diff --git a/schema/defs-linux.json b/schema/defs-linux.json
index 0d31897f9..1964e90e5 100644
--- a/schema/defs-linux.json
+++ b/schema/defs-linux.json
@@ -97,8 +97,8 @@
     },
     "blkioWeightPointer": {
       "oneOf": [
-        { "type": "null" },
-        { "$ref": "#/definitions/blkioWeight" }
+        { "$ref": "#/definitions/blkioWeight" },
+        { "type": "null" }
       ]
     },
     "blockIODevice": {
@@ -125,8 +125,8 @@
     },
     "blockIODeviceWeightPointer": {
       "oneOf": [
-        { "type": "null" },
-        { "$ref": "#/definitions/blockIODeviceWeight" }
+        { "$ref": "#/definitions/blockIODeviceWeight" },
+        { "type": "null" }
       ]
     },
     "blockIODeviceThrottle": {
@@ -141,8 +141,8 @@
     },
     "blockIODeviceThrottlePointer": {
       "oneOf": [
-        { "type": "null" },
-        { "$ref": "#/definitions/blockIODeviceThrottle" }
+        { "$ref": "#/definitions/blockIODeviceThrottle" },
+        { "type": "null" }
       ]
     },
     "NetworkInterfacePriority": {
diff --git a/schema/defs.json b/schema/defs.json
index 8f7052245..a2cd01376 100644
--- a/schema/defs.json
+++ b/schema/defs.json
@@ -43,14 +43,20 @@
     },
     "uint16Pointer": {
       "oneOf": [
-        { "type": "null" },
-        { "$ref": "#/definitions/uint16" }
+        { "$ref": "#/definitions/uint16" },
+        { "type": "null" }
       ]
     },
     "uint64Pointer": {
       "oneOf": [
-        { "type": "null" },
-        { "$ref": "#/definitions/uint64" }
+        { "$ref": "#/definitions/uint64" },
+        { "type": "null" }
+      ]
+    },
+    "stringPointer": {
+      "oneOf": [
+        { "type": "string" },
+        { "type": "null" }
       ]
     },
     "mapStringString": {
diff --git a/schema/schema.json b/schema/schema.json
index e719b9087..a1d4bb6c9 100644
--- a/schema/schema.json
+++ b/schema/schema.json
@@ -91,41 +91,41 @@
                                 "blkioThrottleReadBpsDevice": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/blockIO/blkioThrottleReadBpsDevice",
                                     "oneOf": [
-                                        { "type": "null" },
                                         {
                                             "type": "array",
                                             "items": [ { "$ref": "defs-linux.json#/definitions/blockIODeviceThrottlePointer" } ]
-                                        }
+                                        },
+                                        { "type": "null" }
                                     ]
                                 },
                                 "blkioThrottleWriteBpsDevice": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/blockIO/blkioThrottleWriteBpsDevice",
                                     "oneOf": [
-                                        { "type": "null" },
                                         {
                                             "type": "array",
                                             "items": [ { "$ref": "defs-linux.json#/definitions/blockIODeviceThrottlePointer" } ]
-                                        }
+                                        },
+                                        { "type": "null" }
                                     ]
                                 },
                                 "blkioThrottleReadIopsDevice": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/blockIO/blkioThrottleReadIopsDevice",
                                     "oneOf": [
-                                        { "type": "null" },
                                         {
                                             "type": "array",
                                             "items": [ { "$ref": "defs-linux.json#/definitions/blockIODeviceThrottlePointer" } ]
-                                        }
+                                        },
+                                        { "type": "null" }
                                     ]
                                 },
                                 "blkioThrottleWriteIopsDevice": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/blockIO/blkioThrottleWriteIopsDevice",
                                     "oneOf": [
-                                        { "type": "null" },
                                         {
                                             "type": "array",
                                             "items": [ { "$ref": "defs-linux.json#/definitions/blockIODeviceThrottlePointer" } ]
-                                        }
+                                        },
+                                        { "type": "null" }
                                     ]
                                 },
                                 "blkioWeightDevice": {
@@ -142,31 +142,31 @@
                             "properties": {
                                 "cpus": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/cpu/cpus",
-                                    "type": "string"
+                                    "$ref": "defs.json#/definitions/stringPointer"
                                 },
                                 "mems": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/cpu/mems",
-                                    "type": "string"
+                                    "$ref": "defs.json#/definitions/stringPointer"
                                 },
                                 "period": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/cpu/period",
-                                    "$ref": "defs.json#/definitions/uint64"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "quota": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/cpu/quota",
-                                    "$ref": "defs.json#/definitions/uint64"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "realtimePeriod": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/cpu/realtimePeriod",
-                                    "$ref": "defs.json#/definitions/uint64"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "realtimeRuntime": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/cpu/realtimeRuntime",
-                                    "$ref": "defs.json#/definitions/uint64"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "shares": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/cpu/shares",
-                                    "$ref": "defs.json#/definitions/uint64"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 }
                             },
                             "type": "object"
@@ -190,29 +190,29 @@
                         },
                         "memory": {
                             "id": "https://www.opencontainers.org/jsonschema/linux/resources/memory",
+                            "type": "object",
                             "properties": {
                                 "kernel": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/memory/kernel",
-                                    "type": "integer"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "limit": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/memory/limit",
-                                    "type": "integer"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "reservation": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/memory/reservation",
-                                    "type": "integer"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "swap": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/memory/swap",
-                                    "type": "integer"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 },
                                 "swappiness": {
                                     "id": "https://www.opencontainers.org/jsonschema/linux/resources/memory/swappiness",
-                                    "type": "integer"
+                                    "$ref": "defs.json#/definitions/uint64Pointer"
                                 }
-                            },
-                            "type": "object"
+                            }
                         },
                         "network": {
                             "id": "https://www.opencontainers.org/jsonschema/linux/resources/network",