  3. Extract instruction-level changes: which windows were modified?
  4. Label: (original_window, replacement_window, cost_delta)
  5. Train the conv net to detect original_windows and predict replacements

The patterns it discovers (examples from manual analysis of Triton VM):

  • push 0; add → identity (saves 1 Processor row)
  • dup 0; swap 1 → dup 0 (redundant swap)
  • push X; push Y; mul → push X*Y if X, Y are constants (saves 2 rows)
  • Sequences that push a value, hash it, but never use the hash → dead code elimination

Key insight: These patterns are Triton-VM-specific. No classical compiler would discover them because they depend on the AET cost model, not CPU cycle cost. The NN learns what matters for proof machines.

Composability: Discovered patterns become rewrite rules in a rule database. The rule database is applied deterministically (fast) before the neural compiler runs (expensive). Over time, the deterministic rules handle the easy cases, and the neural compiler focuses on the hard cases.

2.5 Neural Decompilation (TASM → TIR)

What: Given an optimized TASM program, reconstruct a plausible TIR representation that would compile to equivalent TASM.

Why:

  • Learn from hand-written TASM (expert knowledge → compiler training data)
  • Cross-pollinate optimizations between programs (decompile → re-optimize → recompile)
  • Sanity-check the neural compiler's output (does the optimized TASM correspond to sensible TIR?)
  • Enable round-trip testing: TIR → TASM → TIR' → TASM' should yield equivalent programs

Architecture: Sequence-to-graph model. Input: TASM instruction sequence. Output: TIR DAG (node types + edges). Attention-based encoder, autoregressive graph decoder.

Model size: ~50K parameters. Larger than the compiler because decompilation has more ambiguity (many TIR programs can produce the same TASM).

Training data: Every compilation (TIR → TASM) generates a training pair. Run the compiler on 100,000 programs → 100,000 (TASM, TIR) pairs for free.

Correctness: The decompiled TIR is a suggestion, not a proof. Verify by recompiling TIR' → TASM' and checking equivalence (via execution on test inputs or STARK proof).

Priority 3 — Proving Acceleration

3.1 NN-Guided STARK Prover Configuration

What: An RL agent that selects STARK prover parameters per-program to minimize proving time. The proof remains mathematically valid regardless of the agent's choices — the agent only affects speed.

Why: STARK proving has multiple tunable parameters where the optimal setting is program-dependent. Current heuristics leave significant performance on the table.

Configurable parameters:

Parameter Current Learned
FRI folding factor Fixed (e.g., 8) Per-program adaptive
Grinding bits Fixed (e.g., 20) Trade proof size vs. time
Blowup factor Fixed (e.g., 4) Soundness-cost tradeoff
Evaluation domain offset Default coset Numerically-tuned per program
Memory layout Sequential Cache-optimized per program
Parallelism strategy Default threading Program-structure-aware

Agent architecture: MLP. Input: program features from trace predictor (§1.3) + actual AET heights (9 values) + available hardware (cores, memory). Output: prover configuration vector. ~10K parameters.

Training:

  1. For each program in the training set, run the prover with K random configurations
  2. Record (program_features, config, proving_time) triples
  3. Train the agent to predict config → time, then argmin over configs

Safety: The agent cannot compromise soundness. All configurations produce valid proofs (or the prover rejects the config and falls back to defaults). The agent is strictly speculative.

Expected impact: 10-30% proving time reduction from per-program configuration. On high-volume programs (e.g., transfer circuits), this compounds to significant savings.

3.2 Neural Proof Compression

What: Train a predictor that anticipates "obvious" parts of STARK cryptographic proofs, transmitting only the delta.

Why: STARK proofs are large (hundreds of KB). If a predictor can correctly guess 80% of proof elements, you only transmit the 20% it got wrong + a bitfield indicating which elements were predicted correctly. ~5× compression.

Architecture: The predictor is a small autoregressive model over proof elements (field elements in the proof stream). It conditions on (a) the program being proven, (b) the public inputs, (c) previous proof elements.

Training: Collect thousands of proofs. Train the predictor to minimize prediction error on proof elements.

Verification: The verifier runs the same predictor. For each proof element: if predictor output matches the transmitted value (or the bitfield says "predicted"), use the prediction. Otherwise, use the transmitted value. Verification is identical — you still check the full proof. Only transmission is compressed.

Compatibility: Works with any STARK proof system. No changes to the prover or verifier logic. The compression is a transport-layer optimization.

Caveat: The predictor must be deterministic and identical on both sides. Ship it as a versioned artifact (itself a Trident program, naturally).

3.3 Neural Theorem Prover for TASM Equivalence

What: Given two TASM sequences (original and optimized), find a sequence of valid rewrite steps that transforms one into the other. Each rewrite is a known-correct transformation.

Why: Currently, equivalence is checked by execution on matching inputs + STARK proof. A rewrite-based proof is structural — it proves equivalence (formal verification) for ALL inputs, not just tested ones. And it generates reusable optimization knowledge.

Rewrite rules (enumerable, finite set):

Rule From To Condition
Dead push elimination push X; pop ∅ X unused
Constant folding push X; push Y; add push (X+Y) X,Y constants
Identity elimination push 0; add ∅ Always valid
Swap cancellation swap K; swap K ∅ Always valid
Commutativity push X; push Y; add push Y; push X; add Always valid
Associativity Complex Complex Dependency-safe
Instruction reorder A; B B; A No data dependency

Neural search: Embed each TASM sequence as a vector (GNN on dependency DAG). The NTP predicts which rewrite rule to apply at each step, guided by the embedding distance between current state and target sequence. Search terminates when sequences match.

Training: Generate (original, optimized, rewrite_path) triples from the compiler. The compiler already produces pairs — the rewrite path can be recovered by A* search with the NTP as heuristic (bootstrap from random search, improve with trained heuristic).

Byproduct: Every successful rewrite path IS a new peephole pattern (§2.4). The NTP feeds the peephole database. The peephole database speeds up the NTP (fewer steps needed). Flywheel.

Priority 4 — Developer Experience

4.1 Neural Type Inference

What: Predict type theory annotations for Trident programs, reducing developer burden and choosing types that minimize TASM cost.

Why: Different type representations (bool as field element vs. bit, integer width choices) produce different instruction sequences with different AET profiles. The "right" type is the one that minimizes proof cost.

Architecture: Tree-LSTM on the Trident AST. Each node predicts its type. Train on existing annotated programs.

Cost-aware mode: The model predicts not just valid types but optimal types. Two-headed output: (type_prediction, expected_cost_delta). Trained on (program, type_choice, resulting_TASM_cost) triples.

Developer interface: Like LSP (Language Server Protocol) autocomplete, but for types. Developer writes code, the model suggests types inline. Red underline if the type choice is >2× more expensive than the optimal.

4.2 Incremental Recompilation via Neural Diff

What: When a Trident source file changes, predict which TIR nodes are affected and only recompile those subgraphs.

Why: Full recompilation on every edit is slow for large programs. Incremental compilation enables interactive development with instant feedback.

Architecture: GNN on the TIR dependency graph. Input: (old_TIR, edit_location, new_TIR_fragment). Output: per-node binary classification (affected / stable).

Training data: Record (old_source, new_source, changed_TIR_nodes) from actual development sessions. Augment with synthetic edits (random single-line changes to existing programs).

Correctness: Conservative — if uncertain, mark as affected (recompile). False positives (unnecessary recompilation) waste time. False negatives (missed changes) produce wrong output. Bias the model toward recall >99.9%.

Integration: Plugs into trident watch mode. Developer saves file → model predicts diff → incremental compile → incremental prove (only changed subgraphs). Latency target: <100ms for single-line edits.

4.3 Fuzzing-Guided Program Synthesis

What: Given input/output examples (as field element pairs), synthesize a Trident program that satisfies the specification. Triton VM proves correctness.

Why: Enables a "specification-first" development workflow. Write the test cases, let the network generate the code, prove it's correct.

Architecture: Seq2seq model. Encoder: set of (input, output) pairs → fixed-size representation. Decoder: autoregressive TIR operation sequence (vocabulary of 54 ops, max length 32).

Model size: ~40K parameters. The constrained vocabulary and short sequence length make this feasible with tiny models.

Training: Generate random TIR programs, execute them on random inputs, collect (I/O_pairs, TIR_program) examples. Train the seq2seq to invert this mapping.

Verification: Synthesized program is compiled and executed on the specification inputs. If outputs match, run STARK proof. If not, generate more candidates (beam search with K=16 candidates).

Iteration: Failed candidates provide negative training signal. Successful candidates are added to the training set. The synthesizer improves as the corpus grows.

Priority 5 — Adversarial Hardening

5.1 Adversarial Program Generation

What: A neural network (neural proofs) that generates Trident programs specifically designed to defeat the neural compiler — programs where the optimized TASM is no better than naive lowering.

Why: Finds the compiler's blind spots. Satisfies the "100× adversarial load" quality gate. Automated, continuous, and creative.

Architecture: Autoregressive TIR generator. Same architecture as the program synthesizer (§4.3) but with an adversarial objective: maximize (naive_cost - optimized_cost) → make this delta zero or negative.

GAN-like training loop:

Epoch:
  1. Adversary generates 100 programs
  2. Neural compiler optimizes each
  3. Measure improvement ratio for each
  4. Adversary reward = programs where compiler failed
  5. Compiler trains on adversarial programs
  6. Repeat

What the adversary discovers (predicted):

  • Programs with unusual control flow that the compiler's GNN encoder doesn't represent well
  • Programs that exploit table coupling — where optimizing one table necessarily worsens another
  • Programs near cliff boundaries where any change is harmful
  • Programs with deeply nested dependencies that resist reordering

Convergence: The adversary and compiler reach equilibrium when the adversary can no longer find programs the compiler handles poorly. This equilibrium IS the quality gate passing.

5.2 Equivalence Checker Stress Testing

What: Generate pairs of TASM programs that are "almost equivalent" — they agree on 99.99% of inputs but differ on edge cases. Test whether the verification pipeline catches the discrepancy.

Why: The STARK verifier is mathematically sound, but implementation bugs exist. The equivalence checker (whether execution-based or NTP-based) needs stress testing.

Generation strategy: Take a correct TASM program. Apply a single mutation (change one operand, swap two instructions with a subtle dependency). The mutant is "almost the same" but semantically different.

Automated pipeline:

  1. Generate 10,000 (original, mutant) pairs
  2. Run equivalence checker on each pair
  3. Report any pair where the checker says "equivalent" (false positive = critical bug)
  4. Track false negative rate (checker says "different" when they're actually equivalent) — these are optimization opportunities

Priority 6 — Cross-Target Transfer

6.1 Transfer Learning Between Proof Backends

What: When Trident adds a new compilation target (Miden vm, SP1, OpenVM), transfer the neural compiler's knowledge from Triton VM to the new backend.

Why: Each backend has different cost functions. Training from scratch for each is expensive. But TIR-level patterns ("this subgraph structure is expensive") generalize across backends.

Architecture: Split the neural compiler into:

  • TIR encoder (shared): GNN that embeds TIR subgraphs → latent representation
  • Backend decoder (per-target): MLP that maps latent → target instruction sequence

Transfer procedure:

  1. Train full model on Triton VM (richest training data)
  2. Freeze TIR encoder
  3. Train only the backend decoder for Miden VM (small dataset suffices)
  4. Fine-tune encoder with small learning rate if decoder plateaus

Expected data efficiency: New backend needs ~10% of Triton VM's training data to reach comparable performance. The TIR encoder captures "what's structurally expensive" — backend-independent knowledge.

Long-term vision: A single Trident compilation produces optimized output for ALL backends simultaneously, using shared TIR analysis and specialized lowering.

Summary: Dependency Graph

[1.1 nn.trd] ──────→ [1.2 Evolutionary Training]
     │                        │
     │                        ├──→ [1.3 Trace Predictor]
     │                        │           │
     │                        │           ├──→ [2.1 Cost Surrogate]
     │                        │           │           │
     │                        │           │           └──→ [2.3 Compiler Ensemble]
     │                        │           │
     │                        │           └──→ [3.1 Prover Config Agent]
     │                        │
     │                        ├──→ [2.2 Instruction Scheduling]
     │                        │
     │                        ├──→ [2.4 Peephole Patterns]
     │                        │           ↑
     │                        │           │ (feeds back)
     │                        │           │
     │                        ├──→ [2.5 Neural Decompilation]
     │                        │
     │                        ├──→ [3.3 NTP Equivalence]──→ [2.4]
     │                        │
     │                        ├──→ [4.1 Type Inference]
     │                        │
     │                        ├──→ [4.3 Program Synthesis]
     │                        │           │
     │                        │           └──→ [5.1 Adversarial Gen]
     │                        │
     │                        └──→ [6.1 Transfer Learning]
     │
     └──────→ [3.2 Proof Compression]

[4.2 Incremental Recompilation] ← independent, needs only TIR dependency graph
[5.2 Equivalence Stress Test]  ← independent, needs only TASM mutation + verifier

Implementation Order (Recommended)

Phase Items Effort Prerequisite
Phase 0: Bootstrap 1.1, 1.2 2 weeks Trident compiler exists
Phase 1: Cost Intelligence 1.3, 2.1 2 weeks Phase 0
Phase 2: Compiler Core 2.2, 2.3, 2.4 3 weeks Phase 1
Phase 3: Proving 3.1, 3.2 3 weeks Phase 1
Phase 4: Developer UX 4.1, 4.2, 4.3 4 weeks Phase 2
Phase 5: Hardening 5.1, 5.2, 3.3 3 weeks Phase 2
Phase 6: Multi-Target 6.1, 2.5 2 weeks Phase 2

Total: ~19 weeks for full pipeline. Phase 0 alone produces a publishable result.

The compiler that proves its own optimization. The optimizer that improves its own compilation. The prover that accelerates its own verification. Not by trust, but by proof.

purpose. link. energy.

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