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10 — Glossary

Canonical terms for the Lensemble corpus. Each entry is defined exactly as the rest of the corpus uses it, with a parenthetical link to the RFC or spec section that owns the term. Notation follows RFC-0002 §3-4 and the canonical symbol table; for the authoritative type signatures see 03 — Data Model, for the error names see 04 — Error Model, and for invariant IDs (INV-*) see the named-invariant set threaded through both.

Terms are grouped by topic. Within each group they appear in the order a reader meets them when building up the concept. A symbol index closes the document.

Architecture & model

JEPA (Joint-Embedding Predictive Architecture). A self-supervised architecture that predicts in a learned latent space rather than reconstructing raw pixels: an encoder maps an observation to an embedding, and a predictor maps a context embedding (plus, here, an action) to the embedding of a future observation. The training target is another embedding produced by the same network, not an external label. Lensemble trains an action-conditioned JEPA and uses it as a latent world model for planning (RFC-0001 §2).

V-JEPA 2. The released foundation-scale video JEPA (Assran et al., 2025; 1.2B parameters, pretrained on >1M hours of video) and its action-conditioned-predictor plus latent-MPC recipe. Lensemble warm-starts its encoder from released V-JEPA 2 weights; that warm-start also serves as the gauge anchor at round 0 (RFC-0001 §2; RFC-0008 design).

Action-conditioned predictor. The latent predictor $g_\phi$: a compact transformer that predicts future latents autoregressively, conditioned on an action embedding produced by the per-embodiment action head. It follows the LeWM ARPredictor shape and consumes a WMCP LatentState (RFC-0001 §2; detailed in RFC-0008 design).

Encoder ($f_\theta$). The video Vision Transformer mapping a video clip to $\mathbb{R}^{N\times d}$, warm-started from V-JEPA 2 and co-trained under the objective (Fork B). It emits a WMCP-conformant LatentState (RFC-0001 §2).

Fork A / Fork B. The two federation regimes. Fork B (the target) co-trains encoder and predictor end-to-end; this is the hard regime that opens the latent gauge and defines the full-model research path. Fork A (the documented safe-degrade fallback) freezes the warm-started shared encoder and federates only the predictor; the frozen encoder is itself a shared frame, so the gauge problem dissolves and the anchoring layers become unnecessary, while the scope narrows to predictor federation (RFC-0001 §7; RFC-0002 Fork A fallback).

Warm-start. Initializing every participant's encoder from the same released V-JEPA 2 weights. It buys foundation-scale credibility without an INTELLECT-class pretraining bill and, critically, closes the gauge at $t{=}0$: round-0 encoder weights are hash-identical across participants (INV-WARMSTART-T0). The round-0 encoder snapshot is frozen as the anchoring reference $f_{\text{ref}}$ (RFC-0002 §4).

WMCP (World-Model Contract Protocol; WM-RFC-0001). The shared latent/action interface — the shape, dtype, and semantics every encoder must emit and every predictor must consume, plus the action-conditioning interface every per-embodiment head must satisfy. It is the type-safety layer that makes heterogeneous-embodiment federation well-posed: the explicit analogue of the fixed token vocabulary that LLM federation gets for free. Conformance is a precondition for joining a federation (INV-WMCP) (RFC-0004 §6; RFC-0007).

Latent state (LatentState). The WMCP-governed encoder output: a tensor of shape $(N, d)$ with a pinned dtype and a wmcp_version string, carrying the per-clip latent tokens. Every conforming encoder emits it and every conforming predictor consumes it; a shape, dtype, or semantics mismatch raises ContractViolation (RFC-0007 design; schema in 03 — Data Model).

Action head (action encoder, embodiment head; $h_\psi^{(c)}$). The per-participant module mapping participant $c$'s embodiment-specific action space into the shared latent-conditioning space, validated against that embodiment's ActionSpec. Action heads are local: never broadcast and never aggregated, because action spaces genuinely differ across embodiments (INV-ACTIONHEAD-LOCAL) (RFC-0001 §2-3; RFC-0007 design).

Embodiment. A physical or simulated agent class with a specific action space and morphology (for example a quadruped versus a 7-DoF arm). Different embodiments share the encoder and predictor core but keep their own action head and ActionSpec; the WMCP contract is what lets them co-train one model (RFC-0001 §2; RFC-0007).

The objective

SIGReg (Sketched Isotropic Gaussian Regularization). The LeJEPA / LeWM regularizer that pushes the embedding marginal toward an isotropic Gaussian $\mathcal{N}(0, I_d)$ by projecting embeddings onto random 1-D directions and matching each univariate marginal to a standard Gaussian via the Epps-Pulley characteristic-function statistic. SIGReg removes the EMA target, stop-gradient, and teacher-student machinery, which is exactly what makes it federation-friendly — there is no momentum-encoder state to reconcile across participants. It is also the source of the latent gauge, because an isotropic Gaussian target is itself basis-free (RFC-0002 §1; RFC-0008 design).

Cramér-Wold / Epps-Pulley characteristic-function statistic. The statistical tools SIGReg rests on. The Cramér-Wold device reduces matching a high-dimensional distribution to its target to matching all of its 1-D projections; SIGReg samples those projections via the random sketch matrix. The Epps-Pulley statistic then tests, per projected direction, whether the univariate marginal matches a standard Gaussian by comparing empirical and target characteristic functions over a fixed set of integration knots (reference default ~17 knots) (RFC-0002 §1; defaults in RFC-0003 §2).

Sketch / random-projection matrix ($A$). The matrix that projects $d$-dimensional embeddings onto a batch of random 1-D directions for the SIGReg statistic (reference sketch dimension 64). All participants in round $t$ derive the identical $A$ from the broadcast round sketch seed $s_t$, so every participant minimizes the same regularizer rather than $C$ different empirical objectives (INV-SKETCH-CONSISTENCY). A shared sketch fixes objective consistency but does not close the gauge (RFC-0002 §3).

Function-space distillation (Layer 4). The heterogeneity / instability fallback: rather than average weights, aggregate behaviors — each participant emits predictions on the public probe, the coordinator forms a frame-aligned consensus, and a global student distills it. It is gauge-invariant by construction (it compares functions on shared inputs) and admits participants with different encoder sizes, at a higher per-round cost; held in reserve (RFC-0002 §6).

The latent gauge & frame anchoring

Latent gauge. The $O(d)$ rotational symmetry of the SIGReg-JEPA objective: the entire objective is invariant under a global orthogonal rotation of the latent space, so nothing pins a shared coordinate frame. Independently-updated participants therefore drift into mutually-rotated frames, and averaging their weight matrices in parameter space averages features expressed in different bases — producing neither participant's representation. This is the irreducible, JEPA-specific obstruction Lensemble exists to control (RFC-0002 §2).

$O(d)$ rotation symmetry. The formal statement of the gauge. For any orthogonal $Q \in O(d)$, the transform $f_\theta \mapsto Q f_\theta,\ g_\phi \mapsto Q g_\phi Q^{\top}$ leaves the objective unchanged: the prediction loss depends only on inner products and distances, which $Q$ preserves, and $\mathcal{N}(0, I)$ is invariant under $O(d)$, so every projected SIGReg marginal of $Qz$ is still standard normal. The $O(d)$ latent rotation is the extra symmetry that anchored models (supervised nets, LLMs with a fixed vocabulary) never see; the neuron-permutation symmetries present in any network are a separate, lesser matter handled by the same alignment machinery (RFC-0002 §2).

Frame anchor. The mechanism that manufactures the shared coordinate frame the objective otherwise lacks, so weight-averaging becomes valid again (Layer 2). It combines a shared warm-start (the gauge is closed at $t{=}0$) with a light public-probe anchor loss that re-pins the frame during fine-tuning. The probe is public data, so nothing private crosses a boundary; the same construction also keeps the eventual proof-of-contribution circuit cheap (RFC-0002 §4).

Landmark anchoring (Variant A). The recommended default anchor: choose $k \ge d$ generic landmark points on the probe with fixed absolute targets $t_i = f_{\text{ref}}(p_i)$ from the round-0 encoder, and penalize $\tfrac1k\sum_i \lVert f_\theta(p_i) - t_i\rVert^2$. Because $k \ge d$ generic absolute constraints admit only $Q = I$ as the satisfying orthogonal map, this pins the frame while leaving all other points free — "pin the frame, not the content." It needs no differentiable SVD, which is why it is the safe starting point (RFC-0002 §4).

Rotational-drift penalty (Variant B). The principled alternative anchor: decompose probe drift into a frame part and a content part, compute the optimal Procrustes rotation $Q^\star$ between the probe embeddings and $E_{\text{ref}}$, and penalize only the rotation, $\lVert Q^\star - I\rVert_F^2$. Gradients flow through the differentiable SVD into the encoder, pushing the frame toward the reference while leaving the post-alignment content residual unpenalized. It is the cleaner statement of "pin the frame, not the content" but risks instability near degenerate singular values, which must be clamped or conditioned (RFC-0002 §4).

Public probe ($\mathcal{P}$). The small, fixed, content-hash-pinned set of public (licensed-for- redistribution) data points that is the substrate for the frame anchor and for publicly-recomputable alignment. It must be representative enough to anchor a meaningful frame (under-coverage weakens the anchor; over-size raises per-round alignment cost), is governed openly, and includes the designated $k \ge d$ landmark subset. Because it redefines the reference frame, changing it is a versioned re-anchoring event; the probe hash equals the hash committed in RoundOpen (INV-PROBE-PIN) (RFC-0004 §3).

Procrustes alignment. The closed-form computation of the optimal orthogonal rotation $Q^\star$ aligning one set of probe embeddings to a reference: from the SVD $E_{\text{ref}}^\top f_\theta(\mathcal{P}) = U\Sigma V^\top$, the solution is $Q^\star = V U^\top$. It appears in three places — inside Variant B's anchor loss, as the Layer-3 backstop (re-aligning each participant's raw local full weights before release when drift exceeds threshold), and as the per-pair frame-drift diagnostic. Alignment of a committed model on the public probe is publicly recomputable. Applying a participant-specific pre-release backstop is not: it needs that participant's raw local weights and is assumed unless attested/proven or performed inside a trusted/MPC boundary (INV-ALIGN-BEFORE-RELEASE). A near-degenerate or ill-conditioned SVD raises DegenerateProcrustes; the public API exposes it as procrustes_align(source, target) -> (Q*, residual) (RFC-0002 §5).

Frame drift. An inter-participant Procrustes residual (or mean rotation angle) on the public probe over training, computed per participant pair and also against the global model. The gauge-control hypothesis predicts divergence under naive FedAvg and lower drift under an effective anchored configuration; the metric does not assume that outcome. When it exceeds the configured threshold the Layer-3 backstop fires; beyond a hard limit the system raises FrameDriftExceeded (RFC-0002 §9; RFC-0005 §2; emission contract in RFC-0015 design).

Federated training

DiLoCo. The low-communication outer/inner optimizer Lensemble builds on (Douillard et al.; OpenDiLoCo / INTELLECT, Prime Intellect). Each participant runs $H$ local inner steps, then a single outer step synchronizes the resulting pseudo-gradients; communication happens only every $H$ steps rather than every step. This is the standard low-communication engineering substrate rather than a project-specific mechanism (RFC-0001 §4; RFC-0003 §2).

Inner / outer loop. The two-level training topology. The inner loop is intra-participant optimization (standard FSDP / tensor / context parallelism with AdamW) over local data only — the only place the large-model-parallelism playbook applies. The outer loop is the inter-participant DiLoCo step that aggregates pseudo-gradients across the federation (RFC-0001 §4; RFC-0003 §2).

Inner horizon ($H$). The number of local inner steps each participant runs between outer synchronizations (reference range $[50, 500]$; DiLoCo/INTELLECT use $H \approx 500$ for LLMs). Larger $H$ means cheaper communication but more frame drift to anchor, so it is started small while characterizing drift and tuned against the gauge (RFC-0003 §2).

Pseudo-gradient ($\Delta_c$). Participant $c$'s contribution for a round: the difference between its post-inner-loop parameters and the round's global parameters, $\Delta_c = (\theta_c^{\text{local}}, \phi_c^{\text{local}}) - (\theta_t, \phi_t)$. DiLoCo treats the whole $H$-step local update as a single "gradient." Only released $\Delta_c$ crosses the boundary; it carries its own L2 norm and is bound to exactly one dataset Merkle root. The current coordinator sees the released value individually; effective noising and masking are target protections (INV-COMMIT-BINDING) (RFC-0003 §3; type in 03 — Data Model).

Outer Nesterov step. The outer-loop parameter update: Nesterov momentum applied to the averaged pseudo-gradient, $(\theta_{t+1}, \phi_{t+1}) = (\theta_t, \phi_t) + \eta_{\text{out}}\, \mathrm{Nesterov}(\tfrac1C \sum_c \Delta_c)$. Lensemble's $\Delta_c=\text{local}-\text{global}$ is a displacement; equivalently, DiLoCo's outer gradient is $G_c=\text{global}-\text{local}=-\Delta_c$ and is subtracted. This step is on the aggregation path and MUST be a pure, bitwise-reproducible function of the committed deltas, round seed, and prior global parameters (INV-AGG-DETERMINISM); a non-deterministic reduction raises NonDeterministicAggregation (RFC-0003 §2).

Coordinator. The role that orchestrates rounds, holds the canonical global model, and runs the outer optimizer. It is untrusted with respect to raw data: treated as honest-but-curious in Phase 1 and as a proving target in Phase 2. In Phase 1 it is a single point of trust and failure; Phase 2 makes its aggregation provable (RFC-0003 §1; runtime in RFC-0013 design).

Participant. The role that holds sovereign data, runs the local inner loop with intra-participant parallelism, and emits pseudo-gradients. Raw data never leaves a participant boundary (INV-RESIDENCY); only the released $\Delta_c$ and the dataset commitment cross. The current coordinator sees that $\Delta_c$ individually; privatization and masking are target protections (RFC-0003 §1; runtime in RFC-0013 design).

Round. One outer iteration of the protocol, progressing through the state machine OPEN -> COLLECTING -> AGGREGATING -> ALIGNING -> COMMITTING -> CLOSED (with an ABORTED path): broadcast of global parameters / sketch seed / probe hash, local optimization, pseudo-gradient release, participant-side optional Procrustes backstop before release, aggregation, the outer Nesterov step, and the hash-commit of the new global model. The target path makes that release private and securely aggregated; the current path does not. Bounded by the RoundOpen and RoundClose messages; round faults raise RoundError / FaultToleranceExceeded (RFC-0003 §2, §7; state machine in RFC-0013 design).

Privacy & secure aggregation

Secure aggregation. The protocol that lets the coordinator learn only the sum $\sum_c \Delta_c$ and never an individual $\Delta_c$ (an individual update leaks more about a silo's data than the sum). The reference design is pairwise-mask secure aggregation (Bonawitz-style) with threshold secret sharing for dropout robustness; a TEE-based aggregator is a supported alternative. Falling below the dropout threshold raises SecureAggregationError; masking must not introduce nondeterminism in the revealed sum (RFC-0003 §5; RFC-0011). This defines the target protocol. The current optimizer receives individual plaintext deltas; simulated/TEE sums are post-commit equivalence checks and masking records fallback, so none provides live coordinator confidentiality.

Differential privacy (DP). The per-participant guarantee on a released pseudo-gradient: after any required gauge alignment/re-difference, clip $\Delta'_c$ to a fixed norm, then add calibrated Gaussian noise, so a participant's contribution to a round is privacy-bounded. The unit of privacy is a participant's per-round contribution (update-level DP), not per-example DP-SGD inside the inner loop. The mechanism interacts with SIGReg variance and the anchor term; joint calibration is a Stage-B experiment, not a default (RFC-0003 §4; RFC-0012). The current deterministic replay seed is reconstructible and therefore not claim-grade DP (effective_dp=false).

$(\varepsilon, \delta)$. The differential-privacy budget: $\varepsilon$ bounds the privacy loss and $\delta$ the probability of exceeding it, accumulated over the planned number of rounds by the accountant. When the budget is spent, training stops and the system raises PrivacyBudgetExceeded (RFC-0003 §4; accounting in RFC-0012 design). This is the target persistent-accountant behavior. Current reports independently account one post-commit round and do not compose or enforce a run budget.

Clip norm ($C_{\text{clip}}$). The fixed L2 bound to which each pseudo-gradient is clipped before noising: $\Delta_c \leftarrow \Delta_c \cdot \min(1, C_{\text{clip}}/\lVert\Delta_c\rVert)$. After clipping and before noise, $\lVert\Delta_c\rVert \le C_{\text{clip}}$ is the enforced bound (INV-DP-BOUND); it sets the sensitivity the noise is calibrated against (RFC-0003 §4).

Noise multiplier ($\sigma$). The scale of the Gaussian noise relative to the clip norm: noise $\mathcal{N}(0, \sigma^2 C_{\text{clip}}^2 I)$ is added to the clipped pseudo-gradient, with $\sigma$ calibrated to the target $(\varepsilon, \delta)$ over the planned rounds. It is jointly tuned with $\lambda_{\text{sig}}$, $\lambda_{\text{anc}}$, and $C_{\text{clip}}$ in Stage B (RFC-0003 §4).

Honest-but-curious. The Phase-1 trust assumption on the coordinator and aggregator: they follow the protocol faithfully but may try to infer information from what they legitimately observe. Secure aggregation and effective DP are the target protections for released updates under this model; raw data residency is enforced separately. The current plaintext/replay path provides neither update confidentiality nor a DP guarantee. Phase 2 strengthens the model to detect a malicious coordinator and misreporting participants (RFC-0006 §1; threat model in 06 — Security).

Data & provenance

Sovereign data. The premise: each participant's raw interaction trajectories are siloed by IP, privacy, or safety and cannot be pooled. Federated training is the access strategy; the data stays put and only model deltas move (README thesis; RFC-0004 §1).

Data residency. The enforced property that raw observations, actions, and embeddings of private data never cross a trust boundary — only pseudo-gradients leave. Every local dataset carries a non-exportable flag and the training process must refuse to emit raw data or its embeddings (INV-RESIDENCY). A breach raises ResidencyViolation, which is security-critical and fail-closed: never caught and ignored (RFC-0004 §2; enforcement in 06 — Security, redaction in 05 — Observability).

Merkle root ($R_c$). The root of the binary Merkle tree a participant builds over the content hashes of its episodes, committed before an epoch via the Commitment message. It identifies the dataset that fed a contribution without revealing the data, and supports inclusion proofs for Phase 2. The canonical hash is SHA-256 in Phase 1 (RFC-0004 §4; construction in RFC-0014 design).

Dataset commitment (DatasetCommitment). The committed object binding a participant's data to a round: the Merkle root $R_c$, the episode count, and WMCP metadata. Every released $\Delta_c$ is bound to exactly one $R_c$ (INV-COMMIT-BINDING); a contributed update bound to the wrong root is rejected with CommitmentMismatch. Produced by the public API commit_dataset(dataset) -> DatasetCommitment (RFC-0004 §4; RFC-0014 design).

Contribution accounting. The append-only record of which committed dataset fed which round: per round, the set of contributing participants, their committed roots, and the resulting global-model hash (a ContributionRecord in the ContributionLedger). In Phase 1 it provides credit/governance tracking and tamper-evidence; in Phase 2 it is the audit substrate the verifiable layer formalizes (RFC-0004 §5; ledger in RFC-0014 design).

Evaluation & planning

Latent MPC (model-predictive control). The planning and evaluation procedure: use the trained model as the world model and minimize an $L_1$ goal-energy in latent space over candidate action sequences, re-planning each step, exactly as stable-worldmodel provides. Downstream planning success via latent MPC is the metric that ultimately matters; representation-probe accuracy is supporting evidence (RFC-0001 §2; RFC-0005 §3).

CEM / iCEM / MPPI. The sampling-based planners used inside latent MPC — the Cross-Entropy Method, its improved variant, and Model-Predictive Path Integral control. They search candidate action sequences against the latent goal-energy; the planner choice is an evaluation knob, not part of the training contribution (RFC-0005 §3).

Goal-energy. The $L_1$ distance in latent space between a predicted future state and the encoded goal specification (goal-image), which the latent-MPC planner minimizes to choose actions (RFC-0005 §3).

Effective dimension. The metric guarding against representation collapse: the effective rank of the embedding covariance (from its eigenspectrum), emitted as gauge/effective_dim. It catches silent partial collapse that a downstream success rate alone might mask (RFC-0005 §4; emission in RFC-0015 design).

Representation collapse. The failure mode where the encoder maps inputs into a low-rank or constant subspace, destroying useful structure. SIGReg prevents it locally by enforcing an isotropic marginal; averaging across mutually-rotated frames can re-introduce it ("collapse re-entry"), which the effective-dimension metric and the frame anchor together guard against (RFC-0002 §1, §2.1; RFC-0005 §4).

Ablation ladder. The core experiment: a sequence of configurations each adding one mechanism — (1) naive end-to-end FedAvg; (2) + shared sketch matrix; (3) + Procrustes align-then-average; (4) + frame-anchor loss (the expected recommended configuration); (5) + function-space distillation. All three metric families (frame drift, MPC success, collapse) are reported at each rung; the layers are additive, so the ladder is the rollout plan for the gauge machinery (RFC-0005 §6).

Non-IID. Heterogeneity across silos: each participant's data is partitioned by factor-of-variation or by embodiment so its empirical embedding marginal differs from the others'. Non-IID marginals are one of the failures that compound the gauge problem (SIGReg constrains a different marginal per participant). Stage B sweeps from near-IID to strongly non-IID using controlled factors of variation (RFC-0002 §2.1; RFC-0005 §7).

Factors of variation. The controlled axes of stable-worldmodel (environment, viewpoint, and other generative factors) used to partition data across silos for reproducible non-IID heterogeneity and to hold out factors at evaluation time (RFC-0005 §7).

Verifiability (Phase 2)

Proof-ready. The discipline of building Phase 1 so the Phase-2 proofs require no rework. The required properties are: deterministic aggregation (INV-AGG-DETERMINISM), hash-committed model versions (INV-CHECKPOINT-HASH), episode hashing and Merkle roots from day one, a content-hash-pinned public probe (INV-PROBE-PIN), and a reproducible outer step. These are inexpensive engineering disciplines in scope for v0.1-v1.0, distinct from the actual proofs (Phase 2 / Stage D, out of v1.0 scope) (RFC-0006 §3).

Function-space distillation. (See "The objective" group.) Listed here as well because its gauge-invariance is what makes behavior-level aggregation an option when weight-space aggregation is unstable (RFC-0002 §6).

TEE (Trusted Execution Environment). A hardware-isolated enclave whose attestation is the pragmatic proxy for proving that an inner training step executed faithfully. It is a weaker trust assumption than a SNARK but far cheaper than proving training in zero knowledge, so Lensemble reserves it for the heavy, data-touching inner step while proving the cheap, near-linear aggregation (RFC-0006 §2, §5).

Circle-STARK / Stwo. Stwo is the Circle-STARK prover used in Phase 2 to prove that aggregation was computed correctly over the submitted deltas. The proof is tractable precisely because the anchored frame keeps aggregation a plain weighted-average / Nesterov step — a near-linear operation with a small circuit. This synergy (the gauge fix is also the verifiability enabler) is the structural leverage of the design (RFC-0006 §2, §4).

Symbol index

Symbol Term Group
$d$ latent embedding dimension model
$N$ latent tokens per clip model
$f_\theta$ encoder model
$g_\phi$ action-conditioned predictor model
$h_\psi^{(c)}$ per-participant action head model
$f_{\text{ref}}$ round-0 reference encoder (warm-start) frame anchoring
$C$ participant count ($c$ = participant index) federation
$H$ inner horizon federation
$A$ SIGReg sketch / random-projection matrix objective
$s_t$ round sketch seed objective
$\mathcal{P}$ public probe set ($p_i$ its points) frame anchoring
$t_i$ landmark target $= f_{\text{ref}}(p_i)$ (Variant A) frame anchoring
$E_{\text{ref}}$ reference probe embeddings $= f_{\text{ref}}(\mathcal{P})$ frame anchoring
$Q \in O(d)$ gauge rotation; $Q^\star$ optimal Procrustes rotation latent gauge
$\lambda_{\text{sig}}, \lambda_{\text{anc}}, \lambda_{\text{pred}}$ SIGReg / anchor / prediction loss weights objective
$\Delta_c$ pseudo-gradient of participant $c$ federation
$\eta_{\text{out}}$ outer-optimizer (Nesterov) learning rate federation
$R_c$ dataset Merkle root committed by participant $c$ provenance
$(\varepsilon, \delta)$ differential-privacy budget privacy
$\sigma$ DP noise multiplier privacy
$C_{\text{clip}}$ DP clip norm privacy

References