THE CONSCIOUSNESS ATLAS
Read. Experiment. Follow the evidence.
Every recovered mathematical record has an individual page. Browse original equations, code expressions, indexed components, parameter definitions, and explicitly unresolved source slots.
Counts refer to mathematical records, including implemented expressions and generated instances. They are not counts of independently validated theories. Exact occurrences and unresolved slots remain traceable. Read the complete 1–516 source index ↗ · Inspect the scan decisions ↗
This states that the flattened input-side factor has 13824 real coordinates in the selected module. It defines the column dimension of the effective rank-one update. The vector dimension describes the inspected adapter module, not the total size of the base model.
Zₜ denotes a measured coordinate in an internal representation or a specified steering direction. The coordinate requires a defined layer, extraction procedure, reference basis, and scale. Different choices can produce different apparent trajectories from the same underlying model.
Subtracting the two supplied losses yields 0.20026636123657227 loss units. This is an absolute difference, not a percentage. The claim that it is the largest drop depends on the inspected record and its logging interval.
Subtracting the two supplied losses yields 0.20026636123657227 loss units. This is an absolute difference, not a percentage. The claim that it is the largest drop depends on the inspected record and its logging interval.
Each update retains a fraction λ or ρ of the previous value and adds q. With initial value zero and 0≤λ<1, past inputs decay and the state approaches q/(1−λ). This is a standard finite-capacity accumulation example whose long-term behavior follows from a geometric series.
Both displacement vectors point outward from the center checkpoint: one toward t−k and the other toward t+k. Their normalized inner product measures the angle between those directions. Straight passage through the center gives −1, a right-angle turn gives 0, and return along the same side can give…
If two interpretations assign exactly the same probability to every observation in the study, the likelihood ratio for any observed record is one. Those data therefore supply no likelihood evidence favoring one interpretation over the other. Distinguishing them requires an additional observable,…
This states that the flattened output-side factor has 5120 real coordinates in the selected module. With the 13824-dimensional input factor, the outer product has shape 5120 by 13824 and rank at most one. It is a particular adapter component within the larger model.
For nonzero rank-one matrices with compatible positive scaling, the normalized Frobenius inner product equals the product of the two factor cosines. The provided comparison gives about 0.962359729. This describes directional similarity of the selected operator pair, not equality of matrices or…
The Frobenius inner product separates into two vector dot products, while the norm separates into the product of the two vector lengths and |s|. These identities retain the geometry of the effective matrix while avoiding its explicit construction. They are exact in real arithmetic; numerical…
Multiplying one factor by a nonzero scalar and dividing the other by that scalar cancels in their outer product. The individual vectors can therefore move in magnitude while the effective weight update remains identical. This is why an operator-based distance avoids a basic ambiguity in factor-only…
The final logged evaluation loss is compared with the first logged value through 100(1−final/initial). The supplied values give 63.6935429588%, consistent with the recovered saved arrays. This describes the recorded loss series from the one inspected training run.
This indicator equals one when the fixed detector says the observed history meets the registered declaration criterion. Reproducibility requires the detector, thresholds, and rules for repeated events to be specified. A first-person sentence by itself does not establish that the criterion is…
Expanding the squared Frobenius norm gives two squared norms minus twice the inner product. Combined with rank-one factorization identities, this calculates matrix distance without constructing the matrices. When the two updates are extremely close, subtraction of similar large numbers can lose…
Expanding the squared Frobenius norm gives two squared norms minus twice the inner product. Combined with rank-one factorization identities, this calculates matrix distance without constructing the matrices. When the two updates are extremely close, subtraction of similar large numbers can lose…
Subtracting one from both sides gives error_next=a×error. For 0<a<1, the positive error shrinks geometrically but remains nonzero at every finite step when initialized above one. This supplies an ordinary nonconscious dynamical example of persistent finite-time discrepancy with eventual convergence.
Expanding the two outer products shows that the operator difference equals a changed output factor times the later input factor plus the earlier output factor times a changed input factor. This rearrangement makes small factor differences explicit and can avoid cancellation in a norm subtraction.…
For each candidate split k, a separate straight line is fitted to the observations on each side, and their squared residuals are added. The preferred split minimizes this combined residual cost. Because the two lines are independently fitted, they need not meet at k; the procedure selects a…
For each candidate split k, a separate straight line is fitted to the observations on each side, and their squared residuals are added. The preferred split minimizes this combined residual cost. Because the two lines are independently fitted, they need not meet at k; the procedure selects a…
The next value equals the current value, so induction gives xₜ=x₀ for all subsequent steps. Other parts of a system can evolve while this component stays fixed. A changing surrounding loop cannot alter this state unless the update equation includes an effective coupling term.
Adding the first two explained-variance fractions gives 0.9498998129, or about 94.99% of the variance in the centered representation analyzed. This measures compression of that particular trajectory into two linear directions. It does not mean those directions account for the same fraction of total…
Multiplying the dossier’s 44,050,944 bytes per expert by 464 expert evaluations gives 20,439,638,016 bytes, about 19.04 GiB. This is the stated one-load-per-evaluation accounting assumption. Reuse, resident weights, batches, scale tensors and other model components affect actual storage traffic, so…
The shared expert processes identity, the input representation saved before the routed expert computation. Its output is added to the weighted routed sum. It therefore contributes a parallel transformation of the original input; it does not take the routed output as its input.
An expert-specific correction vector is added to the sigmoid affinities for ranking. This addition can change which groups and experts are selected. The later mixture weights are gathered from the original affinities, so the correction bias does not directly enter their numerical values.
The adjusted expert scores outside the selected groups are masked to negative infinity. Top-k then returns eight expert indices among the 128 eligible entries. The group restriction means this is generally different from simply choosing the globally largest eight scores.
The 128 heads contribute 128 value components each, giving 16,384 components per token. The output linear map then projects that concatenation into the 7,168-dimensional residual stream. The indicated tensor shape describes the weight layout; executing the quantized checkpoint requires the…
Using the conventional count of one multiplication plus one addition per multiply–accumulate,36.52 GMAC corresponds to 73.04 GFLOP, rounded to 73.0. This is arithmetic applied to the dossier’s operation estimate, not a measured throughput rate. Attention work varies with sequence length and the…
Eight selected experts in each of fifty-eight MoE transformer layers give 464 routed expert evaluations for one token’s ordinary pass. The count excludes the dense prefix, shared experts and optional additional MTP work. It is an operation count; the number of physical disk reads also depends on…
The encoded byte first becomes its FP8 numerical value in float32, then is multiplied by the scale shared by its 128-by-128 block. The block indices mean floor(r/128) and floor(c/128). A partial boundary block still requires a scale, so the scale-grid shape uses ceiling division. The companion…
Substitution of scale=40 and adjustment strength 1 gives 1+0.1 ln 40=1.3688879454113936. The displayed 1.3688879 is a rounded form of that calculation. This is a deterministic configured coefficient, not a measured model response.
Flattened token representations h are multiplied by the transpose of the gate weight matrix, giving one raw routing logit per expert. Both operands are cast to float32. None means this linear operation adds no bias; the separate correction bias is added later for expert selection.
The sigmoid 1/(1+exp(−z)) is applied to each expert logit independently. It compresses each finite real logit into (0,1), without normalizing across experts. These values are routing affinities; they become relative mixture weights only after gathering selected entries and normalizing them.
For each token, select the indices of the four largest group scores. This leaves four groups of thirty-two experts eligible for the next selection. The selection is a discrete ranking operation; ties require the implementation’s top-k tie convention.
The arithmetic (512+64)×2=1152 bytes is correct for a cache storing one compressed key/value latent and one rotary key vector per token and layer at two bytes per element. The dossier’s embedded eager code instead caches reconstructed per-head keys and values:128×(192+128)×2=81920 bytes. Its…
For scale>1, the adjustment adds 0.1*mscale*ln(scale) to one. The code returns one for scale≤1. One parameter specifies the context extension, while the other controls adjustment strength; the returned value should not be confused with the input parameter also named mscale.
Apply softmax across key positions for each query and head. The resulting nonnegative weights sum to one when a row has at least one finite eligible score. The source computes this normalization in float32 and then converts it to the query dtype; its eager implementation incorporates a mask…
Each gathered affinity is divided by the sum across the selected experts plus 10⁻²⁰. Ignoring that stabilizer, the selected weights sum to one. With the stabilizer retained, the exact sum is S/(S+10⁻²⁰), so it is approximately one for an ordinary positive sum. This is normalization of sigmoid…
For each selected expert index, gather the corresponding value from the pre-bias sigmoid score array. Ranking used bias-adjusted values, but this weighting stage deliberately uses the original affinities. Changing the correction bias can therefore change membership without directly adding to a…
The base rotary frequency is divided by factor. At a fixed token position, this reduces its phase advance by that factor. The later blend applies this scaled schedule toward the low-frequency end of the rotary dimensions; the formula alone provides a candidate schedule over all indices.
This is the original geometric rotary frequency schedule, base^(−2 i/dim). Its frequency decreases as i grows when base>1. The later blend retains the unscaled schedule at the higher-frequency end and combines it with the divided schedule at intermediate indices.
rotate_half maps a pair of coordinate blocks(x 1,x 2) to(−x 2,x 1). Multiplication by cosine and addition of the sine-weighted rotated vector implements a two-dimensional rotation for each coordinate pair. The surrounding interleave-to-block reshape determines which coordinates are paired. Norm is…
After normalization, all selected mixture weights are multiplied by 2.5 in this DeepSeek configuration. Their sum is then approximately 2.5, so the routed contribution is amplified relative to a unit-sum mixture. This factor is separate from the unscaled shared-expert addition.
The query–key matrix product forms similarities between each query position and key position. The prose uses 0.135237 as its attention multiplier. From the displayed exact settings, the multiplier is (1+0.1 ln 40)²/√192≈0.1352337789; the text’s decimal is an approximation. This equation precedes…
The 256 experts are arranged as eight groups of thirty-two. Within each token and group, take the two largest bias-adjusted scores and add them. The resulting eight group scores decide which groups are eligible for the final expert selection.