{ "credit": "Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved: the solved policy, Gaussian filter, fee rule, qm tables, replica and exact-arithmetic arb/retail tell that LEAN, AGE, fastlean and this test are all built on.", "mech": "sd-extrap: what the qm lookup does outside its tables' range of offset and belief standard deviation. Linear extrapolation in place of clipping (sd axis, offset axis, rival-offset axis) and a linear add-on to both quote levels per bps of sd beyond the last sd level. Tested on the fast LEAN replica (fastlean, artifact a88ff982eba7e078bc6ccb1555b90a211c00c9fd76ec90a62ab13a4074f2c3d0, fastlean.py sha256 d9c758bb280fe24e09c039496f84ab0804173ff70cec24c332f8683f28efa582).", "already_present": false, "already_present_where": "Read: leanbase.py and stalerival.py (LEANBASE artifact efb8e653f8fd061cecf3e92b186470c9c96c5188523364b60ed101e9672869aa, reference_zb64), real.py, tellpol.py, evalpol.py (amm-sim@66604b3426d8e97a73e2c39940b9b4dece51cc73 research/solved and research/tell). leanbase.py, stalerival.py and tellpol.py do not touch the table range; stalerival only calls self.lookup again after the rival pull. The whole treatment is in real.RealPolicy.lookup and evalpol.DPPolicy._pos2, and it is clipping on every axis: sd: \"if tt > 1.0: tt = 1.0\" holds the tables at the last sd level S[-1] = 34 bps (S = 0,4,8,12,16,20,26,34); sd >= 0 so the lower edge is never passed. offset w: pw is clipped to [0, NW-1], i.e. the quote levels a, b are read at w = -800 or +800 bps (W0 = 160 cells of H_bps = 5). rival offset w2: clipped to +-FB = +-30 bps in phase 0 and to the ends of W2L (+-160 cells = +-800 bps) by _pos2 in phases 1 and 2. No extrapolation and no add-on exists on any axis, so the answer is false. One qualification for the offset axis: the fee is computed from the clipped quote level and the unclipped offset (fa = 1 - exp(-(a - w)*1e-4), fb = 1 - exp(-(b + w)*1e-4)), so in fee terms a one-for-one linear add-on per bps of offset beyond the edge is already there (the quote is pinned in price, the fee grows with the offset up to the 10% cap). For the offset I therefore tested the nearest variant that is not present: extrapolating the quote-level tables themselves along the last cell.", "definition": { "formula": [ "sd axis, extrapolation: tt = (sd - S[k]) / (S[k+1] - S[k]) on the last segment (26..34 bps) is allowed up to 1 + sd_ext_bps / 8 instead of 1; a = bl(A[k])*(1-tt) + bl(A[k+1])*tt as before, same for b. sd_ext_bps = 0 is LEAN.", "sd axis, add-on: if sd > S[-1]: a += sd_add*(sd - 34), b += sd_add*(sd - 34) (bps of quote level per bps of sd; positive widens both quotes). sd_add = 0 is LEAN.", "offset axis, extrapolation: pw = w/5 + 160 is clipped to [-w_ext_bps/5, 320 + w_ext_bps/5] instead of [0, 320]; the cell index stays in 0..319, so f = pw - i leaves [0,1] and the bilinear form extrapolates along the edge cell. w_ext_bps = 0 is LEAN.", "rival-offset axis, extrapolation: phase 0: l2 = w2/5 clipped to +-(6 + w2_ext_bps/5) instead of +-6; phases 1, 2: beyond W2L[0] / W2L[-1] the position continues linearly along the end cell for at most w2_ext_bps. w2_ext_bps = 0 is LEAN.", "The fees then follow unchanged: fa = 1 - exp(-(a - w)*1e-4) if a > w else 0, fb likewise, then LEANBASE's own clamp to [0, 10%]." ], "parameters": { "sd_ext_bps": "bps of sd beyond 34 over which the last sd segment is extrapolated", "sd_add": "bps added to both quote levels per bps of sd beyond 34", "w_ext_bps": "bps of offset beyond +-800 over which the edge cell is extrapolated", "w2_ext_bps": "the same for the rival offset" }, "state_kept": "none: the mechanism only changes how the lookup reads sd, w and w2, which the policy already has", "inputs_used": "nothing beyond what LEAN already derives from afterSwap (side, amounts, timestamp, own reserves) and its own state", "where": "fastlean.py lookup(); parameters ride in F[7..10], run_batch(tabs, seeds, x=(sd_ext_bps, sd_add, w_ext_bps, w2_ext_bps)); x=None or zeros is LEANBASE bit for bit" }, "how_often_the_edges_are_passed": { "LEAN": { "seeds": "64000..64127", "callbacks": 1384962, "sd_gt_34": 10, "sd_excess_mean_bps_when_over": 3.6593203361033644, "sd_max_bps": 48.15274026860846, "absw_gt_800": 884, "absw_800_to_1800": 882, "phase0_absw2_gt_30": 358643, "phase0_absw2_gt_30.05": 0, "phase12_absw2_gt_800": 139 }, "AGE": { "seeds": "64000..64127", "callbacks": 1385898, "sd_gt_34": 9, "sd_excess_mean_bps_when_over": 3.233219335458539, "sd_max_bps": 45.008683985081724, "absw_gt_800": 885, "absw_800_to_1800": 883, "phase0_absw2_gt_30": 360125, "phase0_absw2_gt_30.05": 0, "phase12_absw2_gt_800": 141 }, "note": "Counted on the baselines without the mechanism (stats pass added by the patch). Per run of about 10,800 callbacks: sd > 34 bps on 0.08 callbacks (10 in 128 runs, mean excess 3.7 bps, largest sd 48.15); |offset| > 800 bps on 6.9 callbacks, all but two below 1,800; phase-0 rival offset beyond 30 bps on 26% of callbacks but never by more than 0.05 bps (the band clip is -ln(0.997) = 30.045 bps, the table ends at 30); phases 1-2 rival offset beyond 800 bps on 1.1 callbacks." }, "table_edges": "From qm_k1e-5.json: along sd the quote level at w = 0 rises 27.65 -> 30.39 (0c), 27.30 -> 28.45 (1s), 26.93/27.64 -> 29.84 (1c), 27.26 -> 28.69 (2s), 27.43 -> 29.60 (2c) between the last two levels 26 and 34 bps, so extrapolation adds 0.14 to 0.36 bps per bps of sd. Along the offset the edge cells have slope 1 on one side (A = 790, 795, 800 at w = 790, 795, 800: ask fee 0) and about 0.003 bps per bps on the other (-21.39, -21.40, -21.42), so extrapolating them changes almost nothing. Along the rival offset the phase-1/2 tables are flat at both ends (1s, 1c, 2c) or nearly (2s: 139.0, 140.49, 141.22); phase 0 has slope about 0.34 bps per bps but the edge is passed by at most 0.045 bps.", "method": { "selection_seeds": "64000..65023 in 8 rounds of 128, every setting paired with LEAN (a0=0.35 ainf=0.35 tau=2) on the same seeds; drop rule mean_diff + 3*se < 0 checked after each round; se = sd of paired differences (n-1) / sqrt(n)", "choice_rule": "the surviving setting with the largest mean_diff after 1,024 seeds", "settings_count": 12, "dropped": 0, "report_seeds": "10000..12047, the chosen setting once paired with LEAN and once stacked on AGE (a0=0 ainf=0.7 tau=1) paired with AGE", "parity_of_the_patched_file": { "seeds": "64000..64063 and 10000..10063", "mean_edge_original": 527.8724874783702, "mean_edge_patched_x_none": 527.8724874783702, "bit_identical_x_none": 128, "bit_identical_x_zeros": 128, "n": 128, "age_bit_identical_of_32": 32, "note": "patched fastlean with x=None and with x=zeros against the unpatched fastlean.py, edge per seed; mean_edge equals the replica artifact's mean_edge_fast 527.8724874783702" }, "environment": "CPython 3.12.3, numpy 2.2.6, llvmlite 0.44.0, numba 0.61.2 (PyPI cp312 manylinux x86_64 wheels, sha256 checked against PyPI), Linux x86_64; research files of amm-sim@66604b3426d8e97a73e2c39940b9b4dece51cc73 research/solved and research/tell, 34 files, 0 sha256 mismatches" }, "settings_tried": [ { "name": "sd_ext8", "parameters": { "sd_ext_bps": 8, "sd_add": 0, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -2e-06, "se": 2.4e-05, "dropped_early": false, "seeds_positive": 21, "seeds_negative": 24, "min": -0.019606, "max": 0.011638 }, { "name": "sd_ext16", "parameters": { "sd_ext_bps": 16, "sd_add": 0, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -3.6e-05, "se": 4e-05, "dropped_early": false, "seeds_positive": 20, "seeds_negative": 25, "min": -0.03286, "max": 0.011638 }, { "name": "sd_ext_uncapped", "parameters": { "sd_ext_bps": 1000, "sd_add": 0, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -3.6e-05, "se": 4e-05, "dropped_early": false, "seeds_positive": 20, "seeds_negative": 25, "min": -0.03286, "max": 0.011638 }, { "name": "sd_add0.25", "parameters": { "sd_ext_bps": 0, "sd_add": 0.25, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -1.7e-05, "se": 4.5e-05, "dropped_early": false, "seeds_positive": 13, "seeds_negative": 34, "min": -0.027524, "max": 0.02699 }, { "name": "sd_add0.5", "parameters": { "sd_ext_bps": 0, "sd_add": 0.5, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -0.0001, "se": 5.8e-05, "dropped_early": false, "seeds_positive": 14, "seeds_negative": 33, "min": -0.036662, "max": 0.010324 }, { "name": "sd_add1", "parameters": { "sd_ext_bps": 0, "sd_add": 1.0, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -5.9e-05, "se": 6.2e-05, "dropped_early": false, "seeds_positive": 15, "seeds_negative": 32, "min": -0.039606, "max": 0.02289 }, { "name": "sd_add2", "parameters": { "sd_ext_bps": 0, "sd_add": 2.0, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -0.000191, "se": 0.000114, "dropped_early": false, "seeds_positive": 11, "seeds_negative": 36, "min": -0.067784, "max": 0.035136 }, { "name": "sd_add-0.5", "parameters": { "sd_ext_bps": 0, "sd_add": -0.5, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -4.9e-05, "se": 4.1e-05, "dropped_early": false, "seeds_positive": 27, "seeds_negative": 18, "min": -0.027238, "max": 0.015311 }, { "name": "w_ext_uncapped", "parameters": { "sd_ext_bps": 0, "sd_add": 0, "w_ext_bps": 1000, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": 0.000678, "se": 0.000568, "dropped_early": false, "seeds_positive": 245, "seeds_negative": 400, "min": -0.171298, "max": 0.348072 }, { "name": "w2_ext0.05", "parameters": { "sd_ext_bps": 0, "sd_add": 0, "w_ext_bps": 0, "w2_ext_bps": 0.05 }, "n": 1024, "mean_diff": -0.002392, "se": 0.002643, "dropped_early": false, "seeds_positive": 506, "seeds_negative": 518, "min": -0.722507, "max": 0.532597 }, { "name": "w2_ext30", "parameters": { "sd_ext_bps": 0, "sd_add": 0, "w_ext_bps": 0, "w2_ext_bps": 30 }, "n": 1024, "mean_diff": -0.002336, "se": 0.002636, "dropped_early": false, "seeds_positive": 506, "seeds_negative": 518, "min": -0.722557, "max": 0.5326 }, { "name": "sd_ext_uncapped+sd_add0.5", "parameters": { "sd_ext_bps": 1000, "sd_add": 0.5, "w_ext_bps": 0, "w2_ext_bps": 0 }, "n": 1024, "mean_diff": -5.6e-05, "se": 5.1e-05, "dropped_early": false, "seeds_positive": 21, "seeds_negative": 26, "min": -0.034211, "max": 0.010087 } ], "chosen": { "name": "w_ext_uncapped", "parameters": { "sd_ext_bps": 0, "sd_add": 0, "w_ext_bps": 1000, "w2_ext_bps": 0 }, "why": "Largest mean_diff of the 12 after 1,024 selection seeds and the only positive one: +0.00068 se 0.00057 (1.2 se), which is not distinguishable from zero. No setting was dropped early because every one is within a few thousandths of LEAN; none shows a gain. The sd settings, which the item is named for, are all between -0.0002 and 0.0000 with se <= 0.00011: sd passes 34 bps on about one callback in 138,000." }, "report": { "vs_lean": { "n": 2048, "mean_diff": -0.000105, "se": 0.000258, "seeds_positive": 480, "seeds_negative": 777, "seeds_changed": 1257, "min": -0.17161, "max": 0.177194, "base_mean_edge": 536.603391, "mech_mean_edge": 536.603286 }, "on_age": { "n": 2048, "mean_diff": 0.000152, "se": 0.000432, "seeds_positive": 493, "seeds_negative": 765, "seeds_changed": 1258, "min": -0.594051, "max": 0.297582, "base_mean_edge": 536.6231, "mech_mean_edge": 536.623253 }, "reading": "Chosen setting minus its baseline on 2,048 report seeds: -0.00011 se 0.00026 on LEAN and +0.00015 se 0.00043 on AGE. Both are zero within one standard error and two orders of magnitude below the +0.03 bar. About 1,257 of the 2,048 seeds change at all, more of them down than up (480 up, 777 down on LEAN; 493 up, 765 down on AGE)." }, "promote": false, "conclusion": "No. Nothing in how the lookup treats values beyond the tables' range is worth a pipeline: the sd edge is passed too rarely to matter, the offset edge cells already have the slope an extrapolation would give them, and the rival-offset edge is either flat or passed by 0.045 bps at most. Largest absolute effect of any of the 12 settings on 1,024 seeds: 0.0024 (se 0.0026).", "contract_cost": { "basis": "Estimated by reading fees() and surf() of the QLX5 source (code_zb64.QLX5 of artifact 1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15, sha256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40). Not compiled and not run on the engine: these are estimates, not measurements.", "storage_words": 0, "chosen_setting_offset_extrapolation": { "change": "widen the bounds in \"int256 pw=clip(w/5+160*U,0,320*U)\" and guard the unsigned cast \"uint256 i=uint256(pw/U)\" in surf() for a negative pw (the mirrored call passes 320*U-pw); lerp() is already signed, so f outside [0,1] needs nothing else. The contract's tables hold the fee form (level minus grid offset, nodes floored at 0), which extrapolates to the same quotes.", "gas": "about +50 to +150 per afterSwap (one extra comparison in each of the two surf() calls); peak about 208,100..208,500 of 245,000", "characters": "about +30 to +60; about 47,290 of 50,000", "runtime_bytes": "about +20 to +50; about 22,490 of 24,576" }, "sd_extrapolation": { "change": "replace the upper bound U in \"int256 tt=clip((sd-sdl(k)*U)/(sdl(k+1)-sdl(k)),0,U)\" by e.g. 3*U", "gas": "about 0", "characters": "+2", "runtime_bytes": "about 0 to +5" }, "sd_add_on": { "change": "one branch after the two surf() calls: if(sd>34*U){int256 e=mul(sd-34*U,C);xa+=e;xb+=e;}", "gas": "about +30 when sd <= 34 bps (nearly always), about +150 otherwise", "characters": "about +50", "runtime_bytes": "about +40 to +70" }, "fits": "Each variant fits the 208,000 / 245,000 gas, 22,440 / 24,576 byte and 47,230 / 50,000 character budgets with room; none is worth spending them on." }, "patch_zb64": "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", "patch_note": "base64(zlib(unified diff, -p1, a/fastlean/fastlean.py -> b/fastlean/fastlean.py)) against fastlean.py sha256 d9c758bb280fe24e09c039496f84ab0804173ff70cec24c332f8683f28efa582. It adds the four parameters to lookup(), the x argument to run_batch() and, under stats=True only, counters of how often each table edge is passed.", "not_done": [ "An add-on for the offset axis with a slope of its own (quote level shifted per bps of |offset| beyond 800) was not given a setting: the 12-setting limit was spent, and two pairs turned out to be the same test (sd_ext16 and sd_ext_uncapped agree to every printed digit because sd never passed 50 bps; w2_ext0.05 and w2_ext30 differ by 0.00005). The offset edge is passed on about 7 callbacks a run, so this is the one untested corner; nothing here measures it.", "Only the chosen setting was run on the report seeds, as the method says; the sd settings have selection-seed numbers only.", "Replica only, on LEAN and AGE. QLX5's drift-tolerant rival split test is not in fastlean, so nothing was run on QLX5 itself. No Solidity port, no compile, no gas or size measurement, no engine seeds used, no gate run, nothing submitted.", "Seeds 10000..10063 were also run once without the mechanism (x=None and x=zeros) for the bit-identity check of the patched file; no mechanism setting saw report seeds before the choice. The JIT warm-up runs seed 64000 once with x=(1, 0.1, 1, 1) and discards the result; it is not one of the 12 settings.", "The run lines' \"sh fetch.sh\" and \"pip install\" were not executed as written (no pip on this machine): the 34 research files were fetched by an equivalent script with the same SHA256SUMS check, and the three wheels were downloaded from PyPI and unpacked. The kit's setup_fast.sh was not used.", "The selection never dropped a setting, so early stopping saved nothing; all 12 ran the full 1,024 seeds." ] }