https://www.gero.uz/research/ Mathematical assurance for AI-generated reasoning. en Sun, 13 Sep 2026 09:30:00 +0000 https://www.gero.uz/research/articles/pyxirr-rate-vector-convergence.htmlhttps://www.gero.uz/research/articles/pyxirr-rate-vector-convergence.htmlSun, 13 Sep 2026 11:00:00 +0000Released PyXIRR 0.10.8 returns an unconverged vector RATE and fails at zero starting guesses. Independent discounting, compiled Rust checks and a tested candidate correction.Independent Numerical Audit https://www.gero.uz/research/articles/financepy-equity-vector-expiry-pricing.htmlhttps://www.gero.uz/research/articles/financepy-equity-vector-expiry-pricing.htmlSun, 13 Sep 2026 09:30:00 +0000A list of distinct expiries is reduced to its final horizon and broadcast across every option. Released-wheel reproduction, independent oracle and submitted correction.Independent Numerical Audit https://www.gero.uz/research/articles/mlx-cross-axis-broadcast.htmlhttps://www.gero.uz/research/articles/mlx-cross-axis-broadcast.htmlSun, 13 Sep 2026 08:11:42 GMTNative CPU evidence of a component-axis alignment error during broadcasting. A tested C++ candidate fixes the generated cases while preserving 2,789 control records.https://www.gero.uz/research/articles/mlx-norm-integer-promotion.htmlhttps://www.gero.uz/research/articles/mlx-norm-integer-promotion.htmlSun, 13 Sep 2026 07:40:31 GMTClean native CPU evidence of integer arithmetic before float promotion. Tested bounded repair, unchanged inexact controls, and unresolved large-value range cases. https://www.gero.uz/research/articles/financepy-mortgage-zero-small-rate.htmlhttps://www.gero.uz/research/articles/financepy-mortgage-zero-small-rate.htmlSun, 13 Sep 2026 06:54:05 +0000A zero rate raises ZeroDivisionError; tiny nonzero rates can leave a material unpaid or overpaid balance in synthetic amortization checks.Independent Numerical Audit https://www.gero.uz/research/articles/financepy-bond-principal-face-scaling.htmlhttps://www.gero.uz/research/articles/financepy-bond-principal-face-scaling.htmlSun, 13 Sep 2026 06:00:00 +0000Dirty price is scaled by the requested face while accrued interest remains at face one, violating the clean-value identity in a released-wheel reproduction.Independent Numerical Audit https://www.gero.uz/research/articles/onnx-reducemean-finite-range.htmlhttps://www.gero.uz/research/articles/onnx-reducemean-finite-range.htmlSun, 13 Sep 2026 04:30:00 +0000Finite means become infinity in both the reference evaluator and Runtime CPU provider because the input-type sum overflows before division.Independent Numerical Audit https://www.gero.uz/research/articles/onnx-reducel2-finite-range.htmlhttps://www.gero.uz/research/articles/onnx-reducel2-finite-range.htmlSun, 13 Sep 2026 04:15:00 +0000Finite Euclidean norms become infinity or zero in both the reference evaluator and Runtime CPU provider because values are squared before scaling.Independent Numerical Audit https://www.gero.uz/research/fineract-calculation-contracts/https://www.gero.uz/research/fineract-calculation-contracts/Sun, 13 Sep 2026 04:00:00 GMTA scoped Apache Fineract case: executable calculation checks, candidate corrections and a short GERO service demonstration. Synthetic component evidence; no customer impact established. https://www.gero.uz/research/articles/onnx-lpnormalization-finite-range.htmlhttps://www.gero.uz/research/articles/onnx-lpnormalization-finite-range.htmlSun, 13 Sep 2026 03:41:00 +0000Finite L1 and L2 inputs collapse to zero in both the reference evaluator and Runtime CPU kernel because avoidable intermediate norms overflow or underflow.Independent Numerical Audit https://www.gero.uz/research/articles/mlx-slogdet-range.htmlhttps://www.gero.uz/research/articles/mlx-slogdet-range.htmlSun, 13 Sep 2026 03:30:00 GMTClean CPU reproduction of a small-matrix slogdet range defect. Tested FP32 workaround; LU autodiff limitation and rejected repair counterexample retained. https://www.gero.uz/research/articles/mlx-layernorm-bias-dtype.htmlhttps://www.gero.uz/research/articles/mlx-layernorm-bias-dtype.htmlClean native CPU reproduction: an absent weight narrows finite float32 bias. A one-line candidate changes 106 failed assertions out of 385 to zero; 16 controls remain unchanged.Sat, 12 Sep 2026 19:45:00 GMT https://www.gero.uz/research/articles/mlx-groupnorm-low-precision.htmlhttps://www.gero.uz/research/articles/mlx-groupnorm-low-precision.htmlStandard GroupNorm returns zeros for finite FP16 inputs because a sum of squares overflows before division. A CPU research patch preserves channel grouping: 45 main-suite failures become zero, with 41 compatibility checks passing.Independent Numerical AuditSat, 12 Sep 2026 13:15:34 +0000 https://www.gero.uz/research/articles/mlx-batchnorm-low-precision-state.htmlhttps://www.gero.uz/research/articles/mlx-batchnorm-low-precision-state.htmlA finite float16 batch makes the default running variance infinite, leaving later evaluation at zero. A CPU research patch changes 102 main-suite failures to zero, with 33 compatibility checks passing. Existing corrupted state is not restored.Independent Numerical AuditThu, 10 Sep 2026 18:02:47 +0000 https://www.gero.uz/research/articles/mlx-clip-grad-norm-range.htmlhttps://www.gero.uz/research/articles/mlx-clip-grad-norm-range.htmlFloat16 [3072,4096] should clip to approximately [0.6,0.8], but MLX returns zero. A CPU research patch passes 1701 assertions across 219 scenarios, plus 39 compatibility and autodiff checks.Independent Numerical AuditThu, 10 Sep 2026 15:29:54 +0000 https://www.gero.uz/research/articles/mlx-divide-scale-autodiff.htmlhttps://www.gero.uz/research/articles/mlx-divide-scale-autodiff.htmlFor C/(C*t), the derivative at t=1 must remain −1. MLX returns zero or negative infinity at extreme scales. A research patch passes 1328 native comparisons, plus 1886 compatibility checks.Independent Numerical AuditThu, 10 Sep 2026 14:16:16 +0000 https://www.gero.uz/research/articles/mlx-arctan2-scale-autodiff.htmlhttps://www.gero.uz/research/articles/mlx-arctan2-scale-autodiff.htmlFor atan2(C*t,C), the derivative at t=1 must remain 0.5. MLX returns zero or infinity at extreme scales. A research patch passes 1368 native comparisons; both failed intermediate patches are preserved.Independent Numerical AuditThu, 10 Sep 2026 08:23:51 +0000 https://www.gero.uz/research/articles/mlx-inverse-hyperbolic-overflow.htmlhttps://www.gero.uz/research/articles/mlx-inverse-hyperbolic-overflow.htmlAt float16 x=1000, arcsinh and arccosh return finite values but zero derivatives. A normalized real-derivative patch passes 518 native comparisons across four dtypes; GPU and speed are untested.Independent Numerical AuditThu, 10 Sep 2026 07:50:20 +0000 https://www.gero.uz/research/articles/mlx-expm1-tail-vjp.htmlhttps://www.gero.uz/research/articles/mlx-expm1-tail-vjp.htmlAt x=-20, reverse mode returns zero for a derivative near 0.20611536. A local VJP repair plus the known exp control passes 216 native comparisons; the VJP-only patch can regress float64.Independent Numerical AuditThu, 10 Sep 2026 06:09:14 +0000 https://www.gero.uz/research/articles/mlx-logcumsumexp-shift-gradient.htmlhttps://www.gero.uz/research/articles/mlx-logcumsumexp-shift-gradient.htmlAt two equal float32 inputs of 100000000, MLX returns gradient [1,1] instead of [0.5,0.5]. An isolated CPU study separates a new VJP prototype from an already reported exp limitation.Technical NoteThu, 10 Sep 2026 06:10:33 +0000 https://www.gero.uz/research/articles/mlx-logcumsumexp-hessian-at-zero.htmlhttps://www.gero.uz/research/articles/mlx-logcumsumexp-hessian-at-zero.htmlA smooth x²/2 example returns second derivative 0 instead of 1. A research C++ prototype passes 477 checks; GPU and large-tensor performance remain untested.Technical NoteThu, 10 Sep 2026 04:00:28 +0000 https://www.gero.uz/research/articles/mlx-block-mask-output-gradient.htmlhttps://www.gero.uz/research/articles/mlx-block-mask-output-gradient.htmlAn extra output-mask factor suppresses its derivative at zero. A one-line C++ repair passes 377 scenarios and 604 checks; the demonstrated training step lowers loss from 18 to 0.Technical NoteThu, 10 Sep 2026 02:23:08 +0000 https://www.gero.uz/research/articles/mlx-gather-qmm-transpose-gradients.htmlhttps://www.gero.uz/research/articles/mlx-gather-qmm-transpose-gradients.htmlWith transpose=False, affine gather_qmm miscomputes scale and bias gradients. A local C++ orientation repair passes 205 scenarios and 379 checks; the measured quadratic update then lowers the loss.Technical NoteWed, 09 Sep 2026 17:18:11 +0000 https://www.gero.uz/research/articles/mlx-gather-vjp-preconditions.htmlhttps://www.gero.uz/research/articles/mlx-gather-vjp-preconditions.htmlValid sorted-index calls produce incorrect gather_mm and affine gather_qmm gradients. A bounded local FP32 CPU repair passes 69 scenarios and 626 checks; quantized FP16 fallback remains a limitation.Technical NoteWed, 09 Sep 2026 13:55:24 +0000 https://www.gero.uz/research/articles/mlx-hadamard-adjoint.htmlhttps://www.gero.uz/research/articles/mlx-hadamard-adjoint.htmlMLX uses the forward Hadamard transform in reverse differentiation for nonsymmetric factors 20 and 28. A local C++ repair passes 64 scenarios and 624 checks; measured energy steps confirm the correction.Technical NoteWed, 09 Sep 2026 12:43:40 +0000 https://www.gero.uz/research/articles/mlx-power-zero-derivatives.htmlhttps://www.gero.uz/research/articles/mlx-power-zero-derivatives.htmlMLX power returns NaN derivatives at zero for smooth fixed-exponent polynomials. A local C++ patch passes 41 scenarios and 396 checks; prior work and test-discovery limits are documented.Technical NoteWed, 09 Sep 2026 12:24:54 +0000 https://www.gero.uz/research/articles/mlx-masked-assignment-batch-gradients.htmlhttps://www.gero.uz/research/articles/mlx-masked-assignment-batch-gradients.htmlMLX mapped boolean assignment routes gradients across batch examples. A local C++ patch passes 19 scenarios and 255 checks; explicit loops and actual-forward finite differences agree.Technical NoteWed, 09 Sep 2026 12:03:18 +0000 https://www.gero.uz/research/articles/mlx-scatter-block-gradient.htmlhttps://www.gero.uz/research/articles/mlx-scatter-block-gradient.htmlA strict C++ scatter_max/min block update loses a winning gradient. Independent finite differences confirm the reference; a minimal extent correction passes 26 targeted checks.Technical NoteWed, 09 Sep 2026 11:40:24 +0000 https://www.gero.uz/research/articles/onnx-reference-reducelogsumexp-infinite-slices.html https://www.gero.uz/research/articles/onnx-reference-reducelogsumexp-infinite-slices.html Wed, 09 Sep 2026 00:00:00 +0000 Slices [inf, -inf] and [-inf, -inf] both become NaN, although the exact results and ONNX Runtime give +inf and -inf respectively. Independent Numerical Audit https://www.gero.uz/research/articles/onnx-reference-batchnorm-opset9-modes.html https://www.gero.uz/research/articles/onnx-reference-batchnorm-opset9-modes.html Wed, 09 Sep 2026 00:00:00 +0000 Inference uses blended training statistics and five-output training cannot return its requested statistics because mode is selected from momentum instead of output count. Independent Numerical Audit https://www.gero.uz/research/articles/onnx-reference-unique-unsorted-nonzero-axis.html https://www.gero.uz/research/articles/onnx-reference-unique-unsorted-nonzero-axis.html Wed, 09 Sep 2026 00:00:00 +0000 With sorted=0 and a nonzero axis, first-occurrence indices are always applied to axis 0, producing wrong data or an immediate out-of-bounds exception. Independent Numerical Audit https://www.gero.uz/research/articles/onnx-reference-gatherelements-rejects-subshapes.html https://www.gero.uz/research/articles/onnx-reference-gatherelements-rejects-subshapes.html Wed, 09 Sep 2026 00:00:00 +0000 Inputs of equal rank with smaller non-gather index dimensions are mathematically well-defined and accepted by ONNX Runtime, but the reference oracle requires exact shape equality. Independent Numerical Audit https://www.gero.uz/research/articles/onnx-reference-lpnormalization-p1-signed-sum.html https://www.gero.uz/research/articles/onnx-reference-lpnormalization-p1-signed-sum.html Mon, 07 Sep 2026 00:00:00 +0000 The input [1, -1] becomes [0, 0], while the exact L1-normalized result and ONNX Runtime both return [0.5, -0.5]. Independent Numerical Audit https://www.gero.uz/research/articles/onnx-groupnormalization-divisibility-doc.html https://www.gero.uz/research/articles/onnx-groupnormalization-divisibility-doc.html Mon, 07 Sep 2026 00:00:00 +0000 The summaries of versions 18 and 21 contradict the num_groups attribute and the operator's own four-channel, two-group example. Independent Numerical Audit https://www.gero.uz/research/articles/onnx-reference-logsoftmax-underflow.html https://www.gero.uz/research/articles/onnx-reference-logsoftmax-underflow.html Sun, 06 Sep 2026 00:00:00 +0000 A 104-logit gap makes the reference loss infinite while the mathematical result and ONNX Runtime output remain finite. Independent Numerical Audit https://www.gero.uz/research/articles/dinero-js-safe-intermediate-overflow.html https://www.gero.uz/research/articles/dinero-js-safe-intermediate-overflow.html Sun, 06 Sep 2026 00:00:00 +0000 All inputs remain JavaScript safe integers, yet binary64 rounding changes a 3-unit allocation from the exact [2, 1, 0] to [3, 0, 0]. Independent Numerical Audit https://www.gero.uz/research/articles/dinerojs-todecimal-non-decimal-base-guard.html https://www.gero.uz/research/articles/dinerojs-todecimal-non-decimal-base-guard.html Sun, 06 Sep 2026 00:00:00 +0000 Scalar base 240 is accepted and formatted as 1.10 for the exact value 250/240, while the equivalent multi-base currency [20, 12] is correctly rejected. Independent Numerical Audit https://www.gero.uz/research/articles/onnx-runtime-float16-quantizelinear-rounding.html https://www.gero.uz/research/articles/onnx-runtime-float16-quantizelinear-rounding.html Sat, 05 Sep 2026 00:00:00 +0000 A two-value counterexample shows the CPU float16 path returning [0, 0] where the ONNX rounding contract requires [1, -1]. Independent Numerical Audit https://www.gero.uz/research/articles/moneyphp-largest-remainder-float-collapse.html https://www.gero.uz/research/articles/moneyphp-largest-remainder-float-collapse.html Sat, 05 Sep 2026 00:00:00 +0000 An accepted 7-quadrillion-unit amount makes two exact residuals collapse to zero in binary64, assigning the final unit to the wrong share. Independent Numerical Audit https://www.gero.uz/research/articles/apache-fineract-nop-inverse-error.html https://www.gero.uz/research/articles/apache-fineract-nop-inverse-error.html Sat, 05 Sep 2026 00:00:00 +0000 Fineract's public number-of-payments helper returns 7 when its adjacent payment function was given a 12-period loan. Independent Numerical Audit https://www.gero.uz/research/articles/mlx-affine-quantization-doc-runtime-mismatch.html https://www.gero.uz/research/articles/mlx-affine-quantization-doc-runtime-mismatch.html Fri, 04 Sep 2026 00:00:00 +0000 MLX 0.32.2 returns a valid affine parameterization that differs from the formula stated in its public documentation. Independent Numerical Audit https://www.gero.uz/research/articles/swift-numerics-nearest-or-zero-doc-error.html https://www.gero.uz/research/articles/swift-numerics-nearest-or-zero-doc-error.html Thu, 03 Sep 2026 00:00:00 +0000 An exact arithmetic check found that one Swift Numerics example reported 3 where its stated rounding rule and its own explanation require 2. Independent Numerical Audit https://www.gero.uz/research/articles/swift-numerics-double-root-one-ulp-counterexample.html https://www.gero.uz/research/articles/swift-numerics-double-root-one-ulp-counterexample.html Thu, 03 Sep 2026 00:00:00 +0000 Double.root(3125, 5) returns 5.000000000000001 although the exact, representable result is 5.0. Independent Numerical Audit https://www.gero.uz/research/articles/where-mathematics-meets-ai-reliability.html https://www.gero.uz/research/articles/where-mathematics-meets-ai-reliability.html Wed, 02 Sep 2026 00:00:00 +0000 A research perspective connecting the reliability problems named by frontier labs to observability, control, verification and calibrated abstention. Original Research https://www.gero.uz/research/articles/who-certifies-ai-generated-proofs.html https://www.gero.uz/research/articles/who-certifies-ai-generated-proofs.html Wed, 02 Sep 2026 00:00:00 +0000 A falsification-first protocol for turning AI-generated mathematical arguments into dependency graphs, bounded verdicts and replayable evidence. Original Research https://www.gero.uz/research/articles/uncertainty-contract-for-ai.html https://www.gero.uz/research/articles/uncertainty-contract-for-ai.html Wed, 02 Sep 2026 00:00:00 +0000 Why scope, evidence, calibration, falsification, escalation and traceability should be a single contract around every high-consequence AI answer. Original Research https://www.gero.uz/research/articles/kondratiev-constant-left-open.html https://www.gero.uz/research/articles/kondratiev-constant-left-open.html Wed, 02 Sep 2026 00:00:00 +0000 Krol proved the leading narrow-cone constant in 1973 and left the next term as O(1). Identifying it took analysis; establishing who owned the first term took archive retrieval. Original Research https://www.gero.uz/research/articles/collatz-retraction-log.html https://www.gero.uz/research/articles/collatz-retraction-log.html Wed, 02 Sep 2026 00:00:00 +0000 Six claims, zero arithmetic errors, five failures. Every one failed above the arithmetic layer: wrong quantity, prior art, or a fabricated citation. Original Research https://www.gero.uz/research/articles/smoke-benchmark-reproduction.html https://www.gero.uz/research/articles/smoke-benchmark-reproduction.html Wed, 02 Sep 2026 00:00:00 +0000 The dataset, the command and the full result behind the 60-pair claim — including the distinction between a refuted defect and an abstention that the short phrasing hides. Original Research https://www.gero.uz/research/articles/chain-of-thought-observability.html https://www.gero.uz/research/articles/chain-of-thought-observability.html Wed, 02 Sep 2026 00:00:00 +0000 Anthropic's faithfulness results suggest that a visible chain of thought is a noisy sensor, not a guaranteed transcript of computation. Frontier Lab Watch https://www.gero.uz/research/articles/attribution-graphs-semantic-gap.html https://www.gero.uz/research/articles/attribution-graphs-semantic-gap.html Wed, 02 Sep 2026 00:00:00 +0000 Mechanistic interpretability can expose computational structure, but the map is partial and the meaning assigned to it remains a scientific claim. Frontier Lab Watch https://www.gero.uz/research/articles/research-proof-certification.html https://www.gero.uz/research/articles/research-proof-certification.html Wed, 02 Sep 2026 00:00:00 +0000 OpenAI's correction to a First Proof submission exposes false acceptance as the central metric for AI-assisted mathematics. Frontier Lab Watch https://www.gero.uz/research/articles/chain-of-thought-monitorability.html https://www.gero.uz/research/articles/chain-of-thought-monitorability.html Wed, 02 Sep 2026 00:00:00 +0000 OpenAI's monitorability evaluations raise a systems question: will a useful safety signal remain informative after training, scaling and distribution shift? Frontier Lab Watch https://www.gero.uz/research/articles/aletheia-research-math.html https://www.gero.uz/research/articles/aletheia-research-math.html Wed, 02 Sep 2026 00:00:00 +0000 Google DeepMind's Aletheia separates research mathematics from bounded contests and makes revision and failure admission part of the system. Frontier Lab Watch https://www.gero.uz/research/articles/self-correction-decomposition.html https://www.gero.uz/research/articles/self-correction-decomposition.html Wed, 02 Sep 2026 00:00:00 +0000 Google Research separates finding a mistake from repairing it; GERO turns that distinction into separate evidence contracts. Frontier Lab Watch https://www.gero.uz/research/articles/olympiad-to-research-gap.html https://www.gero.uz/research/articles/olympiad-to-research-gap.html Wed, 02 Sep 2026 00:00:00 +0000 DeepMind's IMO result is a major capability milestone; the next mathematical question is how performance transfers beyond a bounded contest distribution. Frontier Lab Watch https://www.gero.uz/research/articles/mlx-cumprod-hessian-at-zero.htmlhttps://www.gero.uz/research/articles/mlx-cumprod-hessian-at-zero.htmlMLX returns NaN second derivatives for a smooth cumulative-product polynomial at zero. A division-free C++ prototype passes 57 local scenarios, with an explicit O(N log N) cost.Technical NoteWed, 09 Sep 2026 10:43:25 +0000 https://www.gero.uz/research/articles/mlx-complex-autodiff-reversed-gradient.htmlhttps://www.gero.uz/research/articles/mlx-complex-autodiff-reversed-gradient.htmlA real loss increases after a gradient-descent step in MLX. Native tests isolate missing complex conjugation and an arccosh branch error; the local C++ patch passes 131 scenarios.Technical NoteWed, 09 Sep 2026 10:26:27 +0000 https://www.gero.uz/research/articles/mlx-muon-convolution-scaling.htmlhttps://www.gero.uz/research/articles/mlx-muon-convolution-scaling.htmlA native CPU reproduction isolates a shape-dependent Muon update in MLX. Equivalent convolution and linear layers agree before the optimizer step; a minimal reorder passes 31 focused tests.Technical NoteWed, 09 Sep 2026 10:04:18 +0000 https://www.gero.uz/research/articles/mlx-gaussian-nll-gradient-stability.htmlhttps://www.gero.uz/research/articles/mlx-gaussian-nll-gradient-stability.htmlNative MLX 0.32.2 CPU reproduction: finite Gaussian NLL with a variance gradient of the wrong sign. Inputs, references, regression tests and limits of a mitigation.Technical NoteWed, 09 Sep 2026 08:15:41 +0000 https://www.gero.uz/research/articles/nntrainer-dropout-gradient-routing.htmlhttps://www.gero.uz/research/articles/nntrainer-dropout-gradient-routing.htmlA native C++ nntrainer case study: zero-rate Dropout forwards correctly but misroutes multiple input gradients. Finite differences, a local patch and 19 passing tests.Technical NoteWed, 09 Sep 2026 04:18:53 +0000 https://www.gero.uz/research/articles/nntrainer-average-pool-asymmetric-padding.html https://www.gero.uz/research/articles/nntrainer-average-pool-asymmetric-padding.html nntrainer returns correct average-pooling forward values but loses three quarters of the gradient sum when SAME padding is asymmetric. Independent Numerical Audit Wed, 09 Sep 2026 12:00:00 +0000 https://www.gero.uz/research/articles/when-causal-attention-sees-the-future.htmlhttps://www.gero.uz/research/articles/when-causal-attention-sees-the-future.htmlA reproducible nntrainer causal-mask report: future values affect earlier outputs. Native tests, a local repair and an upstream issue are available.Technical NoteMon, 07 Sep 2026 16:12:38 +0000 https://www.gero.uz/research/articles/formal-proof-statement-contract.html https://www.gero.uz/research/articles/formal-proof-statement-contract.html Mon, 07 Sep 2026 00:00:00 +0000 Anthropic's Fermat formalization shows the scale now possible in Lean; the remaining assurance problem is preserving meaning, provenance and dependency scope from source theorem to checked root. Frontier Lab Watch https://www.gero.uz/research/articles/research-acceleration-causal-contract.html https://www.gero.uz/research/articles/research-acceleration-causal-contract.html Mon, 07 Sep 2026 00:00:00 +0000 OpenAI reports rapidly growing agent use while warning that activity metrics are hard to interpret; the mathematical task is to estimate validated progress under steering, selection and changing compute. Frontier Lab Watch https://www.gero.uz/research/articles/cosine-and-layernorm-contract-failures.htmlhttps://www.gero.uz/research/articles/cosine-and-layernorm-contract-failures.htmlReproduced cosine NaNs in MLX and an incorrect LayerNorm input gradient in nntrainer, with tested local patches and downloadable evidence.Technical NoteMon, 07 Sep 2026 12:06:51 +0000 https://www.gero.uz/research/articles/when-small-losses-and-gradients-disappear.htmlhttps://www.gero.uz/research/articles/when-small-losses-and-gradients-disappear.htmlMon, 07 Sep 2026 00:00:00 GMTReproduced BCE and logaddexp failures in MLX and nntrainer, with mathematical references, tested local patches and downloadable evidence. https://www.gero.uz/research/articles/finite-inputs-nonfinite-activations-mlx-nntrainer.htmlhttps://www.gero.uz/research/articles/finite-inputs-nonfinite-activations-mlx-nntrainer.htmlMon, 07 Sep 2026 00:00:00 GMTReproduced ELU, GELU and Softplus failures in pinned MLX and nntrainer code, with tested local repairs and downloadable evidence. https://www.gero.uz/research/articles/zero-observed-false-positives-small-sample.htmlhttps://www.gero.uz/research/articles/zero-observed-false-positives-small-sample.htmlSun, 06 Sep 2026 00:00:00 GMTA reproducible statistical note showing why zero observed false positives in a tiny validation sample does not establish a zero false-positive rate. https://www.gero.uz/research/articles/onnx-numerical-observatory-reproduced-snapshot.htmlhttps://www.gero.uz/research/articles/onnx-numerical-observatory-reproduced-snapshot.htmlSun, 06 Sep 2026 00:00:00 GMT https://www.gero.uz/research/articles/swift-numerics-complex-reciprocal-contract.htmlhttps://www.gero.uz/research/articles/swift-numerics-complex-reciprocal-contract.htmlSat, 05 Sep 2026 00:00:00 GMTA five-line counterexample shows reciprocal multiplication changing a result that direct complex division preserves, with a separate integer-power phase-error finding. https://www.gero.uz/research/articles/swift-numerics-hyperbolic-signs.htmlhttps://www.gero.uz/research/articles/swift-numerics-hyperbolic-signs.htmlSat, 05 Sep 2026 00:00:00 GMTA large-negative-real fast path flips component signs in complex cosh and sinh, propagates into cos and sin, and is reinforced by incorrect test expectations. https://www.gero.uz/research/articles/numerical-contracts-swift-numerics-nntrainer.htmlhttps://www.gero.uz/research/articles/numerical-contracts-swift-numerics-nntrainer.htmlSat, 05 Sep 2026 00:00:00 GMTFive bounded audit cases show how documented equivalence, exact identities, input preservation and parameter propagation expose failures that fixed expected values can miss. https://www.gero.uz/research/articles/mathematical-invariants-across-ai-stacks.htmlhttps://www.gero.uz/research/articles/mathematical-invariants-across-ai-stacks.htmlFri, 04 Sep 2026 00:00:00 GMTFive compact case studies show how chain rules, shape semantics, special values and execution parity expose silent failures in production AI software. https://www.gero.uz/research/articles/kld-backward-state-mutation.htmlhttps://www.gero.uz/research/articles/kld-backward-state-mutation.htmlFri, 04 Sep 2026 00:00:00 GMTA one-scalar experiment shows how an in-place label negation makes repeated KL-divergence backward calls alternate their gradient sign. https://www.gero.uz/research/articles/nntrainer-loss-scale-contract.htmlhttps://www.gero.uz/research/articles/nntrainer-loss-scale-contract.htmlFri, 04 Sep 2026 00:00:00 GMTFour of five implemented loss derivatives omit the configured loss scale; four runtime counterexamples and a 71-test repair expose the cross-component contract failure. https://www.gero.uz/research/articles/fractional-projective-gap-harmonic-gaussian-chaoses.htmlhttps://www.gero.uz/research/articles/fractional-projective-gap-harmonic-gaussian-chaoses.htmlFri, 04 Sep 2026 00:00:00 GMTAn author preprint proving fractional projective-gap inequalities in the complete second chaos, all split-product degrees and the first fully mixed harmonic cubic case. https://www.gero.uz/research/articles/nntrainer-reduce-mean-default-axis.htmlhttps://www.gero.uz/research/articles/nntrainer-reduce-mean-default-axis.htmlSun, 06 Sep 2026 00:00:00 GMTAn omitted reduction axis throws during initialization; a batch-two regression exposes the broken default and verifies a 23-test local correction. https://www.gero.uz/research/articles/nntrainer-uint8-affine-zero-point.htmlhttps://www.gero.uz/research/articles/nntrainer-uint8-affine-zero-point.htmlThu, 03 Sep 2026 00:00:00 GMTA three-value UINT8 input collapses a negative endpoint and real zero into the same code. The pinned evidence package records a candidate ratio-formula repair and 15 passing local tests. https://www.gero.uz/research/articles/onnx-normalizer-finite-range-stability.html https://www.gero.uz/research/articles/onnx-normalizer-finite-range-stability.html Sun, 13 Sep 2026 00:00:00 +0000 Finite rows at 1e30, 1e-30, 1e300 and 1e-300 produce NaN, zero, unnormalized values, or the wrong dtype in the released reference and Runtime CPU implementations. Independent Numerical Audit