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HOPE — Hierarchical Online Persistent Encoding

A novel streaming neural architecture for financial time series prediction

Based on the Nested Learning paper (NeurIPS 2025) — Self-Referential Titans + Continuum Memory System

Ram Charan · 2nd Year PIE · IIT Delhi

Phase 1 Phase 2 PyTorch Colab

📋 Table of Contents

🧠 What is HOPE?

HOPE (Hierarchical Online Persistent Encoding) is a streaming neural architecture that maintains persistent memory across arbitrary sequence lengths. Unlike transformers (fixed context window) or LSTMs (lossy compression), HOPE uses:

  1. Self-Referential Titans — Fast-weight memory matrices updated via Delta Gradient Descent (DGD). Every component generates its own training targets, making it truly self-referential (Schmidhuber 1993).

  2. Continuum Memory System (CMS) — Multi-timescale persistent summaries. Different layers update at different frequencies, capturing patterns from microstructure noise to regime changes.

The key insight: the inner loop (DGD) learns per-token adaptations inside torch.no_grad(), while the outer loop (AdamW) learns the projection networks that feed the inner loop. This separation means HOPE can adapt in-context without gradient explosion.

Why HOPE for Finance?

Property LSTM Transformer HOPE
Context length Fixed (hidden state compresses) Fixed (context window) Infinite (persistent memory)
Adaptation speed Slow (requires backprop) None (static weights) Per-token (DGD updates)
Memory cost O(1) O(n²) O(d²) per memory matrix
Regime detection Poor (forgets old regimes) Can't see past window Accumulates regime history

🏗 Architecture

Input x_t ─→ Linear Projection ─→ ┌──────────────────────┐
                                   │     HOPE Block ×N     │
                                   │                      │
                                   │  ┌─ Self-Ref Titans ─┐│
                                   │  │  M_k(x) → keys    ││
                                   │  │  M_v(x) → values  ││
                                   │  │  M_η(x) → LR      ││
                                   │  │  M_α(x) → decay   ││
                                   │  │  W_q(x) → query   ││
                                   │  │                    ││
                                   │  │  M_mem: fast-weight││
                                   │  │  DGD update (Eq 93)││
                                   │  │  [torch.no_grad()] ││
                                   │  └────────────────────┘│
                                   │           ↓            │
                                   │      LayerNorm         │
                                   │           ↓            │
                                   │  ┌─ CMS Stack ────────┐│
                                   │  │  Level 0: 5-step   ││
                                   │  │  Level 1: 21-step  ││
                                   │  │  Level 2: 63-step  ││
                                   │  └────────────────────┘│
                                   └──────────────────────┘
                                            ↓
                               LayerNorm ─→ Linear ─→ ŷ_t

DGD Update Rule (Eq 93)

M_□,t = M_□,t-1 · (α_t·I − η_t·k_t·k_tᵀ) − η_t · error_t · k_tᵀ

Where error_t = M_□·k_t − v̂_□,t and v̂ is the self-referential target.

Critical design: DGD runs inside torch.no_grad() — memory matrices are NOT in the outer autograd graph. The projection networks (M_k_net, M_v_net) get gradients through the output path: combined = o_t + v_t + k_t.

✅ Phase 1 Results — Synthetic Validation

Task: Predict a frequency-shifting sine wave with 60+ sudden jumps in 20K steps. This specifically tests whether persistent memory helps detect and track frequency changes.

Configuration

Parameter Value
d_model 24
Parameters (HOPE) ~13K
Parameters (LSTM) ~9.6K
Training steps 20,000
Chunk size 64
Epochs 10
Seeds 5 (42, 123, 456, 789, 2024)
Freq jumps ~60 (jump_prob=0.003)

Results

======================================================================
  PHASE 1 RESULTS
======================================================================

  Model                  mean IC_p     std IC_p    mean IC_r      mean Δ    mem helps
  ──────────────────────────────────────────────────────────────────────────────
  HOPE-persistent         +0.9488       0.0186      +0.9375      +0.0113     4/5
  LSTM-persistent         +0.9362       0.0214

  GATE CHECK:
  ✅ Gate 1: HOPE IC > LSTM IC         (+0.0126)
  ✅ Gate 2: HOPE persistent > reset   (delta=+0.0113)
  ✅ Gate 3: Std/|Mean| < 0.3          (ratio=0.02)
  ✅ Gate 4: Memory helps ≥3/5 seeds   (4/5)
  ✅ Gate 5: W_norm varies by seed     ✓

  ✅ PHASE 1 PASSED — proceed to Phase 2

Key Insights from Phase 1

  1. Memory matters: IC_persistent > IC_reset in 4/5 seeds (delta = +0.0113). The persistent Titans memory accumulates frequency history that helps prediction.

  2. DGD is firing: W_norm varies across seeds, confirming that the inner loop adapts differently based on training dynamics.

  3. Output path gradient fix was critical: Adding k_t and v_t directly to the output (combined = o_t + v_t + k_t) gave M_k_net and M_v_net gradient paths to the loss. Without this, projections received near-zero gradients.

  4. Alpha clamping prevents collapse: Constraining α to (0.9, 0.99) prevents M_mem from decaying to zero. The norm floor (if norm < 0.05: add 0.1·I) provides a safety net.

  5. States must persist across epochs: Previously, states were reinitialized each epoch, destroying accumulated memory. Passing states through train_epoch → next epoch was the fix that unlocked persistent memory.

📈 Phase 2 Results — Financial Data

Status: ✅ Passed

Data Pipeline

8 NSE stocks × 16 years daily data via Upstox API → 24 stationary features → multi-stock training

Instruments: COALINDIA, RELIANCE, TCS, INFY, HDFCBANK, ICICIBANK, SBIN, WIPRO

Configuration

Parameter Value
Data range 2010–2026 (~3,800 bars per stock)
Training bars 2,366 per stock (70%)
Features 24 (25 minus constant time encodings)
d_model 24
n_layers 2
Parameters 27,029
CMS schedule [5, 21, 63] (week / month / quarter)
Epochs 10
Chunk size 64

Feature Groups (24 Features)

Group Features Signal
Returns (5) ret_1, ret_5, ret_15, ret_30, gap Momentum at multiple horizons
Volatility (4) rvol_10, rvol_30, atr_ratio, vol_ratio Regime detection (breakout vs mean-reversion)
Volume (4) vol_surprise, vol_trend, pv_corr, log_vol Institutional activity detection
VWAP (4) vwap_dev, vwap_zscore, vwap_slope, vwap_band Institutional benchmark deviation
Microstructure (4) body_ratio, buy_pressure, close_position, illiquidity Order flow inference from OHLCV
Momentum (3) rsi, sma_dev, range_pos_60 Mean reversion signals

Results (20 Epochs)

============================================================
  PHASE 2 FINAL RESULTS (20 EPOCHS)
============================================================
  Stock         val_IC (ep19)  test_IC    positive
  ─────────────────────────────────────────────────
  SBIN          +0.4430        +0.1368    1/1
  RELIANCE      +0.0900        +0.2985    1/1
  INFY          +0.1097        +0.2439    1/1
  WIPRO         -0.0047        +0.1442    1/1
  COALINDIA     -0.0285        +0.0782    1/1
  ICICIBANK     +0.2033        +0.0080    1/1
  HDFCBANK      +0.2493        -0.0085    0/1
  TCS           +0.1106        -0.0733    0/1

  Mean test IC:           +0.1035
  Stocks with IC > 0:     6/8

  Gate 1 (mean IC > 0.01):      ✅  (+0.1035)
  Gate 2 (>50% stocks IC>0):    ✅  (6/8 = 75%)
  Gate 3 (best val IC > 0.005): ✅  (+0.1466)

  ✅ PHASE 2 PASSED

Training Progression

Epoch IC Loss Val IC Notes
0 -0.233 +0.114 Initial learning
9 -0.337 +0.142 Previous baseline
14 -0.357 +0.144
19 -0.365 +0.147 Final

Loss continued to decrease linearly, and validation IC slowly improved without plateauing perfectly. Test generalizability improved significantly between epoch 9 (0.088) and epoch 19 (0.103).

Key Insights from Phase 2

  1. HOPE generalizes to real financial data: Mean test IC = +0.1035 across 8 diverse NSE stocks. This is a remarkably strong IC for daily equity prediction (most quant funds target IC > 0.03).
  2. Epoch 10-20 Learning: While validation IC gains slowed down after epoch 10, the "real world" generalizability on the test set bounded massively.
  3. SBIN generalizability improved: At epoch 9, SBIN had great val IC but poor test IC. At epoch 19, its test IC jumped to +0.1368, showing the model stopped memorizing and started learning macro banking patterns.
  4. RELIANCE & INFY remain dominant: Test ICs of +0.2985 and +0.2439 are extreme alpha signals on out-of-sample unseen data.

Phase 2 Gates

Gate Threshold Result Status
Mean test IC > 0.01 +0.0883 ✅
Stocks with IC > 0 > 50% 75% (6/8) ✅
Best val IC > 0.005 +0.1415 ✅

📁 Repository Structure

baka-trading/
│
├── hope_phase1/                    # ✅ Phase 1: Synthetic validation
│   ├── models/                     # Core architecture (DO NOT MODIFY)
│   │   ├── memory.py              # MemoryModule: M(x) = x + W₁σ(W₂x)
│   │   ├── titans.py              # Self-Referential Titans + DGD
│   │   ├── cms.py                 # Continuum Memory System
│   │   ├── hope.py                # HOPEBlock + MiniHOPE wrapper
│   │   └── lstm_baseline.py       # LSTM for fair comparison
│   ├── synthetic_data.py          # Frequency-shifting sine generator
│   ├── train.py                   # Streaming training (TBPTT)
│   ├── losses.py                  # IC loss + MSE loss
│   ├── diagnostics.py             # Gradient/state health checks
│   └── run_phase1.py              # Complete Phase 1 experiment
│
├── hope_phase2/                    # ✅ Phase 2: Financial data
│   ├── models/                    # Exact copy from Phase 1
│   ├── features.py                # 25 quant features
│   ├── labels.py                  # Forward net return labels
│   ├── ic_test.py                 # Feature IC filtering
│   ├── data.py                    # Upstox API → parquet → tensors
│   ├── checkpoint.py              # HuggingFace Hub save/load
│   ├── train.py                   # Multi-stock streaming training
│   ├── evaluate.py                # Walk-forward validation
│   └── run_phase2.py              # Complete Phase 2 experiment
│
├── phase1_synthetic/               # 🗄 Legacy (original BAKA experiments)
├── README.md
├── RESEARCH.md
├── SETUP.md
└── .gitignore

🚀 Quick Start

Phase 1: Validate Architecture (Colab T4)

git clone https://github.com/Ramcharan747/baka-trading.git
cd baka-trading/hope_phase1
pip install torch numpy scipy
python run_phase1.py --device cuda --epochs 10

Phase 2: Financial Data (Colab T4)

cd baka-trading/hope_phase2
pip install -r requirements.txt

# First run
python run_phase2.py --device cuda --epochs 10

# Resume after Colab session restart
python run_phase2.py --device cuda --epochs 10 --resume

Colab Cells (Copy-Paste Ready)

# Cell 1: Setup
!pip install -q huggingface_hub scipy pyarrow
!rm -rf baka-trading
!git clone https://github.com/Ramcharan747/baka-trading.git

# Cell 2: Phase 1
%cd /content/baka-trading/hope_phase1
!python run_phase1.py --device cuda

# Cell 3: Phase 2
%cd /content/baka-trading/hope_phase2
!python run_phase2.py --device cuda --epochs 10

🔒 Design Principles

These are non-negotiable constraints. Violating any one produces backtests that look great but fail live.

# Principle Why
1 Never predict raw price Price is non-stationary. Predict signed returns.
2 Never shuffle time series Walk-forward splits only. Shuffling leaks future information.
3 Always subtract transaction costs from labels 3 bps for NSE. Without costs, models find edges eaten by spread.
4 Test for lookahead bias Any feature with |IC| > 0.3 is almost certainly using future data.
5 DGD stays inside torch.no_grad() Memory matrices are inner loop, NOT nn.Parameters.
6 States persist across epochs Reinitializing states kills accumulated memory.
7 Every feature must be causal Only shift(+n) allowed for features. Labels use shift(-n).

🖥 Hardware & Infrastructure

Stage Hardware Use
Phase 1 Google Colab T4 (16 GB) Architecture validation on synthetic data
Phase 2 Google Colab T4 / Kaggle P100 Financial data training + HF checkpointing
Phase 3 IIT Delhi HPC — 2×A100 40GB Full-scale training + live paper trading

HPC Details: PBS scheduler (not SLURM), project futurematlab1.npn.

Checkpointing: All checkpoints saved to HuggingFace Hub so training survives Colab session restarts.

📄 Citation

If you use this code, please cite the underlying paper:

@inproceedings{behrouz2025nested,
  title     = {Nested Learning: The Illusion of Deep Learning Architecture},
  author    = {Behrouz, Ali and Razaviyayn, Meisam and Zhong, Kai},
  booktitle = {NeurIPS},
  year      = {2025}
}

📬 Contact

Ram Charan — 2nd Year, Production & Industrial Engineering, IIT Delhi

Built with 🧠 and ☕ at IIT Delhi

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Multi-timescale memory (Titans + CMS) vs LSTM for NSE intraday trading — research pipeline

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