![[Pasted image 20241031141326.png|300]]
using [Connecting Inductive Bias and Expected Utility cld](https://claude.ai/chat/ea1655e0-aadf-4b56-9fd1-aec618b13d6b)
| Component | Expected Utility per Time ⚡ | Inductive Bias 🧠 |
| ------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **Core Math** | $\underset{a}{\arg\max} \ \underset{s}{\sum} \ U(a; s) \ P(s \mid D)$ | $\underset{g \in F}{\arg\min}\ c(g) \quad \text{s.t.} \quad g(x_i) = f(x_i);\ i=1..N
lt;br>Complexity measure $c: F \rightarrow \mathbb{R}_+lt;br>Hypothesis space $F$ |
| **Statistical Error** | **Error in estimating $P(s \mid D)$ due to finite samples:**<br>$\hat{P}(s \mid D) \approx P(s \mid D)$ | Variance from finite training data <br>inversely proportional to hypothesis space (N) |
| **Approximation Error** | **Error in approximating expected utility $EU[s, a]$:**<br>$\hat{EU}[s, a] = \underset{s}{\sum} \ U(a; s) \ \hat{P}(s \mid D)$ vs. $EU[s, a] = \underset{s}{\sum} \ U(a; s) \ P(s \mid D)$ | Error due to limited hypothesis space or model complexity<br><br>inversely proportional to function space (F) |
| **Optimization Error** | **Difference between optimal and selected action utilities:**<br>$EU(s, a^*) - EU(s, \hat{a})$, where $a^* = \underset{a}{\arg\max} \ EU(s, a)$ and $\hat{a}$ is chosen action | Inability to find the global minimum due to optimization algorithm limitations |
| **Regularization Method** | 🎲 **Sample cost in time units** | 🔧 Explicit: Weight decay, path-norm<br>Implicit: SGD dynamics |
| **Optimal Solution** | **Fastest $k$ that achieves good utility** | Simplest $f$ that fits data |
| **Key Insight** | **Quick decisions accumulate more reward** | Simple functions generalize better |
| **Famous Example** | 🎲 **One-and-done sampling** | 📈 Splines: $\int \|f''(x)\|^2 dx$ |
| Category | Key Points | Why It Matters |
| ---------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------- |
| 🔄 Resource Allocation | • Time split between market, operations & capitalization<br>• Zero-sum game: more time in one means less in others<br>• Currently most founders neglect capitalization | Helps founders make conscious decisions about where to invest their limited time and energy |
| 🎮 Growth Control | • Understanding capitalization = better growth control<br>• OK to grow slowly if aligned with vision<br>• Resist market pressure for rapid scaling | Prevents founders from being pushed into unsustainable growth trajectories |
| 🎓 Skills Gap | • Founders usually come from tech/marketing<br>• Lack capitalization expertise<br>• Need structured learning approach | Identifies critical knowledge gap in typical founder journey |
| 💰 Funding Dynamics | • Public funding creates "growth treadmill"<br>• Quarterly pressure leads to short-term thinking<br>• Bootstrapping offers more control | Helps founders understand trade-offs between funding types |
| 🛠️ Tools & Research | • AI-powered capitalization tools<br>• Testing with 30+ entrepreneurs<br>• Compare vs traditional calculators | Practical solution to bridge knowledge gap |
| 🌏 Cultural Context | • SAFE common in US, rare in Asia<br>• Regional differences in acceptance<br>• Need cultural adaptation | Reminds founders to consider local context |
| ⚖️ Balanced Approach | • Equal focus on cap operations<br>• Control growth pace<br>• Integrate with market/ops strategy | Promotes holistic company building |
| 📚 Education Focus | • Capitalization knowledge crucial<br>• Affects all strategic decisions<br>• Need systematic education | Empowers better decision-making |
[[📝🤝Conversational Inference of Equity Valuation Agreement]]