偏置放大公理(用户08-06指出): 逐坐标归一化把持久小偏置放大成满幅漂移, sign全家同罪(否决只挡

方差不挡偏置); 曲率通道=偏置磁铁(E[s·ĝ]=βc+δ/β, 污染被1/β放大333×), 存活=两档|β|锁相分离;
评分表增第三轴=偏置放大系数, 器件电池预注册排序重排预测(per-matrix优雅退化/sign满幅/Dither翻身)。
附: --dump_grad探针+cautlion已实装。

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

2 files changed, 42 insertions, 3 deletions

diff --git a/ep_run/casc_eq_train.py b/ep_run/casc_eq_train.py
index 6a6865d..e29048c 100644
--- a/ep_run/casc_eq_train.py
+++ b/ep_run/casc_eq_train.py
@@ -22,7 +22,7 @@ ap.add_argument('--wandb_run', default='')
 ap.add_argument('--kmax', type=int, default=8)          # adaptive fb rounds cap
 ap.add_argument('--noguard', action='store_true')       # diagnosis: skip only non-finite grads
 ap.add_argument('--untie', action='store_true')         # separate readout matrix (untied from tok)
-ap.add_argument('--opt', choices=['adamw', 'muon', 'sgdm', 'lion', 'olion', 'adafactor', 'signline', 'conslion', 'ditherlion'], default='adamw')
+ap.add_argument('--opt', choices=['adamw', 'muon', 'sgdm', 'lion', 'olion', 'adafactor', 'signline', 'conslion', 'ditherlion', 'cautlion'], default='adamw')
 ap.add_argument('--muon_lr', type=float, default=0.02)
 ap.add_argument('--tok_init', type=float, default=0.0)  # >0: init tok/pos with this std (GPT-standard 0.02)
 ap.add_argument('--compile', action='store_true')       # torch.compile each block (free speed where supported)
@@ -61,6 +61,7 @@ ap.add_argument('--gen_new', type=int, default=120)
 ap.add_argument('--probe_dgspec', type=int, default=0)      # >0: M1 spectroscopy, value = n batches; exits before training
 ap.add_argument('--probe_gains', default='1,2,4,8,16,32,64,128,256')
 ap.add_argument('--probe_f64', action='store_true')  # fp64 states+model in the probe: the fp-floor decisive arm  # >1: per-STEP log-uniform dgain_top in
+ap.add_argument('--dump_grad', type=int, default=0)  # >0: record per-step grad estimates + beta sign
 ap.add_argument('--dump_mom', type=int, default=0)   # >0: record 3 Muon momentum matrices every step
                                                       # for N steps -> runs/momdump_{tag}.pt, then exit
                                                       # (EqOLion tracking-falsification input)
@@ -344,7 +345,7 @@ if args.bf16:
     if args.untie:
         with torch.no_grad(): W_out.data = W_out.data.to(torch.bfloat16)
     print('[bf16] model cast to bfloat16 (E-accum + sigma stay fp32)', flush=True)
-if args.opt in ('sgdm', 'lion', 'olion', 'adafactor', 'signline', 'conslion', 'ditherlion'):
+if args.opt in ('sgdm', 'lion', 'olion', 'adafactor', 'signline', 'conslion', 'ditherlion', 'cautlion'):
     from muon import build_alt
     opt, sched = build_alt(args.opt, blocks, all_params, args.lr, args.warmup,
                            total_steps=(args.steps if args.cosine else 0), lr_min_ratio=args.lr_min_ratio,
@@ -1050,6 +1051,20 @@ for step in range(start_step, args.steps + 1):
         with torch.no_grad():
             WSNAP['p'] = [p.detach().clone() for p in all_params]
         WSNAP['o'] = _clone_state(opt.state_dict())
+    if args.dump_grad > 0 and args.opt == 'muon':
+        # per-step gradient ESTIMATES + the bsign coin, for the odd/even (curvature-channel)
+        # decomposition test: E[s*ghat] = beta*c. Captured BEFORE opt.step consumes grads.
+        om_ = opt.optimizers[0]
+        _m2 = om_.param_groups[0]['params']
+        _s2 = [_m2[1], _m2[len(_m2) // 2], _m2[-1]]
+        if 'GDUMP' not in globals():
+            GDUMP = {'shapes': [tuple(p.shape) for p in _s2], 'sign': [], 'traj': []}
+        GDUMP['sign'].append(1.0 if beta_t > 0 else -1.0)
+        GDUMP['traj'].append([p.grad.detach().float().cpu().clone() for p in _s2])
+        if step >= args.dump_grad:
+            torch.save(GDUMP, f'runs/graddump_{args.tag}.pt')
+            print(f'[graddump] DONE {len(GDUMP["traj"])} steps -> runs/graddump_{args.tag}.pt', flush=True)
+            import sys; sys.exit(0)
     opt.step(); sched.step(); opt.zero_grad(set_to_none=True)
     if args.dump_mom > 0 and args.opt == 'muon':
         # per-step momentum trajectory for the EqOLion tracking falsification: three
diff --git a/ep_run/muon.py b/ep_run/muon.py
index e6c2692..1289620 100644
--- a/ep_run/muon.py
+++ b/ep_run/muon.py
@@ -176,7 +176,8 @@ def build_alt(opt_name, blocks, other_params, lr, warmup, total_steps=0, lr_min_
               'adafactor': lambda: Adafactor2D(mats, lr=lm, wd=wd),
               'signline': lambda: SignLine(mats, lr=lm, wd=wd),
               'conslion': lambda: ConsensusLion(mats, lr=lm, wd=wd),
-              'ditherlion': lambda: DitherLion(mats, lr=lm, wd=wd)}[opt_name]()
+              'ditherlion': lambda: DitherLion(mats, lr=lm, wd=wd),
+              'cautlion': lambda: CautiousLion(mats, lr=lm, wd=wd)}[opt_name]()
         oa = torch.optim.AdamW(rest, lr=lr, weight_decay=1e-4)
         opts = [om, oa]
     if total_steps > 0:
@@ -247,6 +248,29 @@ class ConsensusLion(torch.optim.Optimizer):
                 p.add_(u, alpha=-g_['lr'])
 
 
+class CautiousLion(torch.optim.Optimizer):
+    """C-Lion (Liang et al., arXiv:2411.16085, ICLR'26): Lion masked where the update sign
+    disagrees with the CURRENT gradient sign. The mandatory prior-art baseline for ConsensusLion;
+    the difference under test is instantaneous-gradient gating (this) vs filtered two-EMA gating."""
+    def __init__(self, params, lr=3e-4, betas=(0.9, 0.99), wd=0.0):
+        super().__init__(params, dict(lr=lr, betas=betas, wd=wd))
+
+    @torch.no_grad()
+    def step(self, closure=None):
+        for g_ in self.param_groups:
+            b1, b2 = g_['betas']
+            for p in g_['params']:
+                if p.grad is None: continue
+                st = self.state[p]
+                if 'm' not in st: st['m'] = torch.zeros_like(p)
+                m = st['m']
+                u = (b1 * m + (1 - b1) * p.grad).sign_()
+                u = u * ((u * p.grad) > 0)
+                if g_['wd'] > 0: p.mul_(1 - g_['lr'] * g_['wd'])
+                p.add_(u, alpha=-g_['lr'])
+                m.mul_(b2).add_(p.grad, alpha=1 - b2)
+
+
 class DitherLion(torch.optim.Optimizer):
     """Lion with dithered sign: sign(m + tau*noise*rms(m)). Free substrate noise turns the hard
     sign into an unbiased soft-sign in expectation, letting small entries carry proportional