M15 Kuala Lumpur stats & predictions

Performance Evaluation : Performance evaluation involves assessing strengths weaknesses areas improvement identifying successes failures mistakes learning lessons drawing insights gaining knowledge experience wisdom discernment judgment prudence circumspection discretion circumspection circumspection circumspection circumspection circumspection circumspection circumspection circumspection circumspection

0: saved_state.update({ k:v.view( len(attns), v.size(0) // len(attns), *v.size()[1:] )for k,v in x_incremental_state.items()} ) if normal_attn: attn_mode='normal' tgt_shape=(tgt_len//x_bsz,self.num_heads,x_bsz,self.kdim) src_shape=(tgt_len//x_bsz,self.num_heads,x_bsz,srckdim) kv=tgt_shape+src_shape+[2] kv=tuple(kv) kv_shape=[ kv[i]for iinrange(len(kv))if i%2==0] kv_perm=[ i+int(i>=len(kv)/2)*len(kv)/2for iinrange(len(kv))] key,value=saved_state_normal[ ['prev_key','prev_value']] new_shape=torch.Size(kv_shape) src_newkey,new_srckey=newshape.view(*kv_perm).transpose(2,3).contiguous().view(*newshape) src_newvalue,new_srcvalue=newshape.view(*kv_perm).transpose(2, 3).contiguous().view(*newshape) new_key=torch.cat((key.view(*tgt_shape),src_newkey),dim=-1) new_value=torch.cat((value.view(*tgt_shape),src_newvalue),dim=-1) else: assert False,"should never reach here" residual=x_embedding+self.pos_bias(query_pos)+self.x_mlp(x_prev_target_embedding)+self.x_mlp_2(x_prev_target_embedding**2)+self.x_mlp_3(torch.abs(x_prev_target_embedding)) residual=residual*self.resid_pdrop_module.mask() if not hasattr(args,'no_scale_residual'): residual=residual*math.sqrt(0.5) def init_type(self): pass ***** Tag Data ***** ID: 4 description: Handling incremental states within TransformerDecoderWithAttn forward start line: 37 end line: 93 dependencies: - type: Class name: TransformerDecoderWithAttn start line: 10 end line: 11 context description: Handles incremental states within transformer decoder's forward. algorithmic depth: 4 algorithmic depth external: N obscurity: 5 advanced coding concepts: 4 interesting for students: 5 self contained: N ************ ## Challenging aspects ### Challenging aspects in above code: #### Incremental State Management: Handling incremental states within transformers adds complexity due to dynamic state updates across multiple layers without reprocessing past computations unnecessarily. #### Normal vs Non-Normal Attention Mechanisms: The code distinguishes between normal attention mechanisms (using encoder states) versus other forms (like self-attention). Managing these separately while maintaining correctness requires careful handling. #### Tensor Manipulations: The snippet performs intricate tensor manipulations including reshaping (`view`), permuting (`permute`), concatenation (`cat`), etc., which require precise dimension matching. #### Dynamic Shape Calculations: The shapes `kv`, `kv_shape`, `kv_perm`, `new_key`, `new_value` are computed dynamically based on input dimensions (`tgt_len`, `x_bsz`, `kdim`, `srckdim`). Ensuring these calculations align correctly across different inputs adds another layer of complexity. #### Conditional Logic Based on State Content: The logic branches based on whether certain keys exist within `x_incremental_state`. This conditional branching needs thorough understanding since incorrect assumptions about state content could lead to runtime errors. ### Extension: #### Multi-head Attention Variants: Extend functionality by supporting multi-head attention variants where heads may have different dimensionalities or configurations. #### Mixed Precision Support: Integrate support for mixed precision training/inference where tensors may reside in half-precision floating-point format (FP16). #### Sparse Attention Mechanisms: Implement support for sparse attention mechanisms where only subsets of positions attend to each other instead of full dense attention matrices. ## Exercise: ### Problem Statement: You are given [SNIPPET], which handles incremental states within transformer decoders using PyTorch tensors. Extend this functionality by adding support for multi-head attention variants where each head has potentially different dimensionalities (`kdim` values) specified via an additional argument called `head_dims`. Additionally, integrate mixed precision support where tensors may reside either in single precision (FP32) or half precision (FP16). ### Requirements: - **Multi-head Attention Variants:** Modify [SNIPPET] so that it supports varying key dimensions per head. - Introduce an additional parameter `head_dims` which specifies dimensions per head. - Ensure correct handling when dimensions differ among heads. - **Mixed Precision Support:** Integrate mixed precision support. - Automatically cast tensors involved in computations between FP32/FP16 based on input tensor types. - Ensure numerical stability when performing operations involving mixed precisions. ### Constraints: - Assume input tensors can be either FP32 or FP16 but will always be consistent within any given call. - Maintain backward compatibility with existing functionality when `head_dims` is not provided. ## Solution: python import torch class TransformerDecoderWithAttn(nn.Module): """Transformer decoder.""" def __init__(self, num_heads, embed_dim): super().__init__() self.num_heads = num_heads self.embed_dim = embed_dim def forward(self, tgt_len_x_bsz_, kdim_, srckdim_, head_dims=None): # Extract batch size from shape assuming first dim is batch size times sequence length divided by batch size. tgt_len,x_bsz,_=tgt_len_x_bsz_.size() pos=torch.arange(0,tgt_len).unsqueeze(1).expand(tgt_len,x_bsz).to(tgt_len_x_bsz_.device) # Handle incremental state existence check. if x_incremental_state is not None: saved_state={} normal_attn=False saved_state_normal={} normal_attns=[] attns=[] # Check presence of encoder states indicating normal attention mechanism usage. if 'encoder_states' in x_incremental_state.keys(): normal_attn=True saved_state_normal['prev_key']=x_incremental_state['encoder_states'][...,:kdim_,:] saved_state_normal['prev_value']=x_incremental_state['encoder_states'][...,kdim_:,:] saved_state_normal['prev_key_padding_mask']=x_incremental_state['encoder_states_padding_mask'] else : attns.append('self') if len(attns)>0 : saved_state.update({k:v.view(len(attns),v.size(0)//len(attns),*v.size()[1:])for k,vinx_incremental_stated.items()}) # Handling multi-head dimensionality setup dynamically based upon provided head_dims parameter. if head_dims is None : head_dims=[kdim_] * self.num_heads assert len(head_dims)==self.num_heads,"Mismatch between number heads provided via head_dims" # Calculate shapes dynamically considering variable head dimensions now included via head_dims parameter. tgt_shapes=[(tgt_len//x_bsz,self.num_heads,x_bsz,dim)for diminhead_dims] src_shapes=[(tgt_len//x_bsz,self.num_heads,x_bsz,dim)for diminhead_dims] kv_shapes=[sum(tgt_shapes[i])+sum(src_shapes[i])for iinrange(self.num_heads)] new_kv_shapes=[tuple(shape[:])for shapein kv_shapes] permuted_kv_shapes=[[idx+(idx>=len(new_kv_shapes)/2)*len(new_kv_shapes)/2for idxinrange(len(new_kv))]forall new_kvinnew_kv_shapes] new_keys_values=[] for i,(target_shape,srctarget_shape,kvshape,newshape,newpermutedshape,key,value)ininzip(tgt_shapes, src_shapes, kvshapes,new_kvshapes, permuted_kvshapes,savedstate_normal["prev_key"],savedstate_normal["prev_value"]): newkey,newvalue=newshape.view(*newpermutedshape).transpose(-2,-1).contiguous().view(*newshape) new_keys_values.append((torch.cat((key.view(target_shape),newkey),axis=-1), torch.cat((value.view(target_shape),newvalue),axis=-1))) return new_keys_values ## Follow-up exercise: ### Problem Statement: Modify your solution above such that it supports sparse attention mechanisms where only subsets of positions attend each other instead of full dense attention matrices. ### Requirements: - Implement sparse attention mechanism handling using PyTorch's built-in sparse tensor operations. - Ensure correct integration with existing logic handling both dense attention scenarios as well as newly introduced sparse ones without breaking existing functionalities. ## Solution: python import torch.sparse class TransformerDecoderWithSparseAttn(nn.Module): """Transformer decoder with sparse attention.""" def __init__(self,num_heads ,embed_dim ): super().__init__() self.num_heads=num_heads self.embed_dim=embed_dim def forward(self,tgt_lensbsz,kdimsrckdims=head_dams=None,is_sparse=False): tgt_len,xbsz,_targ_tlenxbz_.size() pos=torch.arange(0,tgt_lentagge()).unsqueeze_(axis_=None.expand(targ_tlenxbz_,b_sizexbsz)).to(_targ_tlenxbz_.device) sparsedict={} sparsedict.update({"pos":pos}) # Existing logic remains unchanged up until tensor manipulations... ... # Integration point where we introduce sparse tensor logic conditionally... if(is_sparse): # Sparse tensor creation example... sparse_tensor=torch.sparse_coo_tensor(indices=[[row,col]],[val],size=[num_rows,num_cols]) sparse_tensor=sparse_tensor.to(device=_targ_tlenxbz_.device) # Use sparse tensor operations instead wherever applicable... new_keys_values=[] for i,(target_shape,srctarget_shap,kvshapenewshapenewpermuteshape,key,valuenewkeyvaluetosparsetensormethod...)ininzip(tgtsrchshapes,kvshapes,new_kvspearmatricespermuteshape): sparsetensor_method(key,value,...) ... return sparsedict arXiv identifier: hep-th/0301098 DOI: 10.1016/S0550-3213(03)00289-X hep-th/0301098 [hepth] # From Topological Strings To String Theory Dualities II -- Type IIA On Toric Calabi-Yau Threefolds With Fluxes -- Authors: Tadashi Okuda (Yukawa Inst.) Date: hep-th/0303129 category/classification string-theory dualities topological-string-calculations threefolds fluxes susy-breaking supergravity black-holes solitons domain-walls effective-potentials brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theory heterotic-string theory orientifold compactifications string-string-dualities string-string-dualities-between-heterotic-and-type-iia strings-on-cft brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theory heterotic-string theory orientifold compactifications string-string-dualities string-string-dualities-between-heterotic-and-type-iia strings-on-cft brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theory heterotic-string theory orientifold compactifications string-string-dualities string-string-dualities-between-heterotic-and-type-iia strings-on-cft brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theory heterotic-string theory orientifold compactifications string-string-dualities string-string-dualities-between-heterotic-and-type-iia strings-on-cft brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theory heterotic-string theory orientifold compactifications string-string-dualities string-string-dualities-between-heterotic-and-type-iia strings-on-cft brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theory heterotic-string theory orientifold compactifications string-string-dualities string-string-dualities-between-heterotic-and-type-iia strings-on-cft brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theory heterotic-string theory orientifold compactifications string-string-dualities string-string-dualities-between-heterotic-and-type-iia strings-on-cft brane-world cosmology inflation particle-physics phenomenology supersymmetry-breaking moduli-stabilization holography gauge-gravity duality matrix-theory geometry m-theory physics-of-branes d-branes f-theury 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